This is where navigation should be.

PCHIRP - Periodic chirp

Usage

g=pchirp(L,n);

Description

pchirp(L,n) returns a periodic, discrete chirp of length L that revolves n times around the time-frequency plane in frequency. n must be an integer number.

To get a chirp that revolves around the time-frequency plane in time, use

dft(pchirp(L,N));

The chirp is computed by:

\begin{equation*} g\left(l+1\right)=e^{\pi in(l-\lceil L/2\rceil)^{2}(L+1)/L},\quad l=0,\ldots,L-1 \end{equation*}

The chirp has absolute value 1 everywhere. To get a chirp with unit \(l^2\)-norm, divide the chirp by \(\sqrt L\).

Examples:

A spectrogram on a linear scale of an even length chirp:

sgram(pchirp(40,2),'lin');

The DFT of the same chirp, now revolving around in time:

sgram(dft(pchirp(40,2)),'lin');

An odd-length chirp. Notice that the chirp starts at a frequency between two sampling points:

sgram(pchirp(41,2),'lin');

References:

H. G. Feichtinger, M. Hazewinkel, N. Kaiblinger, E. Matusiak, and M. Neuhauser. Metaplectic operators on cn. The Quarterly Journal of Mathematics, 59(1):15--28, 2008.