I find the documentation in PD terse and so confusing. Normally I go the source code if I want to understand what is going on. In this case it is probably not much of a help as FFT is an infamous area in itself. In PD the FFT routines are written by Kevin Peterson, MIT Media Lab, EMS. In themselves they are terse and not exposed in a convenient object oriented style.
There are N array elements (or parts) to an FFT result from N samples. The FFT results are complex numbers (i.e. values with real and/or imaginary parts).
This above is purely a mathematical operation. Interpreting the results in the context of samples that represent audio is not mathematics. The complex results can be transformed into another array of pairs of numbers that can be said to represent 'magnitude' and 'phase'. To fully reconstitute the original samples with a inverse fft it is necessary to use the original FFT complex array.
For human auditory perception phase has little consequence.
In DSP (Digital Signal Processing) it is normal to indicate each element i up to the first N/2 elements of a FFT array result can be used to represent the magnitude of a frequency or a frequency bin (range of frequencies). The particular frequency or end point of a frequency bin is given by the equation sample rate * i / N The equation I gave in my previous posting was incorrect.
The actual magnitude of the frequency or bin is scaled or normalised.
For i = N/2 the frequency represented is the Nyquist frequency (half the sampling rate), since sample rate * (N/2) / N = sample rate / 2. N for FFT must be a power of two and so is always an even number.
PD allows you to plot the real and/or imaginary outlets of the rfft~ object.
I have read the full text of the help patch. It is implied there are N/2
- 1 parts of a real FFT that have values and there are other parts with
value 0. Of the N/2 + 1 parts with values it is stated two parts have no imaginary component. It is stated these are the DC and Nyquist parts.
This is just information. It is not the job of PD to explain or interpret this.
The statement in PD is technically true. There are values produced for i
N/2, however they are said in DSP literature to correspond to
'negative frequencies' and are generally ignored (using mathematics to over interpret physical phenomena causes endless philosophical horrors). At any rate these values don't have to be interpreted if the Nyquist sampling rule is applied. How convenient.
John Heenan
-----Original Message----- From: marius schebella [mailto:marius.schebella@chello.at] Sent: Thursday, 24 January 2002 10:00 PM To: pd-list@iem.kug.ac.at Subject: Re: [PD] fftchannels
Messageagain
----- Original Message ----- From: John Heenan To: pd-list@iem.kug.ac.at Sent: Thursday, January 24, 2002 11:33 AM Subject: RE: [PD] fftchannels
The size of an array result of a FFT is the same size as the number of
samples. So if there are N samples a real domain FFT on > these samples is held in an array of size N.
John Heenan
in the help-patch of the rfft- i also read "the rfft outputs N/2 + 1 real parts". so the first value represents the DC and the last (N/2+1) should represent the nyquist... the imag-parts for both are always 0. (that´s the N/2-1).
marius.