FFT Questions.....

In article 9494fac.0401101259.3e904678@posting.google.com, Todd at
muirt@purdue.edu wrote on 01/10/2004 15:59:

> Actually, the one instrument would be sampled by itself, not in chorus
> with other instruments. Im not looking to identify the instruments out
> of a mixed recording. What Im looking for is the complete harmonic
> structure of an instrument. Then eventually, I want to study the
> harmonic content as it relates to forming the aural tone of different
> unique instruments.  But what is crucial is capturing amplitude,
> phase, and frequency of all harmonics that could possibly effect the
> sound.

Todd, if you want to analyze musical notes (that are quasi-periodic)
consider using the wavetable synthesis model (described in Wavetable
Synthesis 101 on the harmony-central.com web site), and DFTing each
wavetable.  that will give you amplitude and phase of each harmonic and
computing the time derivative of the phase gives you the frequency deviation
of each harmonic from its integer value.

r b-j

Well, for as far as i understand the FFT:
if you have a sample rate of 10kHz and 256 sample points(N) in time you will
have a frequency spectrum for 0 to 5kHz (Nyquist frequency),
from this fft you can use 129 points of the real part: (0..128 -> N/2+1)

So this will give you the frequencies 0, (5000/128)*1, (5000/128)*2,
(5000/128)*128

So if you want to "see" every frequency you'll have to fft at
22050Hz*2=>44100Hz per audio-band (eg: left audiochannel)

Anyway, good luck implementing  i hope i didn't write any mistakes here!

Kind regards,
  Vincent
> > Todd wrote:
> > > I have had some experience with the DFT, and realize that the fft
> > > produces the same results, only faster.  I understand the whole
> > > concept of resolution, that if 128 samples are taken at 10kHz, there
> > > are only 128 possible frequencies (all equally spaced from 0 to 10k)
> > > that can be absolutely determined. Is there an algorithm that performs
> > > a second fft of the same original signal, but over only the frequency
> > > bands that the current transforms resolution can't determine?
> > >
> > > Can you perform an fft over a range of freqencies not including 0Hz?
> >
> > Well, as Fred wrote, if your input is real only (no imaginary parts) you
> > can take a 256 point real FFT for double the resolution.