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From: cpenrose@sdcc13.ucsd.edu (Christopher Penrose)
Newsgroups: comp.music,comp.dsp
Subject: Re: Want algorithm to generate 1/f time series
Summary: more advice
Keywords: phase
Message-ID: <16568@sdcc6.ucsd.edu>
Date: 11 Feb 91 20:01:27 GMT
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In article <40714@genrad.UUCP> ikw@genrad.UUCP (Isaac K. Wong) writes:
>
>1. create a magnitude spectrum of the desired spectral profile.
>2. assign random phase (use a random number generator) to each bin to
>	get complex symmetric spectrum. 
>3. inverse FFT to get pseudo-random time series.
>
>* you can also get true-random (Gaussian) time series by windowing and
>  shuffling the pseuddo-random series.
>* If you know the phase response of all major components in the output
>  signal path, you can also control the peak factor (peak/rms) better.

To avoid obtaining a white spectrum, randomize the phase of each bin for
the first FFT window.  Make sure that you maintain these phases throughout
the signal's synthesis if you choose a multiple FFT window synthesis 
technique.  Instead of assigning random phases, you can offset the phases of
neighboring bins with a real constant that is an irrational factor of 2*pi.
I have done this to synthesize frequency clusters with a minimal amount of
phase cancellation.  There will be noticeable spectral differences between
the signals generated with these two different phase handling techniques.

Christopher Penrose
jesus!penrose@esosun.css.gov
cpenrose@ucsd.edu