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void inverse_mdct_slow(float *buffer, int n)
{
=A0=A0 int i,j;
=A0=A0 int n2 =3D n >> 1;
=A0=A0 float *x =3D (float *) malloc(sizeof(*x) * n2);
=A0=A0 memcpy(x, buffer, sizeof(*x) * n2);
=A0=A0 for (i=3D0; i < n; ++i) {
=A0=A0=A0=A0=A0 float acc =3D 0;
=A0=A0=A0=A0=A0 for (j=3D0; j < n2; ++j)
=A0=A0=A0=A0=A0=A0=A0=A0 // formula from paper:
=A0=A0=A0=A0=A0=A0=A0=A0 //acc +=3D n/4.0f * x[j] * (float) cos(M_PI / 2 / =
n * (2 * i + 1 + n/2.0)*(2*j+1));
=A0=A0=A0=A0=A0=A0=A0=A0 // formula from wikipedia
=A0=A0=A0=A0=A0=A0=A0=A0 //acc +=3D 2.0f / n2 * x[j] * (float) cos(M_PI/n2 =
* (i + 0.5 + n2/2)*(j + 0.5));
=A0=A0=A0=A0=A0=A0=A0=A0 // these are equivalent, except the formula from t=
he paper inverts the multiplier!
=A0=A0=A0=A0=A0=A0=A0=A0 // however, what actually works is NO MULTIPLIER!?=
!
=A0=A0=A0=A0=A0=A0=A0=A0 //acc +=3D 64 * 2.0f / n2 * x[j] * (float) cos(M_P=
I/n2 * (i + 0.5 + n2/2)*(j + 0.5));
=A0=A0=A0=A0=A0=A0=A0=A0 acc +=3D x[j] * (float) cos(M_PI / 2 / n * (2 * i =
+ 1 + n/2.0)*(2*j+1));
=A0=A0=A0=A0=A0 buffer[i] =3D acc;
=A0=A0 }
=A0=A0 free(x);
}

Thanks
Liam Wilson
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<table cellspacing=3D"0" cellpadding=3D"0" border=3D"0" ><tr><td valign=3D"=
top" style=3D"font: inherit;">Hi<br><br>The inverse MDCT formula seems to b=
e missing from the vorbis specification. From reading the source code of st=
b_vorbis (http://nothings.org/stb_vorbis/) I've a good idea of what it migh=
t be, but cannot find the formula anywhere in the official specification (t=
he one on http://xiph.org/vorbis/doc/Vorbis_I_spec.html ). I also understan=
d that the formula stated in the eusipco_corrected.ps paper is incorrect (t=
he link from the specification to the paper is also dead).<br><br>From the =
stb_vorbis.c source:<br><br>void inverse_mdct_slow(float *buffer, int n)<br=
>{<br>&nbsp;&nbsp; int i,j;<br>&nbsp;&nbsp; int n2 =3D n &gt;&gt; 1;<br>&nb=
sp;&nbsp; float *x =3D (float *) malloc(sizeof(*x) * n2);<br>&nbsp;&nbsp; m=
emcpy(x, buffer, sizeof(*x) * n2);<br>&nbsp;&nbsp; for (i=3D0; i &lt; n; ++=
i) {<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; float acc =3D
 0;<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; for (j=3D0; j &lt; n2; ++j)<br>&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // formula from paper:<br>&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; //acc +=3D n/4.0f * x[j] * (floa=
t) cos(M_PI / 2 / n * (2 * i + 1 + n/2.0)*(2*j+1));<br>&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp; // formula from wikipedia<br>&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; //acc +=3D 2.0f / n2 * x[j] * (float) cos(M=
_PI/n2 * (i + 0.5 + n2/2)*(j + 0.5));<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp; // these are equivalent, except the formula from the paper i=
nverts the multiplier!<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =
// however, what actually works is NO MULTIPLIER!?!<br>&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp; //acc +=3D 64 * 2.0f / n2 * x[j] * (float) cos=
(M_PI/n2 * (i + 0.5 + n2/2)*(j + 0.5));<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp; acc +=3D x[j] * (float) cos(M_PI / 2 / n * (2 * i + 1 +
 n/2.0)*(2*j+1));<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; buffer[i] =3D acc;<br>&=
nbsp;&nbsp; }<br>&nbsp;&nbsp; free(x);<br>}<br><br>Thanks<br>Liam Wilson<sp=
an style=3D"text-decoration: underline;"></span><a href=3D"http://www.iocon=
.com/resource/docs/ps/eusipco_corrected.ps" class=3D"url"><span class=3D"cm=
tt-12"></span></a></td></tr></table>
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