PCHIRP Periodic chirp
Usage: g=pchirp(L,n);
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:
g(l+1) = exp(pi*i*n*(l-ceil(L/2))^2*(L+1)/L) for l=0,...,L-1
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 c^n. The Quarterly Journal of
Mathematics, 59(1):15--28, 2008.
Url: http://ltfat.github.io/doc/fourier/pchirp.html
See also: dft, expwave.
Package: ltfat