[xiph-commits] r18832 - websites/xiph.org/video

[giles at svn.xiph.org]

Author: giles
Date: 2013-02-25 16:45:00 -0800 (Mon, 25 Feb 2013)
New Revision: 18832

Added:
   websites/xiph.org/video/02-Digital_Show_and_Tell.en.vtt
Removed:
   websites/xiph.org/video/vid2-en.vtt
Modified:
   websites/xiph.org/video/vid2.shtml
Log:
Rename vid2-en.vtt to match the video filenames.


Copied: websites/xiph.org/video/02-Digital_Show_and_Tell.en.vtt (from rev 18831, websites/xiph.org/video/vid2-en.vtt)
===================================================================
--- websites/xiph.org/video/02-Digital_Show_and_Tell.en.vtt	                        (rev 0)
+++ websites/xiph.org/video/02-Digital_Show_and_Tell.en.vtt	2013-02-26 00:45:00 UTC (rev 18832)
@@ -0,0 +1,1773 @@
+WEBVTT
+
+1
+00:00:08.252 --> 00:00:11.550
+Hi, I'm Monty Montgomery from Red Hat and Xiph.Org.
+
+2
+00:00:11.550 --> 00:00:18.430
+A few months ago, I wrote an article on digital audio and why 24bit/192kHz music downloads don't make sense.
+
+3
+00:00:18.430 --> 00:00:23.433
+In the article, I mentioned--almost in passing--that a digital waveform is not a stairstep,
+
+4
+00:00:23.433 --> 00:00:28.680
+and you certainly don't get a stairstep when you convert from digital back to analog.
+
+5
+00:00:29.865 --> 00:00:33.865
+Of everything in the entire article, <b>that</b> was the number one thing people wrote about.
+
+6
+00:00:33.865 --> 00:00:37.221
+In fact, more than half the mail I got was questions and comments
+
+7
+00:00:37.221 --> 00:00:39.663
+about basic digital signal behavior.
+
+8
+00:00:39.894 --> 00:00:45.285
+Since there's interest, let's take a little time to play with some <u>simple</u> digital signals.
+
+9
+00:00:49.747 --> 00:00:51.006
+Pretend for a moment
+
+10
+00:00:51.006 --> 00:00:54.089
+that we have no idea how digital signals really behave.
+
+11
+00:00:54.734 --> 00:00:56.841
+In that case it doesn't make sense for us
+
+12
+00:00:56.841 --> 00:00:59.049
+to use digital test equipment either.
+
+13
+00:00:59.049 --> 00:01:00.937
+Fortunately for this exercise, there's still
+
+14
+00:01:00.937 --> 00:01:04.020
+plenty of working analog lab equipment out there.
+
+15
+00:01:04.020 --> 00:01:05.972
+First up, we need a signal generator
+
+16
+00:01:05.972 --> 00:01:08.190
+to provide us with analog input signals--
+
+17
+00:01:08.190 --> 00:01:12.692
+in this case, an HP3325 from 1978.
+
+18
+00:01:12.692 --> 00:01:14.153
+It's still a pretty good generator,
+
+19
+00:01:14.153 --> 00:01:15.614
+so if you don't mind the size,
+
+20
+00:01:15.614 --> 00:01:16.532
+the weight,
+
+21
+00:01:16.532 --> 00:01:17.577
+the power consumption,
+
+22
+00:01:17.577 --> 00:01:18.910
+and the noisy fan,
+
+23
+00:01:18.910 --> 00:01:20.329
+you can find them on eBay.
+
+24
+00:01:20.329 --> 00:01:23.863
+Occasionally for only slightly more than you'll pay for shipping.
+
+25
+00:01:24.617 --> 00:01:28.500
+Next, we'll observe our analog waveforms on analog oscilloscopes,
+
+26
+00:01:28.500 --> 00:01:31.550
+like this Tektronix 2246 from the mid-90s,
+
+27
+00:01:31.550 --> 00:01:34.761
+one of the last and very best analog scopes ever made.
+
+28
+00:01:34.761 --> 00:01:36.807
+Every home lab should have one.
+
+29
+00:01:37.716 --> 00:01:40.852
+And finally inspect the frequency spectrum of our signals
+
+30
+00:01:40.852 --> 00:01:43.177
+using an analog spectrum analyzer.
+
+31
+00:01:43.177 --> 00:01:47.732
+This HP3585 from the same product line as the signal generator.
+
+32
+00:01:47.732 --> 00:01:50.615
+Like the other equipment here it has a rudimentary
+
+33
+00:01:50.615 --> 00:01:52.905
+and hilariously large microcontroller,
+
+34
+00:01:52.905 --> 00:01:56.276
+but the signal path from input to what you see on the screen
+
+35
+00:01:56.276 --> 00:01:58.537
+is completely analog.
+
+36
+00:01:58.537 --> 00:02:00.329
+All of this equipment is vintage,
+
+37
+00:02:00.329 --> 00:02:01.993
+but aside from its raw tonnage,
+
+38
+00:02:01.993 --> 00:02:03.844
+the specs are still quite good.
+
+39
+00:02:04.536 --> 00:02:06.868
+At the moment, we have our signal generator
+
+40
+00:02:06.868 --> 00:02:12.829
+set to output a nice 1kHz sine wave at one volt RMS,
+
+41
+00:02:13.414 --> 00:02:15.220
+we see the sine wave on the oscilloscope,
+
+42
+00:02:15.220 --> 00:02:21.428
+can verify that it is indeed 1kHz at one volt RMS,
+
+43
+00:02:21.428 --> 00:02:24.108
+which is 2.8V peak-to-peak,
+
+44
+00:02:24.308 --> 00:02:27.561
+and that matches the measurement on the spectrum analyzer as well.
+
+45
+00:02:27.561 --> 00:02:30.644
+The analyzer also shows some low-level white noise
+
+46
+00:02:30.644 --> 00:02:32.190
+and just a bit of harmonic distortion,
+
+47
+00:02:32.190 --> 00:02:36.649
+with the highest peak about 70dB or so below the fundamental.
+
+48
+00:02:36.649 --> 00:02:38.612
+Now, this doesn't matter at all in our demos,
+
+49
+00:02:38.612 --> 00:02:40.574
+but I wanted to point it out now
+
+50
+00:02:40.574 --> 00:02:42.452
+just in case you didn't notice it until later.
+
+51
+00:02:44.036 --> 00:02:47.142
+Now, we drop digital sampling in the middle.
+
+52
+00:02:48.557 --> 00:02:51.024
+For the conversion, we'll use a boring,
+
+53
+00:02:51.024 --> 00:02:53.374
+consumer-grade, eMagic USB1 audio device.
+
+54
+00:02:53.374 --> 00:02:55.337
+It's also more than ten years old at this point,
+
+55
+00:02:55.337 --> 00:02:57.257
+and it's getting obsolete.
+
+56
+00:02:57.964 --> 00:03:02.676
+A recent converter can easily have an order of magnitude better specs.
+
+57
+00:03:03.076 --> 00:03:07.924
+Flatness, linearity, jitter, noise behavior, everything...
+
+58
+00:03:07.924 --> 00:03:09.353
+you may not have noticed.
+
+59
+00:03:09.353 --> 00:03:11.604
+Just because we can measure an improvement
+
+60
+00:03:11.604 --> 00:03:13.609
+doesn't mean we can hear it,
+
+61
+00:03:13.609 --> 00:03:16.404
+and even these old consumer boxes were already
+
+62
+00:03:16.404 --> 00:03:18.643
+at the edge of ideal transparency.
+
+63
+00:03:20.244 --> 00:03:22.825
+The eMagic connects to my ThinkPad,
+
+64
+00:03:22.825 --> 00:03:26.121
+which displays a digital waveform and spectrum for comparison,
+
+65
+00:03:26.121 --> 00:03:28.788
+then the ThinkPad sends the digital signal right back out
+
+66
+00:03:28.788 --> 00:03:30.921
+to the eMagic for re-conversion to analog
+
+67
+00:03:30.921 --> 00:03:33.332
+and observation on the output scopes.
+
+68
+00:03:33.332 --> 00:03:35.582
+Input to output, left to right.
+
+69
+00:03:40.211 --> 00:03:41.214
+OK, it's go time.
+
+70
+00:03:41.214 --> 00:03:43.924
+We begin by converting an analog signal to digital
+
+71
+00:03:43.924 --> 00:03:47.347
+and then right back to analog again with no other steps.
+
+72
+00:03:47.347 --> 00:03:49.268
+The signal generator is set to produce
+
+73
+00:03:49.268 --> 00:03:52.649
+a 1kHz sine wave just like before.
+
+74
+00:03:52.649 --> 00:03:57.428
+We can see our analog sine wave on our input-side oscilloscope.
+
+75
+00:03:57.428 --> 00:04:01.694
+We digitize our signal to 16 bit PCM at 44.1kHz,
+
+76
+00:04:01.694 --> 00:04:03.828
+same as on a CD.
+
+77
+00:04:03.828 --> 00:04:07.156
+The spectrum of the digitized signal matches what we saw earlier. and...
+
+78
+00:04:07.156 --> 00:04:10.836
+what we see now on the analog spectrum analyzer,
+
+79
+00:04:10.836 --> 00:04:15.154
+aside from its high-impedance input being just a smidge noisier.
+
+80
+00:04:15.154 --> 00:04:15.956
+For now
+
+81
+00:04:18.248 --> 00:04:20.798
+the waveform display shows our digitized sine wave
+
+82
+00:04:20.798 --> 00:04:23.966
+as a stairstep pattern, one step for each sample.
+
+83
+00:04:23.966 --> 00:04:26.388
+And when we look at the output signal
+
+84
+00:04:26.388 --> 00:04:29.054
+that's been converted from digital back to analog, we see...
+
+85
+00:04:29.054 --> 00:04:32.052
+It's exactly like the original sine wave.
+
+86
+00:04:32.052 --> 00:04:33.483
+No stairsteps.
+
+87
+00:04:33.914 --> 00:04:37.193
+OK, 1kHz is still a fairly low frequency,
+
+88
+00:04:37.193 --> 00:04:40.633
+maybe the stairsteps are just
+hard to see or they're being smoothed away.
+
+89
+00:04:40.739 --> 00:04:49.492
+Fair enough. Let's choose
+a higher frequency, something close to Nyquist, say 15kHz.
+
+90
+00:04:49.492 --> 00:04:53.545
+Now the sine wave is represented by less than three samples per cycle, and...
+
+91
+00:04:53.545 --> 00:04:55.838
+the digital waveform looks pretty awful.
+
+92
+00:04:55.838 --> 00:04:59.798
+Well, looks can be deceiving. The analog output...
+
+93
+00:05:01.876 --> 00:05:06.033
+is still a perfect sine wave, exactly like the original.
+
+94
+00:05:06.633 --> 00:05:09.228
+Let's keep going up.
+
+95
+00:05:17.353 --> 00:05:20.151
+16kHz....
+
+96
+00:05:23.198 --> 00:05:25.616
+17kHz...
+
+97
+00:05:28.201 --> 00:05:29.945
+18kHz...
+
+98
+00:05:33.822 --> 00:05:35.548
+19kHz...
+
+99
+00:05:40.457 --> 00:05:42.465
+20kHz.
+
+100
+00:05:49.097 --> 00:05:52.350
+Welcome to the upper limits of human hearing.
+
+101
+00:05:52.350 --> 00:05:54.377
+The output waveform is still perfect.
+
+102
+00:05:54.377 --> 00:05:58.025
+No jagged edges, no dropoff, no stairsteps.
+
+103
+00:05:58.025 --> 00:06:01.342
+So where'd the stairsteps go?
+
+104
+00:06:01.342 --> 00:06:03.198
+Don't answer, it's a trick question.
+
+105
+00:06:03.198 --> 00:06:04.318
+They were never there.
+
+106
+00:06:04.318 --> 00:06:06.652
+Drawing a digital waveform as a stairstep
+
+107
+00:06:08.712 --> 00:06:10.772
+was wrong to begin with.
+
+108
+00:06:10.942 --> 00:06:11.998
+Why?
+
+109
+00:06:11.998 --> 00:06:14.366
+A stairstep is a continuous-time function.
+
+110
+00:06:14.366 --> 00:06:16.201
+It's jagged, and it's piecewise,
+
+111
+00:06:16.201 --> 00:06:19.700
+but it has a defined value at every point in time.
+
+112
+00:06:19.700 --> 00:06:22.004
+A sampled signal is entirely different.
+
+113
+00:06:22.004 --> 00:06:23.337
+It's discrete-time;
+
+114
+00:06:23.337 --> 00:06:27.337
+it's only got a value right at each instantaneous sample point
+
+115
+00:06:27.337 --> 00:06:32.596
+and it's undefined, there is no value at all, everywhere between.
+
+116
+00:06:32.596 --> 00:06:36.666
+A discrete-time signal is properly drawn as a lollipop graph.
+
+117
+00:06:40.020 --> 00:06:42.974
+The continuous, analog counterpart of a digital signal
+
+118
+00:06:42.974 --> 00:06:45.364
+passes smoothly through each sample point,
+
+119
+00:06:45.364 --> 00:06:50.153
+and that's just as true for high frequencies as it is for low.
+
+120
+00:06:50.153 --> 00:06:53.033
+Now, the interesting and not at all obvious bit is:
+
+121
+00:06:53.033 --> 00:06:55.454
+there's only one bandlimited signal that passes
+
+122
+00:06:55.454 --> 00:06:57.417
+exactly through each sample point.
+
+123
+00:06:57.417 --> 00:06:58.708
+It's a unique solution.
+
+124
+00:06:58.708 --> 00:07:01.246
+So if you sample a bandlimited signal
+
+125
+00:07:01.246 --> 00:07:02.612
+and then convert it back,
+
+126
+00:07:02.612 --> 00:07:06.462
+the original input is also the only possible output.
+
+127
+00:07:06.462 --> 00:07:07.838
+And before you say,
+
+128
+00:07:07.838 --> 00:07:11.721
+"Oh, I can draw a different signal that passes through those points."
+
+129
+00:07:11.721 --> 00:07:14.283
+Well, yes you can, but...
+
+130
+00:07:17.268 --> 00:07:20.521
+if it differs even minutely from the original,
+
+131
+00:07:20.521 --> 00:07:24.905
+it contains frequency content at or beyond Nyquist,
+
+132
+00:07:24.905 --> 00:07:26.185
+breaks the bandlimiting requirement
+
+133
+00:07:26.185 --> 00:07:28.358
+and isn't a valid solution.
+
+134
+00:07:28.574 --> 00:07:30.036
+So how did everyone get confused
+
+135
+00:07:30.036 --> 00:07:32.702
+and start thinking of digital signals as stairsteps?
+
+136
+00:07:32.702 --> 00:07:34.900
+I can think of two good reasons.
+
+137
+00:07:34.900 --> 00:07:37.956
+First: It's easy enough to convert a sampled signal
+
+138
+00:07:37.972 --> 00:07:39.294
+to a true stairstep.
+
+139
+00:07:39.294 --> 00:07:42.409
+Just extend each sample value forward until the next sample period.
+
+140
+00:07:42.409 --> 00:07:44.414
+This is called a zero-order hold,
+
+141
+00:07:44.414 --> 00:07:47.913
+and it's an important part of how some digital-to-analog converters work,
+
+142
+00:07:47.913 --> 00:07:50.089
+especially the simplest ones.
+
+143
+00:07:50.089 --> 00:07:55.591
+So, anyone who looks up digital-to-analog conversion
+
+144
+00:07:55.592 --> 00:07:59.550
+is probably going to see a diagram of a stairstep waveform somewhere,
+
+145
+00:07:59.550 --> 00:08:01.982
+but that's not a finished conversion,
+
+146
+00:08:01.982 --> 00:08:04.250
+and it's not the signal that comes out.
+
+147
+00:08:04.944 --> 00:08:05.684
+Second,
+
+148
+00:08:05.684 --> 00:08:07.529
+and this is probably the more likely reason,
+
+149
+00:08:07.529 --> 00:08:09.449
+engineers who supposedly know better,
+
+150
+00:08:09.449 --> 00:08:10.441
+like me,
+
+151
+00:08:10.441 --> 00:08:13.193
+draw stairsteps even though they're technically wrong.
+
+152
+00:08:13.193 --> 00:08:15.571
+It's a sort of like a one-dimensional version of
+
+153
+00:08:15.571 --> 00:08:17.395
+fat bits in an image editor.
+
+154
+00:08:17.395 --> 00:08:19.241
+Pixels aren't squares either,
+
+155
+00:08:19.241 --> 00:08:23.081
+they're samples of a 2-dimensional function space and so they're also,
+
+156
+00:08:23.081 --> 00:08:26.366
+conceptually, infinitely small points.
+
+157
+00:08:26.366 --> 00:08:28.500
+Practically, it's a real pain in the ass to see
+
+158
+00:08:28.500 --> 00:08:30.804
+or manipulate infinitely small anything.
+
+159
+00:08:30.804 --> 00:08:32.212
+So big squares it is.
+
+160
+00:08:32.212 --> 00:08:35.966
+Digital stairstep drawings are exactly the same thing.
+
+161
+00:08:35.966 --> 00:08:37.684
+It's just a convenient drawing.
+
+162
+00:08:37.684 --> 00:08:40.404
+The stairsteps aren't really there.
+
+163
+00:08:45.652 --> 00:08:48.233
+When we convert a digital signal back to analog,
+
+164
+00:08:48.233 --> 00:08:50.900
+the result is <u>also</u> smooth regardless of the bit depth.
+
+165
+00:08:50.900 --> 00:08:53.193
+24 bits or 16 bits...
+
+166
+00:08:53.193 --> 00:08:54.196
+or 8 bits...
+
+167
+00:08:54.196 --> 00:08:55.486
+it doesn't matter.
+
+168
+00:08:55.486 --> 00:08:57.534
+So does that mean that the digital bit depth
+
+169
+00:08:57.534 --> 00:08:58.953
+makes no difference at all?
+
+170
+00:08:59.245 --> 00:09:00.521
+Of course not.
+
+171
+00:09:02.121 --> 00:09:06.046
+Channel 2 here is the same sine wave input,
+
+172
+00:09:06.046 --> 00:09:09.086
+but we quantize with dither down to eight bits.
+
+173
+00:09:09.086 --> 00:09:14.174
+On the scope, we still see a nice
+smooth sine wave on channel 2.
+
+174
+00:09:14.174 --> 00:09:18.014
+Look very close, and you'll also see a
+bit more noise.
+
+175
+00:09:18.014 --> 00:09:19.305
+That's a clue.
+
+176
+00:09:19.305 --> 00:09:21.273
+If we look at the spectrum of the signal...
+
+177
+00:09:22.889 --> 00:09:23.732
+aha!
+
+178
+00:09:23.732 --> 00:09:26.398
+Our sine wave is still there unaffected,
+
+179
+00:09:26.398 --> 00:09:28.490
+but the noise level of the eight-bit signal
+
+180
+00:09:28.490 --> 00:09:32.470
+on the second channel is much higher!
+
+181
+00:09:32.948 --> 00:09:36.148
+And that's the difference the number of bits makes.
+
+182
+00:09:36.148 --> 00:09:37.434
+That's it!
+
+183
+00:09:37.822 --> 00:09:39.956
+When we digitize a signal, first we sample it.
+
+184
+00:09:39.956 --> 00:09:42.366
+The sampling step is perfect; it loses nothing.
+
+185
+00:09:42.366 --> 00:09:45.626
+But then we quantize it,
+and quantization adds noise.
+
+186
+00:09:47.827 --> 00:09:50.793
+The number of bits determines how much noise
+
+187
+00:09:50.793 --> 00:09:52.569
+and so the level of the
+noise floor.
+
+188
+00:10:00.170 --> 00:10:03.646
+What does this dithered quantization noise sound like?
+
+189
+00:10:03.646 --> 00:10:06.012
+Let's listen to our eight-bit sine wave.
+
+190
+00:10:12.521 --> 00:10:15.273
+That may have been hard to hear anything but the tone.
+
+191
+00:10:15.273 --> 00:10:18.740
+Let's listen to just the noise after we notch out the sine wave
+
+192
+00:10:18.740 --> 00:10:21.683
+and then bring the gain up a bit because the noise is quiet.
+
+193
+00:10:32.009 --> 00:10:35.049
+Those of you who have used analog recording equipment
+
+194
+00:10:35.049 --> 00:10:36.670
+may have just thought to yourselves,
+
+195
+00:10:36.670 --> 00:10:40.382
+"My goodness! That sounds like tape hiss!"
+
+196
+00:10:40.382 --> 00:10:41.929
+Well, it doesn't just sound like tape hiss,
+
+197
+00:10:41.929 --> 00:10:43.433
+it acts like it too,
+
+198
+00:10:43.433 --> 00:10:45.225
+and if we use a gaussian dither
+
+199
+00:10:45.225 --> 00:10:47.646
+then it's mathematically equivalent in every way.
+
+200
+00:10:47.646 --> 00:10:49.225
+It <u>is</u> tape hiss.
+
+201
+00:10:49.225 --> 00:10:51.774
+Intuitively, that means that we can measure tape hiss
+
+202
+00:10:51.774 --> 00:10:54.196
+and thus the noise floor of magnetic audio tape
+
+203
+00:10:54.196 --> 00:10:56.233
+in bits instead of decibels,
+
+204
+00:10:56.233 --> 00:10:59.902
+in order to put things in a digital perspective.
+
+205
+00:10:59.902 --> 00:11:03.028
+Compact cassettes...
+
+206
+00:11:03.028 --> 00:11:05.449
+for those of you who are old enough to remember them,
+
+207
+00:11:05.449 --> 00:11:09.161
+could reach as
+deep as nine bits in perfect conditions,
+
+208
+00:11:09.161 --> 00:11:11.209
+though five to six bits was more typical,
+
+209
+00:11:11.209 --> 00:11:13.876
+especially if it was a recording made on a tape deck.
+
+210
+00:11:13.876 --> 00:11:19.422
+That's right... your mix tapes were only about six bits
+deep... if you were lucky!
+
+211
+00:11:19.837 --> 00:11:22.345
+The very best professional open reel tape
+
+212
+00:11:22.345 --> 00:11:24.553
+used in studios could barely hit...
+
+213
+00:11:24.553 --> 00:11:26.473
+any guesses?...
+
+214
+00:11:26.473 --> 00:11:27.604
+13 bits
+
+215
+00:11:27.604 --> 00:11:28.980
+<u>with</u> advanced noise reduction.
+
+216
+00:11:28.980 --> 00:11:32.062
+And that's why seeing 'DDD' on a Compact Disc
+
+217
+00:11:32.062 --> 00:11:35.208
+used to be such a big, high-end deal.
+
+218
+00:11:40.116 --> 00:11:42.825
+I keep saying that I'm quantizing with dither,
+
+219
+00:11:42.825 --> 00:11:44.734
+so what is dither exactly?
+
+220
+00:11:44.734 --> 00:11:47.284
+More importantly, what does it do?
+
+221
+00:11:47.284 --> 00:11:49.876
+The simple way to quantize a signal is to choose
+
+222
+00:11:49.876 --> 00:11:52.329
+the digital amplitude value closest
+
+223
+00:11:52.329 --> 00:11:54.377
+to the original analog amplitude.
+
+224
+00:11:54.377 --> 00:11:55.337
+Obvious, right?
+
+225
+00:11:55.337 --> 00:11:57.545
+Unfortunately, the exact noise you get
+
+226
+00:11:57.545 --> 00:11:59.220
+from this simple quantization scheme
+
+227
+00:11:59.220 --> 00:12:02.174
+depends somewhat on the input signal,
+
+228
+00:12:02.174 --> 00:12:04.596
+so we may get noise that's inconsistent,
+
+229
+00:12:04.596 --> 00:12:06.142
+or causes distortion,
+
+230
+00:12:06.142 --> 00:12:09.054
+or is undesirable in some other way.
+
+231
+00:12:09.054 --> 00:12:11.764
+Dither is specially-constructed noise that
+
+232
+00:12:11.764 --> 00:12:15.273
+substitutes for the noise produced by simple quantization.
+
+233
+00:12:15.273 --> 00:12:18.025
+Dither doesn't drown out or mask quantization noise,
+
+234
+00:12:18.025 --> 00:12:20.190
+it actually replaces it
+
+235
+00:12:20.190 --> 00:12:22.612
+with noise characteristics of our choosing
+
+236
+00:12:22.612 --> 00:12:24.794
+that aren't influenced by the input.
+
+237
+00:12:25.256 --> 00:12:27.081
+Let's <u>watch</u> what dither does.
+
+238
+00:12:27.081 --> 00:12:30.078
+The signal generator has too much noise for this test
+
+239
+00:12:30.431 --> 00:12:33.161
+so we'll produce a mathematically
+
+240
+00:12:33.161 --> 00:12:34.782
+perfect sine wave with the ThinkPad
+
+241
+00:12:34.782 --> 00:12:38.205
+and quantize it to eight bits with dithering.
+
+242
+00:12:39.006 --> 00:12:41.342
+We see a nice sine wave on the waveform display
+
+243
+00:12:41.342 --> 00:12:43.452
+and output scope
+
+244
+00:12:44.222 --> 00:12:44.972
+and...
+
+245
+00:12:46.588 --> 00:12:49.375
+once the analog spectrum analyzer catches up...
+
+246
+00:12:50.713 --> 00:12:53.588
+a clean frequency peak with a uniform noise floor
+
+247
+00:12:56.864 --> 00:12:58.611
+on both spectral displays
+
+248
+00:12:58.611 --> 00:12:59.646
+just like before
+
+249
+00:12:59.646 --> 00:13:01.549
+Again, this is with dither.
+
+250
+00:13:02.196 --> 00:13:04.225
+Now I turn dithering off.
+
+251
+00:13:05.779 --> 00:13:07.913
+The quantization noise, that dither had spread out
+
+252
+00:13:07.913 --> 00:13:09.577
+into a nice, flat noise floor,
+
+253
+00:13:09.577 --> 00:13:12.286
+piles up into harmonic distortion peaks.
+
+254
+00:13:12.286 --> 00:13:16.030
+The noise floor is lower, but the level of distortion becomes nonzero,
+
+255
+00:13:16.030 --> 00:13:19.668
+and the distortion peaks sit higher than the dithering noise did.
+
+256
+00:13:19.668 --> 00:13:22.318
+At eight bits this effect is exaggerated.
+
+257
+00:13:22.488 --> 00:13:24.200
+At sixteen bits,
+
+258
+00:13:24.692 --> 00:13:25.929
+even without dither,
+
+259
+00:13:25.929 --> 00:13:28.308
+harmonic distortion is going to be so low
+
+260
+00:13:28.308 --> 00:13:30.708
+as to be completely inaudible.
+
+261
+00:13:30.708 --> 00:13:34.581
+Still, we can use dither to eliminate it completely
+
+262
+00:13:34.581 --> 00:13:36.489
+if we so choose.
+
+263
+00:13:37.642 --> 00:13:39.273
+Turning the dither off again for a moment,
+
+264
+00:13:40.934 --> 00:13:43.444
+you'll notice that the absolute level of distortion
+
+265
+00:13:43.444 --> 00:13:47.070
+from undithered quantization stays approximately constant
+
+266
+00:13:47.070 --> 00:13:49.033
+regardless of the input amplitude.
+
+267
+00:13:49.033 --> 00:13:51.998
+But when the signal level drops below a half a bit,
+
+268
+00:13:51.998 --> 00:13:54.036
+everything quantizes to zero.
+
+269
+00:13:54.036 --> 00:13:54.910
+In a sense,
+
+270
+00:13:54.910 --> 00:13:58.557
+everything quantizing to zero is just 100% distortion!
+
+271
+00:13:58.833 --> 00:14:01.588
+Dither eliminates this distortion too.
+
+272
+00:14:01.588 --> 00:14:03.599
+We reenable dither and...
+
+273
+00:14:03.599 --> 00:14:06.377
+there's our signal back at 1/4 bit,
+
+274
+00:14:06.377 --> 00:14:09.076
+with our nice flat noise floor.
+
+275
+00:14:09.630 --> 00:14:11.220
+The noise floor doesn't have to be flat.
+
+276
+00:14:11.220 --> 00:14:12.798
+Dither is noise of our choosing,
+
+277
+00:14:12.798 --> 00:14:15.006
+so let's choose a noise as inoffensive
+
+278
+00:14:15.006 --> 00:14:17.017
+and difficult to notice as possible.
+
+279
+00:14:18.142 --> 00:14:22.484
+Our hearing is most sensitive in the midrange from 2kHz to 4kHz,
+
+280
+00:14:22.484 --> 00:14:25.438
+so that's where background noise is going to be the most obvious.
+
+281
+00:14:25.438 --> 00:14:29.406
+We can shape dithering noise away from sensitive frequencies
+
+282
+00:14:29.406 --> 00:14:31.241
+to where hearing is less sensitive,
+
+283
+00:14:31.241 --> 00:14:33.910
+usually the highest frequencies.
+
+284
+00:14:34.249 --> 00:14:37.460
+16-bit dithering noise is normally much too quiet to hear at all,
+
+285
+00:14:37.460 --> 00:14:39.668
+but let's listen to our noise shaping example,
+
+286
+00:14:39.668 --> 00:14:42.234
+again with the gain brought way up...
+
+287
+00:14:56.020 --> 00:14:59.977
+Lastly, dithered quantization noise <u>is</u> higher power overall
+
+288
+00:14:59.977 --> 00:15:04.276
+than undithered quantization noise even when it sounds quieter.
+
+289
+00:15:04.276 --> 00:15:07.902
+You can see that on a VU meter during passages of near-silence.
+
+290
+00:15:07.902 --> 00:15:10.537
+But dither isn't only an on or off choice.
+
+291
+00:15:10.537 --> 00:15:14.712
+We can reduce the dither's power to balance less noise against
+
+292
+00:15:14.712 --> 00:15:18.313
+a bit of distortion to minimize the overall effect.
+
+293
+00:15:19.605 --> 00:15:22.790
+We'll also modulate the input signal like this:
+
+294
+00:15:27.098 --> 00:15:30.206
+...to show how a varying input affects the quantization noise.
+
+295
+00:15:30.206 --> 00:15:33.289
+At full dithering power, the noise is uniform, constant,
+
+296
+00:15:33.289 --> 00:15:35.643
+and featureless just like we expect:
+
+297
+00:15:40.937 --> 00:15:42.772
+As we reduce the dither's power,
+
+298
+00:15:42.772 --> 00:15:46.356
+the input increasingly affects the amplitude and the character
+
+299
+00:15:46.356 --> 00:15:47.977
+of the quantization noise:
+
+300
+00:16:09.883 --> 00:16:13.844
+Shaped dither behaves similarly,
+
+301
+00:16:13.844 --> 00:16:16.553
+but noise shaping lends one more nice advantage.
+
+302
+00:16:16.553 --> 00:16:18.804
+To make a long story short, it can use
+
+303
+00:16:18.804 --> 00:16:20.937
+a somewhat lower dither power before the input
+
+304
+00:16:20.937 --> 00:16:23.662
+has as much effect on the output.
+
+305
+00:16:49.172 --> 00:16:51.508
+Despite all the time I just spent on dither,
+
+306
+00:16:51.508 --> 00:16:53.012
+we're talking about differences
+
+307
+00:16:53.012 --> 00:16:56.372
+that start 100 decibels below full scale.
+
+308
+00:16:56.372 --> 00:16:59.806
+Maybe if the CD had been 14 bits as originally designed,
+
+309
+00:16:59.806 --> 00:17:01.513
+dither <u>might</u> be more important.
+
+310
+00:17:01.989 --> 00:17:02.644
+Maybe.
+
+311
+00:17:02.644 --> 00:17:05.438
+At 16 bits, really, it's mostly a wash.
+
+312
+00:17:05.438 --> 00:17:08.019
+You can think of dither as an insurance policy
+
+313
+00:17:08.019 --> 00:17:11.443
+that gives several extra decibels of dynamic range
+
+314
+00:17:11.443 --> 00:17:12.804
+just in case.
+
+315
+00:17:12.990 --> 00:17:14.196
+The simple fact is, though,
+
+316
+00:17:14.196 --> 00:17:16.361
+no one ever ruined a great recording
+
+317
+00:17:16.361 --> 00:17:19.182
+by not dithering the final master.
+
+318
+00:17:24.414 --> 00:17:25.790
+We've been using sine waves.
+
+319
+00:17:25.790 --> 00:17:28.254
+They're the obvious choice when what we want to see
+
+320
+00:17:28.254 --> 00:17:32.212
+is a system's behavior at a given isolated frequency.
+
+321
+00:17:32.212 --> 00:17:34.217
+Now let's look at something a bit more complex.
+
+322
+00:17:34.217 --> 00:17:35.923
+What should we expect to happen
+
+323
+00:17:35.923 --> 00:17:39.671
+when I change the input to a square wave...
+
+324
+00:17:42.718 --> 00:17:45.921
+The input scope confirms our 1kHz square wave.
+
+325
+00:17:45.921 --> 00:17:47.351
+The output scope shows..
+
+326
+00:17:48.614 --> 00:17:51.102
+Exactly what it should.
+
+327
+00:17:51.102 --> 00:17:53.900
+What is a square wave really?
+
+328
+00:17:54.654 --> 00:17:57.982
+Well, we can say it's a waveform that's some positive value
+
+329
+00:17:57.982 --> 00:18:00.788
+for half a cycle and then transitions instantaneously
+
+330
+00:18:00.788 --> 00:18:02.910
+to a negative value for the other half.
+
+331
+00:18:02.910 --> 00:18:05.076
+But that doesn't really tell us anything useful
+
+332
+00:18:05.076 --> 00:18:07.241
+about how this input
+
+333
+00:18:07.241 --> 00:18:09.378
+becomes this output.
+
+334
+00:18:10.132 --> 00:18:12.713
+Then we remember that any waveform
+
+335
+00:18:12.713 --> 00:18:15.508
+is also the sum of discrete frequencies,
+
+336
+00:18:15.508 --> 00:18:18.302
+and a square wave is a particularly simple sum
+
+337
+00:18:18.302 --> 00:18:19.636
+a fundamental and
+
+338
+00:18:19.636 --> 00:18:22.228
+an infinite series of odd harmonics.
+
+339
+00:18:22.228 --> 00:18:24.597
+Sum them all up, you get a square wave.
+
+340
+00:18:26.398 --> 00:18:27.433
+At first glance,
+
+341
+00:18:27.433 --> 00:18:29.225
+that doesn't seem very useful either.
+
+342
+00:18:29.225 --> 00:18:31.561
+You have to sum up an infinite number of harmonics
+
+343
+00:18:31.561 --> 00:18:33.108
+to get the answer.
+
+344
+00:18:33.108 --> 00:18:35.977
+Ah, but we don't have an infinite number of harmonics.
+
+345
+00:18:36.960 --> 00:18:39.902
+We're using a quite sharp anti-aliasing filter
+
+346
+00:18:39.902 --> 00:18:42.206
+that cuts off right above 20kHz,
+
+347
+00:18:42.206 --> 00:18:44.158
+so our signal is band-limited,
+
+348
+00:18:44.158 --> 00:18:46.421
+which means we get this:
+
+349
+00:18:52.500 --> 00:18:56.468
+..and that's exactly what we see on the output scope.
+
+350
+00:18:56.468 --> 00:18:59.550
+The rippling you see around sharp edges in a bandlimited signal
+
+351
+00:18:59.550 --> 00:19:00.926
+is called the Gibbs effect.
+
+352
+00:19:00.926 --> 00:19:04.137
+It happens whenever you slice off part of the frequency domain
+
+353
+00:19:04.137 --> 00:19:07.006
+in the middle of nonzero energy.
+
+354
+00:19:07.006 --> 00:19:09.854
+The usual rule of thumb you'll hear is the sharper the cutoff,
+
+355
+00:19:09.854 --> 00:19:11.188
+the stronger the rippling,
+
+356
+00:19:11.188 --> 00:19:12.777
+which is approximately true,
+
+357
+00:19:12.777 --> 00:19:14.900
+but we have to be careful how we think about it.
+
+358
+00:19:14.900 --> 00:19:15.774
+For example...
+
+359
+00:19:15.774 --> 00:19:19.529
+what would you expect our quite sharp anti-aliasing filter
+
+360
+00:19:19.529 --> 00:19:23.181
+to do if I run our signal through it a second time?
+
+361
+00:19:34.136 --> 00:19:37.588
+Aside from adding a few fractional cycles of delay,
+
+362
+00:19:37.588 --> 00:19:39.348
+the answer is...
+
+363
+00:19:39.348 --> 00:19:40.857
+nothing at all.
+
+364
+00:19:41.257 --> 00:19:43.302
+The signal is already bandlimited.
+
+365
+00:19:43.656 --> 00:19:46.590
+Bandlimiting it again doesn't do anything.
+
+366
+00:19:46.590 --> 00:19:50.686
+A second pass can't remove frequencies that we already removed.
+
+367
+00:19:52.070 --> 00:19:53.737
+And that's important.
+
+368
+00:19:53.737 --> 00:19:56.233
+People tend to think of the ripples as a kind of artifact
+
+369
+00:19:56.233 --> 00:19:59.945
+that's added by anti-aliasing and anti-imaging filters,
+
+370
+00:19:59.945 --> 00:20:01.737
+implying that the ripples get worse
+
+371
+00:20:01.737 --> 00:20:03.913
+each time the signal passes through.
+
+372
+00:20:03.913 --> 00:20:05.950
+We can see that in this case that didn't happen.
+
+373
+00:20:05.950 --> 00:20:09.492
+So was it really the filter that added the ripples the first time through?
+
+374
+00:20:09.492 --> 00:20:10.537
+No, not really.
+
+375
+00:20:10.537 --> 00:20:12.126
+It's a subtle distinction,
+
+376
+00:20:12.126 --> 00:20:15.252
+but Gibbs effect ripples aren't added by filters,
+
+377
+00:20:15.252 --> 00:20:18.836
+they're just part of what a bandlimited signal <u>is</u>.
+
+378
+00:20:18.836 --> 00:20:20.798
+Even if we synthetically construct
+
+379
+00:20:20.798 --> 00:20:23.508
+what looks like a perfect digital square wave,
+
+380
+00:20:23.508 --> 00:20:26.206
+it's still limited to the channel bandwidth.
+
+381
+00:20:26.206 --> 00:20:29.140
+Remember the stairstep representation is misleading.
+
+382
+00:20:29.140 --> 00:20:32.222
+What we really have here are instantaneous sample points,
+
+383
+00:20:32.222 --> 00:20:36.148
+and only one bandlimited signal fits those points.
+
+384
+00:20:36.148 --> 00:20:39.614
+All we did when we drew our apparently perfect square wave
+
+385
+00:20:39.614 --> 00:20:43.198
+was line up the sample points just right so it appeared
+
+386
+00:20:43.198 --> 00:20:47.785
+that there were no ripples if we played connect-the-dots.
+
+387
+00:20:47.785 --> 00:20:49.449
+But the original bandlimited signal,
+
+388
+00:20:49.449 --> 00:20:52.742
+complete with ripples, was still there.
+
+389
+00:20:54.004 --> 00:20:56.542
+And that leads us to one more important point.
+
+390
+00:20:56.542 --> 00:20:59.550
+You've probably heard that the timing precision of a digital signal
+
+391
+00:20:59.550 --> 00:21:02.409
+is limited by its sample rate; put another way,
+
+392
+00:21:02.409 --> 00:21:05.140
+that digital signals can't represent anything
+
+393
+00:21:05.140 --> 00:21:08.041
+that falls between the samples...
+
+394
+00:21:08.041 --> 00:21:11.422
+implying that impulses or fast attacks have to align
+
+395
+00:21:11.422 --> 00:21:14.473
+exactly with a sample, or the timing gets mangled...
+
+396
+00:21:14.473 --> 00:21:16.219
+or they just disappear.
+
+397
+00:21:16.711 --> 00:21:20.820
+At this point, we can easily see why that's wrong.
+
+398
+00:21:20.820 --> 00:21:23.742
+Again, our input signals are bandlimited.
+
+399
+00:21:23.742 --> 00:21:26.036
+And digital signals are samples,
+
+400
+00:21:26.036 --> 00:21:29.340
+not stairsteps, not 'connect-the-dots'.
+
+401
+00:21:31.572 --> 00:21:34.592
+We most certainly can, for example,
+
+402
+00:21:36.777 --> 00:21:39.337
+put the rising edge of our bandlimited square wave
+
+403
+00:21:39.337 --> 00:21:42.004
+anywhere we want between samples.
+
+404
+00:21:42.004 --> 00:21:44.354
+It's represented perfectly
+
+405
+00:21:47.508 --> 00:21:50.218
+and it's reconstructed perfectly.
+
+406
+00:22:04.620 --> 00:22:06.526
+Just like in the previous episode,
+
+407
+00:22:06.526 --> 00:22:08.393
+we've covered a broad range of topics,
+
+408
+00:22:08.393 --> 00:22:10.868
+and yet barely scratched the surface of each one.
+
+409
+00:22:10.868 --> 00:22:13.620
+If anything, my sins of omission are greater this time around...
+
+410
+00:22:13.620 --> 00:22:16.286
+but this is a good stopping point.
+
+411
+00:22:16.286 --> 00:22:17.833
+Or maybe, a good starting point.
+
+412
+00:22:17.833 --> 00:22:18.708
+Dig deeper.
+
+413
+00:22:18.708 --> 00:22:19.710
+Experiment.
+
+414
+00:22:19.710 --> 00:22:21.374
+I chose my demos very carefully
+
+415
+00:22:21.374 --> 00:22:23.668
+to be simple and give clear results.
+
+416
+00:22:23.668 --> 00:22:26.217
+You can reproduce every one of them on your own if you like.
+
+417
+00:22:26.217 --> 00:22:28.766
+But let's face it, sometimes we learn the most
+
+418
+00:22:28.766 --> 00:22:30.516
+about a spiffy toy by breaking it open
+
+419
+00:22:30.516 --> 00:22:32.553
+and studying all the pieces that fall out.
+
+420
+00:22:32.553 --> 00:22:35.230
+That's OK, we're engineers.
+
+421
+00:22:35.230 --> 00:22:36.350
+Play with the demo parameters,
+
+422
+00:22:36.350 --> 00:22:37.972
+hack up the code,
+
+423
+00:22:37.972 --> 00:22:39.774
+set up alternate experiments.
+
+424
+00:22:39.774 --> 00:22:40.692
+The source code for everything,
+
+425
+00:22:40.692 --> 00:22:42.398
+including the little pushbutton demo application,
+
+426
+00:22:42.398 --> 00:22:44.361
+is up at Xiph.Org.
+
+427
+00:22:44.361 --> 00:22:45.940
+In the course of experimentation,
+
+428
+00:22:45.940 --> 00:22:47.401
+you're likely to run into something
+
+429
+00:22:47.401 --> 00:22:49.950
+that you didn't expect and can't explain.
+
+430
+00:22:49.950 --> 00:22:51.198
+Don't worry!
+
+431
+00:22:51.198 --> 00:22:54.537
+My earlier snark aside, Wikipedia is fantastic for
+
+432
+00:22:54.537 --> 00:22:56.788
+exactly this kind of casual research.
+
+433
+00:22:56.788 --> 00:22:59.956
+If you're really serious about understanding signals,
+
+434
+00:22:59.956 --> 00:23:03.337
+several universities have advanced materials online,
+
+435
+00:23:03.337 --> 00:23:07.380
+such as the 6.003 and 6.007 Signals and Systems modules
+
+436
+00:23:07.380 --> 00:23:08.798
+at MIT OpenCourseWare.
+
+437
+00:23:08.798 --> 00:23:11.593
+And of course, there's always the community here at Xiph.Org.
+
+438
+00:23:12.792 --> 00:23:13.929
+Digging deeper or not,
+
+439
+00:23:13.929 --> 00:23:14.974
+I am out of coffee,
+
+440
+00:23:14.974 --> 00:23:16.436
+so, until next time,
+
+441
+00:23:16.436 --> 00:23:19.316
+happy hacking!

Deleted: websites/xiph.org/video/vid2-en.vtt
===================================================================
--- websites/xiph.org/video/vid2-en.vtt	2013-02-26 00:18:29 UTC (rev 18831)
+++ websites/xiph.org/video/vid2-en.vtt	2013-02-26 00:45:00 UTC (rev 18832)
@@ -1,1773 +0,0 @@
-WEBVTT
-
-1
-00:00:08.252 --> 00:00:11.550
-Hi, I'm Monty Montgomery from Red Hat and Xiph.Org.
-
-2
-00:00:11.550 --> 00:00:18.430
-A few months ago, I wrote an article on digital audio and why 24bit/192kHz music downloads don't make sense.
-
-3
-00:00:18.430 --> 00:00:23.433
-In the article, I mentioned--almost in passing--that a digital waveform is not a stairstep,
-
-4
-00:00:23.433 --> 00:00:28.680
-and you certainly don't get a stairstep when you convert from digital back to analog.
-
-5
-00:00:29.865 --> 00:00:33.865
-Of everything in the entire article, <b>that</b> was the number one thing people wrote about.
-
-6
-00:00:33.865 --> 00:00:37.221
-In fact, more than half the mail I got was questions and comments
-
-7
-00:00:37.221 --> 00:00:39.663
-about basic digital signal behavior.
-
-8
-00:00:39.894 --> 00:00:45.285
-Since there's interest, let's take a little time to play with some <u>simple</u> digital signals.
-
-9
-00:00:49.747 --> 00:00:51.006
-Pretend for a moment
-
-10
-00:00:51.006 --> 00:00:54.089
-that we have no idea how digital signals really behave.
-
-11
-00:00:54.734 --> 00:00:56.841
-In that case it doesn't make sense for us
-
-12
-00:00:56.841 --> 00:00:59.049
-to use digital test equipment either.
-
-13
-00:00:59.049 --> 00:01:00.937
-Fortunately for this exercise, there's still
-
-14
-00:01:00.937 --> 00:01:04.020
-plenty of working analog lab equipment out there.
-
-15
-00:01:04.020 --> 00:01:05.972
-First up, we need a signal generator
-
-16
-00:01:05.972 --> 00:01:08.190
-to provide us with analog input signals--
-
-17
-00:01:08.190 --> 00:01:12.692
-in this case, an HP3325 from 1978.
-
-18
-00:01:12.692 --> 00:01:14.153
-It's still a pretty good generator,
-
-19
-00:01:14.153 --> 00:01:15.614
-so if you don't mind the size,
-
-20
-00:01:15.614 --> 00:01:16.532
-the weight,
-
-21
-00:01:16.532 --> 00:01:17.577
-the power consumption,
-
-22
-00:01:17.577 --> 00:01:18.910
-and the noisy fan,
-
-23
-00:01:18.910 --> 00:01:20.329
-you can find them on eBay.
-
-24
-00:01:20.329 --> 00:01:23.863
-Occasionally for only slightly more than you'll pay for shipping.
-
-25
-00:01:24.617 --> 00:01:28.500
-Next, we'll observe our analog waveforms on analog oscilloscopes,
-
-26
-00:01:28.500 --> 00:01:31.550
-like this Tektronix 2246 from the mid-90s,
-
-27
-00:01:31.550 --> 00:01:34.761
-one of the last and very best analog scopes ever made.
-
-28
-00:01:34.761 --> 00:01:36.807
-Every home lab should have one.
-
-29
-00:01:37.716 --> 00:01:40.852
-And finally inspect the frequency spectrum of our signals
-
-30
-00:01:40.852 --> 00:01:43.177
-using an analog spectrum analyzer.
-
-31
-00:01:43.177 --> 00:01:47.732
-This HP3585 from the same product line as the signal generator.
-
-32
-00:01:47.732 --> 00:01:50.615
-Like the other equipment here it has a rudimentary
-
-33
-00:01:50.615 --> 00:01:52.905
-and hilariously large microcontroller,
-
-34
-00:01:52.905 --> 00:01:56.276
-but the signal path from input to what you see on the screen
-
-35
-00:01:56.276 --> 00:01:58.537
-is completely analog.
-
-36
-00:01:58.537 --> 00:02:00.329
-All of this equipment is vintage,
-
-37
-00:02:00.329 --> 00:02:01.993
-but aside from its raw tonnage,
-
-38
-00:02:01.993 --> 00:02:03.844
-the specs are still quite good.
-
-39
-00:02:04.536 --> 00:02:06.868
-At the moment, we have our signal generator
-
-40
-00:02:06.868 --> 00:02:12.829
-set to output a nice 1kHz sine wave at one volt RMS,
-
-41
-00:02:13.414 --> 00:02:15.220
-we see the sine wave on the oscilloscope,
-
-42
-00:02:15.220 --> 00:02:21.428
-can verify that it is indeed 1kHz at one volt RMS,
-
-43
-00:02:21.428 --> 00:02:24.108
-which is 2.8V peak-to-peak,
-
-44
-00:02:24.308 --> 00:02:27.561
-and that matches the measurement on the spectrum analyzer as well.
-
-45
-00:02:27.561 --> 00:02:30.644
-The analyzer also shows some low-level white noise
-
-46
-00:02:30.644 --> 00:02:32.190
-and just a bit of harmonic distortion,
-
-47
-00:02:32.190 --> 00:02:36.649
-with the highest peak about 70dB or so below the fundamental.
-
-48
-00:02:36.649 --> 00:02:38.612
-Now, this doesn't matter at all in our demos,
-
-49
-00:02:38.612 --> 00:02:40.574
-but I wanted to point it out now
-
-50
-00:02:40.574 --> 00:02:42.452
-just in case you didn't notice it until later.
-
-51
-00:02:44.036 --> 00:02:47.142
-Now, we drop digital sampling in the middle.
-
-52
-00:02:48.557 --> 00:02:51.024
-For the conversion, we'll use a boring,
-
-53
-00:02:51.024 --> 00:02:53.374
-consumer-grade, eMagic USB1 audio device.
-
-54
-00:02:53.374 --> 00:02:55.337
-It's also more than ten years old at this point,
-
-55
-00:02:55.337 --> 00:02:57.257
-and it's getting obsolete.
-
-56
-00:02:57.964 --> 00:03:02.676
-A recent converter can easily have an order of magnitude better specs.
-
-57
-00:03:03.076 --> 00:03:07.924
-Flatness, linearity, jitter, noise behavior, everything...
-
-58
-00:03:07.924 --> 00:03:09.353
-you may not have noticed.
-
-59
-00:03:09.353 --> 00:03:11.604
-Just because we can measure an improvement
-
-60
-00:03:11.604 --> 00:03:13.609
-doesn't mean we can hear it,
-
-61
-00:03:13.609 --> 00:03:16.404
-and even these old consumer boxes were already
-
-62
-00:03:16.404 --> 00:03:18.643
-at the edge of ideal transparency.
-
-63
-00:03:20.244 --> 00:03:22.825
-The eMagic connects to my ThinkPad,
-
-64
-00:03:22.825 --> 00:03:26.121
-which displays a digital waveform and spectrum for comparison,
-
-65
-00:03:26.121 --> 00:03:28.788
-then the ThinkPad sends the digital signal right back out
-
-66
-00:03:28.788 --> 00:03:30.921
-to the eMagic for re-conversion to analog
-
-67
-00:03:30.921 --> 00:03:33.332
-and observation on the output scopes.
-
-68
-00:03:33.332 --> 00:03:35.582
-Input to output, left to right.
-
-69
-00:03:40.211 --> 00:03:41.214
-OK, it's go time.
-
-70
-00:03:41.214 --> 00:03:43.924
-We begin by converting an analog signal to digital
-
-71
-00:03:43.924 --> 00:03:47.347
-and then right back to analog again with no other steps.
-
-72
-00:03:47.347 --> 00:03:49.268
-The signal generator is set to produce
-
-73
-00:03:49.268 --> 00:03:52.649
-a 1kHz sine wave just like before.
-
-74
-00:03:52.649 --> 00:03:57.428
-We can see our analog sine wave on our input-side oscilloscope.
-
-75
-00:03:57.428 --> 00:04:01.694
-We digitize our signal to 16 bit PCM at 44.1kHz,
-
-76
-00:04:01.694 --> 00:04:03.828
-same as on a CD.
-
-77
-00:04:03.828 --> 00:04:07.156
-The spectrum of the digitized signal matches what we saw earlier. and...
-
-78
-00:04:07.156 --> 00:04:10.836
-what we see now on the analog spectrum analyzer,
-
-79
-00:04:10.836 --> 00:04:15.154
-aside from its high-impedance input being just a smidge noisier.
-
-80
-00:04:15.154 --> 00:04:15.956
-For now
-
-81
-00:04:18.248 --> 00:04:20.798
-the waveform display shows our digitized sine wave
-
-82
-00:04:20.798 --> 00:04:23.966
-as a stairstep pattern, one step for each sample.
-
-83
-00:04:23.966 --> 00:04:26.388
-And when we look at the output signal
-
-84
-00:04:26.388 --> 00:04:29.054
-that's been converted from digital back to analog, we see...
-
-85
-00:04:29.054 --> 00:04:32.052
-It's exactly like the original sine wave.
-
-86
-00:04:32.052 --> 00:04:33.483
-No stairsteps.
-
-87
-00:04:33.914 --> 00:04:37.193
-OK, 1kHz is still a fairly low frequency,
-
-88
-00:04:37.193 --> 00:04:40.633
-maybe the stairsteps are just
-hard to see or they're being smoothed away.
-
-89
-00:04:40.739 --> 00:04:49.492
-Fair enough. Let's choose
-a higher frequency, something close to Nyquist, say 15kHz.
-
-90
-00:04:49.492 --> 00:04:53.545
-Now the sine wave is represented by less than three samples per cycle, and...
-
-91
-00:04:53.545 --> 00:04:55.838
-the digital waveform looks pretty awful.
-
-92
-00:04:55.838 --> 00:04:59.798
-Well, looks can be deceiving. The analog output...
-
-93
-00:05:01.876 --> 00:05:06.033
-is still a perfect sine wave, exactly like the original.
-
-94
-00:05:06.633 --> 00:05:09.228
-Let's keep going up.
-
-95
-00:05:17.353 --> 00:05:20.151
-16kHz....
-
-96
-00:05:23.198 --> 00:05:25.616
-17kHz...
-
-97
-00:05:28.201 --> 00:05:29.945
-18kHz...
-
-98
-00:05:33.822 --> 00:05:35.548
-19kHz...
-
-99
-00:05:40.457 --> 00:05:42.465
-20kHz.
-
-100
-00:05:49.097 --> 00:05:52.350
-Welcome to the upper limits of human hearing.
-
-101
-00:05:52.350 --> 00:05:54.377
-The output waveform is still perfect.
-
-102
-00:05:54.377 --> 00:05:58.025
-No jagged edges, no dropoff, no stairsteps.
-
-103
-00:05:58.025 --> 00:06:01.342
-So where'd the stairsteps go?
-
-104
-00:06:01.342 --> 00:06:03.198
-Don't answer, it's a trick question.
-
-105
-00:06:03.198 --> 00:06:04.318
-They were never there.
-
-106
-00:06:04.318 --> 00:06:06.652
-Drawing a digital waveform as a stairstep
-
-107
-00:06:08.712 --> 00:06:10.772
-was wrong to begin with.
-
-108
-00:06:10.942 --> 00:06:11.998
-Why?
-
-109
-00:06:11.998 --> 00:06:14.366
-A stairstep is a continuous-time function.
-
-110
-00:06:14.366 --> 00:06:16.201
-It's jagged, and it's piecewise,
-
-111
-00:06:16.201 --> 00:06:19.700
-but it has a defined value at every point in time.
-
-112
-00:06:19.700 --> 00:06:22.004
-A sampled signal is entirely different.
-
-113
-00:06:22.004 --> 00:06:23.337
-It's discrete-time;
-
-114
-00:06:23.337 --> 00:06:27.337
-it's only got a value right at each instantaneous sample point
-
-115
-00:06:27.337 --> 00:06:32.596
-and it's undefined, there is no value at all, everywhere between.
-
-116
-00:06:32.596 --> 00:06:36.666
-A discrete-time signal is properly drawn as a lollipop graph.
-
-117
-00:06:40.020 --> 00:06:42.974
-The continuous, analog counterpart of a digital signal
-
-118
-00:06:42.974 --> 00:06:45.364
-passes smoothly through each sample point,
-
-119
-00:06:45.364 --> 00:06:50.153
-and that's just as true for high frequencies as it is for low.
-
-120
-00:06:50.153 --> 00:06:53.033
-Now, the interesting and not at all obvious bit is:
-
-121
-00:06:53.033 --> 00:06:55.454
-there's only one bandlimited signal that passes
-
-122
-00:06:55.454 --> 00:06:57.417
-exactly through each sample point.
-
-123
-00:06:57.417 --> 00:06:58.708
-It's a unique solution.
-
-124
-00:06:58.708 --> 00:07:01.246
-So if you sample a bandlimited signal
-
-125
-00:07:01.246 --> 00:07:02.612
-and then convert it back,
-
-126
-00:07:02.612 --> 00:07:06.462
-the original input is also the only possible output.
-
-127
-00:07:06.462 --> 00:07:07.838
-And before you say,
-
-128
-00:07:07.838 --> 00:07:11.721
-"Oh, I can draw a different signal that passes through those points."
-
-129
-00:07:11.721 --> 00:07:14.283
-Well, yes you can, but...
-
-130
-00:07:17.268 --> 00:07:20.521
-if it differs even minutely from the original,
-
-131
-00:07:20.521 --> 00:07:24.905
-it contains frequency content at or beyond Nyquist,
-
-132
-00:07:24.905 --> 00:07:26.185
-breaks the bandlimiting requirement
-
-133
-00:07:26.185 --> 00:07:28.358
-and isn't a valid solution.
-
-134
-00:07:28.574 --> 00:07:30.036
-So how did everyone get confused
-
-135
-00:07:30.036 --> 00:07:32.702
-and start thinking of digital signals as stairsteps?
-
-136
-00:07:32.702 --> 00:07:34.900
-I can think of two good reasons.
-
-137
-00:07:34.900 --> 00:07:37.956
-First: It's easy enough to convert a sampled signal
-
-138
-00:07:37.972 --> 00:07:39.294
-to a true stairstep.
-
-139
-00:07:39.294 --> 00:07:42.409
-Just extend each sample value forward until the next sample period.
-
-140
-00:07:42.409 --> 00:07:44.414
-This is called a zero-order hold,
-
-141
-00:07:44.414 --> 00:07:47.913
-and it's an important part of how some digital-to-analog converters work,
-
-142
-00:07:47.913 --> 00:07:50.089
-especially the simplest ones.
-
-143
-00:07:50.089 --> 00:07:55.591
-So, anyone who looks up digital-to-analog conversion
-
-144
-00:07:55.592 --> 00:07:59.550
-is probably going to see a diagram of a stairstep waveform somewhere,
-
-145
-00:07:59.550 --> 00:08:01.982
-but that's not a finished conversion,
-
-146
-00:08:01.982 --> 00:08:04.250
-and it's not the signal that comes out.
-
-147
-00:08:04.944 --> 00:08:05.684
-Second,
-
-148
-00:08:05.684 --> 00:08:07.529
-and this is probably the more likely reason,
-
-149
-00:08:07.529 --> 00:08:09.449
-engineers who supposedly know better,
-
-150
-00:08:09.449 --> 00:08:10.441
-like me,
-
-151
-00:08:10.441 --> 00:08:13.193
-draw stairsteps even though they're technically wrong.
-
-152
-00:08:13.193 --> 00:08:15.571
-It's a sort of like a one-dimensional version of
-
-153
-00:08:15.571 --> 00:08:17.395
-fat bits in an image editor.
-
-154
-00:08:17.395 --> 00:08:19.241
-Pixels aren't squares either,
-
-155
-00:08:19.241 --> 00:08:23.081
-they're samples of a 2-dimensional function space and so they're also,
-
-156
-00:08:23.081 --> 00:08:26.366
-conceptually, infinitely small points.
-
-157
-00:08:26.366 --> 00:08:28.500
-Practically, it's a real pain in the ass to see
-
-158
-00:08:28.500 --> 00:08:30.804
-or manipulate infinitely small anything.
-
-159
-00:08:30.804 --> 00:08:32.212
-So big squares it is.
-
-160
-00:08:32.212 --> 00:08:35.966
-Digital stairstep drawings are exactly the same thing.
-
-161
-00:08:35.966 --> 00:08:37.684
-It's just a convenient drawing.
-
-162
-00:08:37.684 --> 00:08:40.404
-The stairsteps aren't really there.
-
-163
-00:08:45.652 --> 00:08:48.233
-When we convert a digital signal back to analog,
-
-164
-00:08:48.233 --> 00:08:50.900
-the result is <u>also</u> smooth regardless of the bit depth.
-
-165
-00:08:50.900 --> 00:08:53.193
-24 bits or 16 bits...
-
-166
-00:08:53.193 --> 00:08:54.196
-or 8 bits...
-
-167
-00:08:54.196 --> 00:08:55.486
-it doesn't matter.
-
-168
-00:08:55.486 --> 00:08:57.534
-So does that mean that the digital bit depth
-
-169
-00:08:57.534 --> 00:08:58.953
-makes no difference at all?
-
-170
-00:08:59.245 --> 00:09:00.521
-Of course not.
-
-171
-00:09:02.121 --> 00:09:06.046
-Channel 2 here is the same sine wave input,
-
-172
-00:09:06.046 --> 00:09:09.086
-but we quantize with dither down to eight bits.
-
-173
-00:09:09.086 --> 00:09:14.174
-On the scope, we still see a nice
-smooth sine wave on channel 2.
-
-174
-00:09:14.174 --> 00:09:18.014
-Look very close, and you'll also see a
-bit more noise.
-
-175
-00:09:18.014 --> 00:09:19.305
-That's a clue.
-
-176
-00:09:19.305 --> 00:09:21.273
-If we look at the spectrum of the signal...
-
-177
-00:09:22.889 --> 00:09:23.732
-aha!
-
-178
-00:09:23.732 --> 00:09:26.398
-Our sine wave is still there unaffected,
-
-179
-00:09:26.398 --> 00:09:28.490
-but the noise level of the eight-bit signal
-
-180
-00:09:28.490 --> 00:09:32.470
-on the second channel is much higher!
-
-181
-00:09:32.948 --> 00:09:36.148
-And that's the difference the number of bits makes.
-
-182
-00:09:36.148 --> 00:09:37.434
-That's it!
-
-183
-00:09:37.822 --> 00:09:39.956
-When we digitize a signal, first we sample it.
-
-184
-00:09:39.956 --> 00:09:42.366
-The sampling step is perfect; it loses nothing.
-
-185
-00:09:42.366 --> 00:09:45.626
-But then we quantize it,
-and quantization adds noise.
-
-186
-00:09:47.827 --> 00:09:50.793
-The number of bits determines how much noise
-
-187
-00:09:50.793 --> 00:09:52.569
-and so the level of the
-noise floor.
-
-188
-00:10:00.170 --> 00:10:03.646
-What does this dithered quantization noise sound like?
-
-189
-00:10:03.646 --> 00:10:06.012
-Let's listen to our eight-bit sine wave.
-
-190
-00:10:12.521 --> 00:10:15.273
-That may have been hard to hear anything but the tone.
-
-191
-00:10:15.273 --> 00:10:18.740
-Let's listen to just the noise after we notch out the sine wave
-
-192
-00:10:18.740 --> 00:10:21.683
-and then bring the gain up a bit because the noise is quiet.
-
-193
-00:10:32.009 --> 00:10:35.049
-Those of you who have used analog recording equipment
-
-194
-00:10:35.049 --> 00:10:36.670
-may have just thought to yourselves,
-
-195
-00:10:36.670 --> 00:10:40.382
-"My goodness! That sounds like tape hiss!"
-
-196
-00:10:40.382 --> 00:10:41.929
-Well, it doesn't just sound like tape hiss,
-
-197
-00:10:41.929 --> 00:10:43.433
-it acts like it too,
-
-198
-00:10:43.433 --> 00:10:45.225
-and if we use a gaussian dither
-
-199
-00:10:45.225 --> 00:10:47.646
-then it's mathematically equivalent in every way.
-
-200
-00:10:47.646 --> 00:10:49.225
-It <u>is</u> tape hiss.
-
-201
-00:10:49.225 --> 00:10:51.774
-Intuitively, that means that we can measure tape hiss
-
-202
-00:10:51.774 --> 00:10:54.196
-and thus the noise floor of magnetic audio tape
-
-203
-00:10:54.196 --> 00:10:56.233
-in bits instead of decibels,
-
-204
-00:10:56.233 --> 00:10:59.902
-in order to put things in a digital perspective.
-
-205
-00:10:59.902 --> 00:11:03.028
-Compact cassettes...
-
-206
-00:11:03.028 --> 00:11:05.449
-for those of you who are old enough to remember them,
-
-207
-00:11:05.449 --> 00:11:09.161
-could reach as
-deep as nine bits in perfect conditions,
-
-208
-00:11:09.161 --> 00:11:11.209
-though five to six bits was more typical,
-
-209
-00:11:11.209 --> 00:11:13.876
-especially if it was a recording made on a tape deck.
-
-210
-00:11:13.876 --> 00:11:19.422
-That's right... your mix tapes were only about six bits
-deep... if you were lucky!
-
-211
-00:11:19.837 --> 00:11:22.345
-The very best professional open reel tape
-
-212
-00:11:22.345 --> 00:11:24.553
-used in studios could barely hit...
-
-213
-00:11:24.553 --> 00:11:26.473
-any guesses?...
-
-214
-00:11:26.473 --> 00:11:27.604
-13 bits
-
-215
-00:11:27.604 --> 00:11:28.980
-<u>with</u> advanced noise reduction.
-
-216
-00:11:28.980 --> 00:11:32.062
-And that's why seeing 'DDD' on a Compact Disc
-
-217
-00:11:32.062 --> 00:11:35.208
-used to be such a big, high-end deal.
-
-218
-00:11:40.116 --> 00:11:42.825
-I keep saying that I'm quantizing with dither,
-
-219
-00:11:42.825 --> 00:11:44.734
-so what is dither exactly?
-
-220
-00:11:44.734 --> 00:11:47.284
-More importantly, what does it do?
-
-221
-00:11:47.284 --> 00:11:49.876
-The simple way to quantize a signal is to choose
-
-222
-00:11:49.876 --> 00:11:52.329
-the digital amplitude value closest
-
-223
-00:11:52.329 --> 00:11:54.377
-to the original analog amplitude.
-
-224
-00:11:54.377 --> 00:11:55.337
-Obvious, right?
-
-225
-00:11:55.337 --> 00:11:57.545
-Unfortunately, the exact noise you get
-
-226
-00:11:57.545 --> 00:11:59.220
-from this simple quantization scheme
-
-227
-00:11:59.220 --> 00:12:02.174
-depends somewhat on the input signal,
-
-228
-00:12:02.174 --> 00:12:04.596
-so we may get noise that's inconsistent,
-
-229
-00:12:04.596 --> 00:12:06.142
-or causes distortion,
-
-230
-00:12:06.142 --> 00:12:09.054
-or is undesirable in some other way.
-
-231
-00:12:09.054 --> 00:12:11.764
-Dither is specially-constructed noise that
-
-232
-00:12:11.764 --> 00:12:15.273
-substitutes for the noise produced by simple quantization.
-
-233
-00:12:15.273 --> 00:12:18.025
-Dither doesn't drown out or mask quantization noise,
-
-234
-00:12:18.025 --> 00:12:20.190
-it actually replaces it
-
-235
-00:12:20.190 --> 00:12:22.612
-with noise characteristics of our choosing
-
-236
-00:12:22.612 --> 00:12:24.794
-that aren't influenced by the input.
-
-237
-00:12:25.256 --> 00:12:27.081
-Let's <u>watch</u> what dither does.
-
-238
-00:12:27.081 --> 00:12:30.078
-The signal generator has too much noise for this test
-
-239
-00:12:30.431 --> 00:12:33.161
-so we'll produce a mathematically
-
-240
-00:12:33.161 --> 00:12:34.782
-perfect sine wave with the ThinkPad
-
-241
-00:12:34.782 --> 00:12:38.205
-and quantize it to eight bits with dithering.
-
-242
-00:12:39.006 --> 00:12:41.342
-We see a nice sine wave on the waveform display
-
-243
-00:12:41.342 --> 00:12:43.452
-and output scope
-
-244
-00:12:44.222 --> 00:12:44.972
-and...
-
-245
-00:12:46.588 --> 00:12:49.375
-once the analog spectrum analyzer catches up...
-
-246
-00:12:50.713 --> 00:12:53.588
-a clean frequency peak with a uniform noise floor
-
-247
-00:12:56.864 --> 00:12:58.611
-on both spectral displays
-
-248
-00:12:58.611 --> 00:12:59.646
-just like before
-
-249
-00:12:59.646 --> 00:13:01.549
-Again, this is with dither.
-
-250
-00:13:02.196 --> 00:13:04.225
-Now I turn dithering off.
-
-251
-00:13:05.779 --> 00:13:07.913
-The quantization noise, that dither had spread out
-
-252
-00:13:07.913 --> 00:13:09.577
-into a nice, flat noise floor,
-
-253
-00:13:09.577 --> 00:13:12.286
-piles up into harmonic distortion peaks.
-
-254
-00:13:12.286 --> 00:13:16.030
-The noise floor is lower, but the level of distortion becomes nonzero,
-
-255
-00:13:16.030 --> 00:13:19.668
-and the distortion peaks sit higher than the dithering noise did.
-
-256
-00:13:19.668 --> 00:13:22.318
-At eight bits this effect is exaggerated.
-
-257
-00:13:22.488 --> 00:13:24.200
-At sixteen bits,
-
-258
-00:13:24.692 --> 00:13:25.929
-even without dither,
-
-259
-00:13:25.929 --> 00:13:28.308
-harmonic distortion is going to be so low
-
-260
-00:13:28.308 --> 00:13:30.708
-as to be completely inaudible.
-
-261
-00:13:30.708 --> 00:13:34.581
-Still, we can use dither to eliminate it completely
-
-262
-00:13:34.581 --> 00:13:36.489
-if we so choose.
-
-263
-00:13:37.642 --> 00:13:39.273
-Turning the dither off again for a moment,
-
-264
-00:13:40.934 --> 00:13:43.444
-you'll notice that the absolute level of distortion
-
-265
-00:13:43.444 --> 00:13:47.070
-from undithered quantization stays approximately constant
-
-266
-00:13:47.070 --> 00:13:49.033
-regardless of the input amplitude.
-
-267
-00:13:49.033 --> 00:13:51.998
-But when the signal level drops below a half a bit,
-
-268
-00:13:51.998 --> 00:13:54.036
-everything quantizes to zero.
-
-269
-00:13:54.036 --> 00:13:54.910
-In a sense,
-
-270
-00:13:54.910 --> 00:13:58.557
-everything quantizing to zero is just 100% distortion!
-
-271
-00:13:58.833 --> 00:14:01.588
-Dither eliminates this distortion too.
-
-272
-00:14:01.588 --> 00:14:03.599
-We reenable dither and...
-
-273
-00:14:03.599 --> 00:14:06.377
-there's our signal back at 1/4 bit,
-
-274
-00:14:06.377 --> 00:14:09.076
-with our nice flat noise floor.
-
-275
-00:14:09.630 --> 00:14:11.220
-The noise floor doesn't have to be flat.
-
-276
-00:14:11.220 --> 00:14:12.798
-Dither is noise of our choosing,
-
-277
-00:14:12.798 --> 00:14:15.006
-so let's choose a noise as inoffensive
-
-278
-00:14:15.006 --> 00:14:17.017
-and difficult to notice as possible.
-
-279
-00:14:18.142 --> 00:14:22.484
-Our hearing is most sensitive in the midrange from 2kHz to 4kHz,
-
-280
-00:14:22.484 --> 00:14:25.438
-so that's where background noise is going to be the most obvious.
-
-281
-00:14:25.438 --> 00:14:29.406
-We can shape dithering noise away from sensitive frequencies
-
-282
-00:14:29.406 --> 00:14:31.241
-to where hearing is less sensitive,
-
-283
-00:14:31.241 --> 00:14:33.910
-usually the highest frequencies.
-
-284
-00:14:34.249 --> 00:14:37.460
-16-bit dithering noise is normally much too quiet to hear at all,
-
-285
-00:14:37.460 --> 00:14:39.668
-but let's listen to our noise shaping example,
-
-286
-00:14:39.668 --> 00:14:42.234
-again with the gain brought way up...
-
-287
-00:14:56.020 --> 00:14:59.977
-Lastly, dithered quantization noise <u>is</u> higher power overall
-
-288
-00:14:59.977 --> 00:15:04.276
-than undithered quantization noise even when it sounds quieter.
-
-289
-00:15:04.276 --> 00:15:07.902
-You can see that on a VU meter during passages of near-silence.
-
-290
-00:15:07.902 --> 00:15:10.537
-But dither isn't only an on or off choice.
-
-291
-00:15:10.537 --> 00:15:14.712
-We can reduce the dither's power to balance less noise against
-
-292
-00:15:14.712 --> 00:15:18.313
-a bit of distortion to minimize the overall effect.
-
-293
-00:15:19.605 --> 00:15:22.790
-We'll also modulate the input signal like this:
-
-294
-00:15:27.098 --> 00:15:30.206
-...to show how a varying input affects the quantization noise.
-
-295
-00:15:30.206 --> 00:15:33.289
-At full dithering power, the noise is uniform, constant,
-
-296
-00:15:33.289 --> 00:15:35.643
-and featureless just like we expect:
-
-297
-00:15:40.937 --> 00:15:42.772
-As we reduce the dither's power,
-
-298
-00:15:42.772 --> 00:15:46.356
-the input increasingly affects the amplitude and the character
-
-299
-00:15:46.356 --> 00:15:47.977
-of the quantization noise:
-
-300
-00:16:09.883 --> 00:16:13.844
-Shaped dither behaves similarly,
-
-301
-00:16:13.844 --> 00:16:16.553
-but noise shaping lends one more nice advantage.
-
-302
-00:16:16.553 --> 00:16:18.804
-To make a long story short, it can use
-
-303
-00:16:18.804 --> 00:16:20.937
-a somewhat lower dither power before the input
-
-304
-00:16:20.937 --> 00:16:23.662
-has as much effect on the output.
-
-305
-00:16:49.172 --> 00:16:51.508
-Despite all the time I just spent on dither,
-
-306
-00:16:51.508 --> 00:16:53.012
-we're talking about differences
-
-307
-00:16:53.012 --> 00:16:56.372
-that start 100 decibels below full scale.
-
-308
-00:16:56.372 --> 00:16:59.806
-Maybe if the CD had been 14 bits as originally designed,
-
-309
-00:16:59.806 --> 00:17:01.513
-dither <u>might</u> be more important.
-
-310
-00:17:01.989 --> 00:17:02.644
-Maybe.
-
-311
-00:17:02.644 --> 00:17:05.438
-At 16 bits, really, it's mostly a wash.
-
-312
-00:17:05.438 --> 00:17:08.019
-You can think of dither as an insurance policy
-
-313
-00:17:08.019 --> 00:17:11.443
-that gives several extra decibels of dynamic range
-
-314
-00:17:11.443 --> 00:17:12.804
-just in case.
-
-315
-00:17:12.990 --> 00:17:14.196
-The simple fact is, though,
-
-316
-00:17:14.196 --> 00:17:16.361
-no one ever ruined a great recording
-
-317
-00:17:16.361 --> 00:17:19.182
-by not dithering the final master.
-
-318
-00:17:24.414 --> 00:17:25.790
-We've been using sine waves.
-
-319
-00:17:25.790 --> 00:17:28.254
-They're the obvious choice when what we want to see
-
-320
-00:17:28.254 --> 00:17:32.212
-is a system's behavior at a given isolated frequency.
-
-321
-00:17:32.212 --> 00:17:34.217
-Now let's look at something a bit more complex.
-
-322
-00:17:34.217 --> 00:17:35.923
-What should we expect to happen
-
-323
-00:17:35.923 --> 00:17:39.671
-when I change the input to a square wave...
-
-324
-00:17:42.718 --> 00:17:45.921
-The input scope confirms our 1kHz square wave.
-
-325
-00:17:45.921 --> 00:17:47.351
-The output scope shows..
-
-326
-00:17:48.614 --> 00:17:51.102
-Exactly what it should.
-
-327
-00:17:51.102 --> 00:17:53.900
-What is a square wave really?
-
-328
-00:17:54.654 --> 00:17:57.982
-Well, we can say it's a waveform that's some positive value
-
-329
-00:17:57.982 --> 00:18:00.788
-for half a cycle and then transitions instantaneously
-
-330
-00:18:00.788 --> 00:18:02.910
-to a negative value for the other half.
-
-331
-00:18:02.910 --> 00:18:05.076
-But that doesn't really tell us anything useful
-
-332
-00:18:05.076 --> 00:18:07.241
-about how this input
-
-333
-00:18:07.241 --> 00:18:09.378
-becomes this output.
-
-334
-00:18:10.132 --> 00:18:12.713
-Then we remember that any waveform
-
-335
-00:18:12.713 --> 00:18:15.508
-is also the sum of discrete frequencies,
-
-336
-00:18:15.508 --> 00:18:18.302
-and a square wave is a particularly simple sum
-
-337
-00:18:18.302 --> 00:18:19.636
-a fundamental and
-
-338
-00:18:19.636 --> 00:18:22.228
-an infinite series of odd harmonics.
-
-339
-00:18:22.228 --> 00:18:24.597
-Sum them all up, you get a square wave.
-
-340
-00:18:26.398 --> 00:18:27.433
-At first glance,
-
-341
-00:18:27.433 --> 00:18:29.225
-that doesn't seem very useful either.
-
-342
-00:18:29.225 --> 00:18:31.561
-You have to sum up an infinite number of harmonics
-
-343
-00:18:31.561 --> 00:18:33.108
-to get the answer.
-
-344
-00:18:33.108 --> 00:18:35.977
-Ah, but we don't have an infinite number of harmonics.
-
-345
-00:18:36.960 --> 00:18:39.902
-We're using a quite sharp anti-aliasing filter
-
-346
-00:18:39.902 --> 00:18:42.206
-that cuts off right above 20kHz,
-
-347
-00:18:42.206 --> 00:18:44.158
-so our signal is band-limited,
-
-348
-00:18:44.158 --> 00:18:46.421
-which means we get this:
-
-349
-00:18:52.500 --> 00:18:56.468
-..and that's exactly what we see on the output scope.
-
-350
-00:18:56.468 --> 00:18:59.550
-The rippling you see around sharp edges in a bandlimited signal
-
-351
-00:18:59.550 --> 00:19:00.926
-is called the Gibbs effect.
-
-352
-00:19:00.926 --> 00:19:04.137
-It happens whenever you slice off part of the frequency domain
-
-353
-00:19:04.137 --> 00:19:07.006
-in the middle of nonzero energy.
-
-354
-00:19:07.006 --> 00:19:09.854
-The usual rule of thumb you'll hear is the sharper the cutoff,
-
-355
-00:19:09.854 --> 00:19:11.188
-the stronger the rippling,
-
-356
-00:19:11.188 --> 00:19:12.777
-which is approximately true,
-
-357
-00:19:12.777 --> 00:19:14.900
-but we have to be careful how we think about it.
-
-358
-00:19:14.900 --> 00:19:15.774
-For example...
-
-359
-00:19:15.774 --> 00:19:19.529
-what would you expect our quite sharp anti-aliasing filter
-
-360
-00:19:19.529 --> 00:19:23.181
-to do if I run our signal through it a second time?
-
-361
-00:19:34.136 --> 00:19:37.588
-Aside from adding a few fractional cycles of delay,
-
-362
-00:19:37.588 --> 00:19:39.348
-the answer is...
-
-363
-00:19:39.348 --> 00:19:40.857
-nothing at all.
-
-364
-00:19:41.257 --> 00:19:43.302
-The signal is already bandlimited.
-
-365
-00:19:43.656 --> 00:19:46.590
-Bandlimiting it again doesn't do anything.
-
-366
-00:19:46.590 --> 00:19:50.686
-A second pass can't remove frequencies that we already removed.
-
-367
-00:19:52.070 --> 00:19:53.737
-And that's important.
-
-368
-00:19:53.737 --> 00:19:56.233
-People tend to think of the ripples as a kind of artifact
-
-369
-00:19:56.233 --> 00:19:59.945
-that's added by anti-aliasing and anti-imaging filters,
-
-370
-00:19:59.945 --> 00:20:01.737
-implying that the ripples get worse
-
-371
-00:20:01.737 --> 00:20:03.913
-each time the signal passes through.
-
-372
-00:20:03.913 --> 00:20:05.950
-We can see that in this case that didn't happen.
-
-373
-00:20:05.950 --> 00:20:09.492
-So was it really the filter that added the ripples the first time through?
-
-374
-00:20:09.492 --> 00:20:10.537
-No, not really.
-
-375
-00:20:10.537 --> 00:20:12.126
-It's a subtle distinction,
-
-376
-00:20:12.126 --> 00:20:15.252
-but Gibbs effect ripples aren't added by filters,
-
-377
-00:20:15.252 --> 00:20:18.836
-they're just part of what a bandlimited signal <u>is</u>.
-
-378
-00:20:18.836 --> 00:20:20.798
-Even if we synthetically construct
-
-379
-00:20:20.798 --> 00:20:23.508
-what looks like a perfect digital square wave,
-
-380
-00:20:23.508 --> 00:20:26.206
-it's still limited to the channel bandwidth.
-
-381
-00:20:26.206 --> 00:20:29.140
-Remember the stairstep representation is misleading.
-
-382
-00:20:29.140 --> 00:20:32.222
-What we really have here are instantaneous sample points,
-
-383
-00:20:32.222 --> 00:20:36.148
-and only one bandlimited signal fits those points.
-
-384
-00:20:36.148 --> 00:20:39.614
-All we did when we drew our apparently perfect square wave
-
-385
-00:20:39.614 --> 00:20:43.198
-was line up the sample points just right so it appeared
-
-386
-00:20:43.198 --> 00:20:47.785
-that there were no ripples if we played connect-the-dots.
-
-387
-00:20:47.785 --> 00:20:49.449
-But the original bandlimited signal,
-
-388
-00:20:49.449 --> 00:20:52.742
-complete with ripples, was still there.
-
-389
-00:20:54.004 --> 00:20:56.542
-And that leads us to one more important point.
-
-390
-00:20:56.542 --> 00:20:59.550
-You've probably heard that the timing precision of a digital signal
-
-391
-00:20:59.550 --> 00:21:02.409
-is limited by its sample rate; put another way,
-
-392
-00:21:02.409 --> 00:21:05.140
-that digital signals can't represent anything
-
-393
-00:21:05.140 --> 00:21:08.041
-that falls between the samples...
-
-394
-00:21:08.041 --> 00:21:11.422
-implying that impulses or fast attacks have to align
-
-395
-00:21:11.422 --> 00:21:14.473
-exactly with a sample, or the timing gets mangled...
-
-396
-00:21:14.473 --> 00:21:16.219
-or they just disappear.
-
-397
-00:21:16.711 --> 00:21:20.820
-At this point, we can easily see why that's wrong.
-
-398
-00:21:20.820 --> 00:21:23.742
-Again, our input signals are bandlimited.
-
-399
-00:21:23.742 --> 00:21:26.036
-And digital signals are samples,
-
-400
-00:21:26.036 --> 00:21:29.340
-not stairsteps, not 'connect-the-dots'.
-
-401
-00:21:31.572 --> 00:21:34.592
-We most certainly can, for example,
-
-402
-00:21:36.777 --> 00:21:39.337
-put the rising edge of our bandlimited square wave
-
-403
-00:21:39.337 --> 00:21:42.004
-anywhere we want between samples.
-
-404
-00:21:42.004 --> 00:21:44.354
-It's represented perfectly
-
-405
-00:21:47.508 --> 00:21:50.218
-and it's reconstructed perfectly.
-
-406
-00:22:04.620 --> 00:22:06.526
-Just like in the previous episode,
-
-407
-00:22:06.526 --> 00:22:08.393
-we've covered a broad range of topics,
-
-408
-00:22:08.393 --> 00:22:10.868
-and yet barely scratched the surface of each one.
-
-409
-00:22:10.868 --> 00:22:13.620
-If anything, my sins of omission are greater this time around...
-
-410
-00:22:13.620 --> 00:22:16.286
-but this is a good stopping point.
-
-411
-00:22:16.286 --> 00:22:17.833
-Or maybe, a good starting point.
-
-412
-00:22:17.833 --> 00:22:18.708
-Dig deeper.
-
-413
-00:22:18.708 --> 00:22:19.710
-Experiment.
-
-414
-00:22:19.710 --> 00:22:21.374
-I chose my demos very carefully
-
-415
-00:22:21.374 --> 00:22:23.668
-to be simple and give clear results.
-
-416
-00:22:23.668 --> 00:22:26.217
-You can reproduce every one of them on your own if you like.
-
-417
-00:22:26.217 --> 00:22:28.766
-But let's face it, sometimes we learn the most
-
-418
-00:22:28.766 --> 00:22:30.516
-about a spiffy toy by breaking it open
-
-419
-00:22:30.516 --> 00:22:32.553
-and studying all the pieces that fall out.
-
-420
-00:22:32.553 --> 00:22:35.230
-That's OK, we're engineers.
-
-421
-00:22:35.230 --> 00:22:36.350
-Play with the demo parameters,
-
-422
-00:22:36.350 --> 00:22:37.972
-hack up the code,
-
-423
-00:22:37.972 --> 00:22:39.774
-set up alternate experiments.
-
-424
-00:22:39.774 --> 00:22:40.692
-The source code for everything,
-
-425
-00:22:40.692 --> 00:22:42.398
-including the little pushbutton demo application,
-
-426
-00:22:42.398 --> 00:22:44.361
-is up at Xiph.Org.
-
-427
-00:22:44.361 --> 00:22:45.940
-In the course of experimentation,
-
-428
-00:22:45.940 --> 00:22:47.401
-you're likely to run into something
-
-429
-00:22:47.401 --> 00:22:49.950
-that you didn't expect and can't explain.
-
-430
-00:22:49.950 --> 00:22:51.198
-Don't worry!
-
-431
-00:22:51.198 --> 00:22:54.537
-My earlier snark aside, Wikipedia is fantastic for
-
-432
-00:22:54.537 --> 00:22:56.788
-exactly this kind of casual research.
-
-433
-00:22:56.788 --> 00:22:59.956
-If you're really serious about understanding signals,
-
-434
-00:22:59.956 --> 00:23:03.337
-several universities have advanced materials online,
-
-435
-00:23:03.337 --> 00:23:07.380
-such as the 6.003 and 6.007 Signals and Systems modules
-
-436
-00:23:07.380 --> 00:23:08.798
-at MIT OpenCourseWare.
-
-437
-00:23:08.798 --> 00:23:11.593
-And of course, there's always the community here at Xiph.Org.
-
-438
-00:23:12.792 --> 00:23:13.929
-Digging deeper or not,
-
-439
-00:23:13.929 --> 00:23:14.974
-I am out of coffee,
-
-440
-00:23:14.974 --> 00:23:16.436
-so, until next time,
-
-441
-00:23:16.436 --> 00:23:19.316
-happy hacking!

Modified: websites/xiph.org/video/vid2.shtml
===================================================================
--- websites/xiph.org/video/vid2.shtml	2013-02-26 00:18:29 UTC (rev 18831)
+++ websites/xiph.org/video/vid2.shtml	2013-02-26 00:45:00 UTC (rev 18832)
@@ -95,7 +95,7 @@
 	<select class="srt-select">
 	  <option>
 	    Subtitles: Off</option>
-	  <option file="vid2-en.vtt">
+	  <option file="02-Digital_Show_and_Tell.en.vtt">
 	    Subtitles: US English</option>
 	</select>