[vorbis-dev] More mdct questions

[Marshall Eubanks]

"Dave, Anish" wrote:

> > "Dave, Anish" wrote:
> > >
> > > Hey thanks for your help!  Your equation works.  It's the
> > same as the one
> >
> > Which one? I guess the +2N one.
>
> Yup, the +2N one.
>
> >
> > > given in the eusipco.corrected.ps document minus the 4/n
> > term outside the
> > > summation.  So was that (4/n) term the typo in the document?
> >
> > It's not a typo. The 4/N is necessary to make the backward
> > transform a true
> > inverse to the forward transform; otherwise, it will have a
> > N/4 scaling. But
> > scaling is not a problem for our purposes, so it's omitted
> > (or maybe it is
> > fused with the window multiply; don't know it off my head,
> > and much too lazy
> > to look it up).
>
> Hm.  I'll try to prove to myself that it really *is* the inverse.

There is no standard for normalization of fourier transforms.
I myself prefer 2/sqrt(n) on both the transform and its inverse, so that these
are the same (except for signs). An FFT is 1/n, spread between the
transform and its inverse. Confusingly, some also throw in 2 PI's
in the normalization. If you actually care about units in the transform
domain, this is a real pain. For these purposes, it doesn't matter.


--
                                 Regards
                                 Marshall Eubanks

T.M. Eubanks
Multicast Technologies, Inc
10301 Democracy Lane, Suite 410
Fairfax, Virginia 22030
Phone : 703-293-9624
Fax     : 703-293-9609
e-mail : tme at on-the-i.com     tme at multicasttech.com

http://www.on-the-i.com http://www.buzzwaves.com

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