HERMBASIS - Orthonormal basis of discrete Hermite functions

Usage

V=hermbasis(L,p);
V=hermbasis(L);
[V,D]=hermbasis(...);

Description

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:

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');