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SHAH - Discrete Shah-distribution

Usage

f=shah(L,a);

Description

shah(L,a) computes the discrete, normalized Shah-distribution of length L with a distance of a between the spikes.

The Shah distribution is defined by

\begin{equation*} f(n\cdot a+1)=\frac{1}{\sqrt(L/a)} \end{equation*}

for integer n, otherwise f is zero.

This is also known as an impulse train or as the comb function, because the shape of the function resembles a comb. It is the sum of unit impulses ('diracs') with the distance a.

If a divides L, then the dft of shah(L,a) is shah(L,L/a).

The Shah function has an extremely bad time-frequency localization. It does not generate a Gabor frame for any L and a.

Examples:

A simple spectrogram of the Shah function (includes the negative frequencies to display the whole TF-plane):

sgram(shah(256,16),'dynrange',80,'nf')