examp_zak.m

linear time－frequency toolbox

%EXAMP_ZAK  Some Zak-transforms
%
%   This scripts creates plots of three different Zak-transforms of a
%   Gaussian, a spline and a Hermite function
%
%   FIGURE 1 Gaussian and spline
%
%     This figure shows the absolute value of the Zak-transform of
%     a Gaussian to the left, and a second order spline to the right.
%     Notice that both Zak-transforms are 0 in only a single
%     point right in the middle of the plot. The spline is constructed
%     by sampling and periodization of the continuous second order spline.
%
%   FIGURE 2 Funny Zaks
%
%     The left figure shows the absolute value of the Zak-transform of
%     a 4th order Hermite function and the left shows a chirp.
%     Notice how the Zak transform of the Hermite functions is zero on a
%     circle centered on the corner.
%
%   SEE ALSO:   ZAK, IZAK

disp('Type "help examp_zak" to see a description of how this example works.');

% Setup parameters and length of signal

% We want critical sampling
a=64;
L=a^2; 

% Make a Gaussian function
g=pgauss(L);

% Compute the Zak-transform in square layout.
zg=zak(g,a);

% Visualize it
figure(1);

subplot(1,2,1);
mesh(abs(zg));
legend('off');

subplot(1,2,2);
mesh(abs(zak(pbspline('ec',L,2,a),a)));
legend('off');

% Do the same for the Hermite function.
figure(2);

subplot(1,2,1);
mesh(abs(zak(pherm(L,4),a)));
legend('off');

subplot(1,2,2);
mesh(abs(zak(pchirp(L,1),a)));
legend('off');