Understanding the Fourier Transform for Sound Resynthesis

[max_planck735]

I want to take an audio recording of a sound, perform a Fourier Transform on this sound, and then use the amplitude/frequency/phase information provided by this transform to set the amplitude/frequency/phase of an set of sine wave oscillators, in order to resynthesize the sound.

I need to know the relative amplitudes of the sinusoidal components of the sound in order to set the relative amplitudes of my set of sine wave oscillators properly.

Will the raw output of the FFT provide the relative amplitude information that I'm looking for, if I plot the real number parts against an appropriate frequency axis and read the relative amplitudes of the peaks from this spectrum? If not, should I be plotting the absolute value of the FFT's output in order to obtain the relative amplitude information that I'm looking for? If not either of these, then can anyone suggest what would work?

Thanks, any help is very much appreciated

 

[rbj]

Will the raw output of the FFT provide the relative amplitude information that I'm looking for, if I plot the real number parts against an appropriate frequency axis and read the relative amplitudes of the peaks from this spectrum? If not, should I be plotting the absolute value of the FFT's output in order to obtain the relative amplitude information that I'm looking for? If not either of these, then can anyone suggest what would work?

this is good question to take to the comp.dsp USENET group and/or the music-dsp mailing list (you can go to http://shoko.calarts.edu/~glmrboy/musicdsp/music-dsp.html to subscribe).

because of windowing effects and smearing of frequency components, the FFT bins will have something to do with the amplitude of the sinusoidal components but it won't be exact. if you assume that the spectral smearing of any frequency component has only neglegibly leaked into the bins of all other frequency components, then the answer would be "yes, you can read the relative amplitudes (and frequency and phase) of the sinusoidal components from the peaks in the spectrum."

 

[max_planck735]

Thanks a lot for the info, especially about the Usenet group/mailing list, that will be very helpful for me. Thanks! =)

 

[rbj]

Thanks a lot for the info, especially about the Usenet group/mailing list, that will be very helpful for me. Thanks! =)

yer welcome. you might recognize me there at comp.dsp or (less often) at the music-dsp mailing list. i sometimes get in fights about the periodic or circular nature of the Discrete Fourier Transform (and where, in the signal path, any windowing happens to that gets applied to the DFT) - I'm in that fight right now. other tiffs had to do with the nature of the dirac delta "function" and the necessary scaling in the Nyquist/Shannon sampling and reconstruction theorem.

oh, and another big fight i once was in on comp.dsp and comp.soft-sys.matlab was about the horrible, awful, fixed-forever-and-can-never-change-it, indexing base in MATLAB. all array indices must start at "1" which makes things very ugly in the DSP world.i try to tread more lightly here, since i am not a physicist.