Matlab listing: tmps.m

Below is the test script (for ease of copy/paste extraction for online viewers). Following is the test script along with its output.

Note that this is a toy example intended only for checking the code on a simple example, and to illustrate how a spectrum gets passed in. In particular, the would-be minimum-phase impulse response computed by this example is clearly not even causal (thus indicating an insufficient spectral sampling density [FFT length]). Moreover, the starting spectrum (a sampled ideal lowpass-filter frequency response) has zeros on the unit circle, so there is no sampling density that is truly sufficient in the frequency domain (no sufficiently long FFT in the time domain).

spec = [1 1 1 0 0 0 1 1]'; % Lowpass cutting off at fs*3/8
format short;
mps(spec)
abs(mps(spec))
ifft(spec)
ifft(mps(spec))

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

Note that this is a toy example intended only for checking the code on a simple example, and to illustrate how a spectrum gets passed in. In particular, the would-be minimum-phase impulse response computed by this example is clearly not even causal (thus indicating an insufficient spectral sampling density [FFT length]).