[Fluxus] More FFT

[Kassen]

Dear list,

I've been thinking about the below section of audioCollector.cpp;

// seem to only have stuff in the lower half - something to do with nyquist?
float UsefulArea = m_BufferLength/2;

for (unsigned int n=0; n<m_NumBars; n++)
{
float Value = 0;

float f = n/(float)m_NumBars;
float t = (n+1)/(float)m_NumBars;
f*=f;
t*=t;
unsigned from = f*UsefulArea;
unsigned to = t*UsefulArea;

for (unsigned int i=from; i<=to; i++)
{
if (i<m_BufferLength)
{
Value += m_FFTBuffer[i];
}
}

if (Value<0) Value=-Value;
Value*=m_Gain;
m_FFTOutput[n]=((m_FFTOutput[n]*m_SmoothingBias)+Value*(1-m_SmoothingBias));
}

return m_FFTOutput;

This section maps the FFT bins to the "bars" that correspond to the
different "gh" bands in Fluxus. The squaring that I highlighted seems to be
a attempt to compensate for how the output of the FFT transform is linear;
the whole of the second half of UsefulArea will refer to the top-most octave
of our bandwith (likely from 11.25 to 22.5KHz, or from "quite high" to
"beyond the hearing"). Without such compensation 8 of the default 16 gh
bands would cover that octave, 4 would cover the next down, etc.

The issue is that squaring the numbers doesn't go far enough; the curve is
logarithmic. Another issue is that the kind of curve we'd ideally get isn't
the same for all numbers of bands; at 10 bands it's easy as we can map each
to one of the octaves (give or take) between 20 and 20K Hz. On the other
hand; when we get 512 bins, due to a FFT frame of 1024 samples then setting
the requested number of bands to 512 should create a linear mapping of one
band per FFT bin. Ideally the curve would crossfade between logarithmic and
linear as the number of bands increases from a relatively low number to
approaching the number of bins (having more bands than bins doesn't make
much sense to me).

I'm not sure what kind of variable curve those concerns imply in practice,
but I do think that currently too many (5 according to my calculations)  of
the 16 bands that we have by default are concerned with the top-most octave
of our hearing. The highlighted lines are better than nothing under all
realistic conditions that I can quickly think of, but I'd like to try coming
up with a better plan.

Yours,
Kas.
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