For those who may be upset by the lack of purity of 'ignoring' beautiful mathematics by ignoring fft values that correspond to values above the Nyquist cut-off frequency, there is a physical phenomena that it may be able to construe as linked to interpreting these values. The phenomena is called aliasing. I am not suggesting it can be an interpretation. Aliasing is akin to a disease in DSP (digital signal processing), to be avoided at all costs.
For the record, for a real FFT, for point N/2 + 1 to point N - 1, The real part of point N/2 + j is the same as the real part of point N/2
- j
The imaginary part of point N/2 + j is the same as the negative of the imaginary part of point N/2 - j
In fact if you want to obtain the real inverse fft to reconstitute signal values and values of the fft above N/2 have been ignored then it is necessary to reinsert them.
John Heenan
-----Original Message----- From: John Heenan [mailto:john@auscyber.com] Sent: Friday, 25 January 2002 4:44 AM To: pd-list@iem.kug.ac.at Subject: RE: [PD] fftchannels
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.