Wednesday, November 15. 2006The exponential in $R^d$, II![]()
(Q15) I’m gonna show you some cool Gabor atoms on
[xx yy] = meshgrid(linspace(-2,2,100));
v=[1 1.5];
e1 = exp(pi*i*( v(1)*xx + v(2)*yy ));
imagesc(real(e1))
w=[-1 4];
e2 = exp(pi*i*( w(1)*xx + w(2)*yy ));
imagesc(real(e2))
![]() ![]()
See how the value of the frequency changes with the length of
g1 = exp(-(xx.^2+yy.^2));
imagesc(g1)
g2 = exp(-4*(xx.^2+yy.^2));
imagesc(g2)
![]() ![]()
And now these are the modulated Gaussians, whose set of translates across
imagesc(real(g1.*e1))
imagesc(real(g2.*e2))
![]() ![]()
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