HERMBASIS Orthonormal basis of discrete Hermite functions
Usage: V=hermbasis(L,p);
V=hermbasis(L);
[V,D]=hermbasis(...);
HERMBASIS(L,p) computes an orthonormal basis of discrete Hermite
functions of length L. The vectors are returned as columns in the
output. p is the order of approximation used to construct the
position and difference operator.
All the vectors in the output are eigenvectors of the discrete Fourier
transform, and resemble samplings of the continuous Hermite functions
to some degree (for low orders).
[V,D]=HERMBASIS(...) also returns the eigenvalues D of the Discrete
Fourier Transform corresponding to the Hermite functions.
Examples:
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The following plot shows the spectrograms of 4 Hermite functions of
length 200 with order 1, 10, 100, and 190:
H=hermbasis(200);
subplot(2,2,1);
sgram(H(:,1),'nf','tc','lin','nocolorbar'); axis('square');
subplot(2,2,2);
sgram(H(:,10),'nf','tc','lin','nocolorbar'); axis('square');
subplot(2,2,3);
sgram(H(:,100),'nf','tc','lin','nocolorbar'); axis('square');
subplot(2,2,4);
sgram(H(:,190),'nf','tc','lin','nocolorbar'); axis('square');
References:
A. Bultheel and S. Martinez. Computation of the Fractional Fourier
Transform. Appl. Comput. Harmon. Anal., 16(3):182--202, 2004.
H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay. The Fractional Fourier
Transform. John Wiley and Sons, 2001.
Url: http://ltfat.github.io/doc/fourier/hermbasis.html
See also: dft, pherm.
Package: ltfat