ISGRAM - Spectrogram inversion

Usage

f=isgram(c,g,a);
f=isgram(c,g,a,Ls);
[f,relres,iter]=isgram(...);

Input parameters

Output parameters

Description

isgram(s,g,a) attempts to invert a spectrogram computed by

s = abs(dgt(f,g,a,M)).^2;

using an iterative method.

isgram(c,g,a,Ls) does as above but cuts or extends f to length Ls.

If the phase of the spectrogram is known, it is much better to use idgt.

[f,relres,iter]=isgram(...) additionally return the residuals in a vector relres and the number of iteration steps iter.

Generally, if the spectrogram has not been modified, the iterative algorithm will converge slowly to the correct result. If the spectrogram has been modified, the algorithm is not guaranteed to converge at all.

isgram takes the following parameters at the end of the line of input arguments:

The BFGS method makes use of the minFunc software. To use the BFGS method, please install the minFunc software from: http://www.cs.ubc.ca/~schmidtm/Software/minFunc.html.

Examples:

To reconstruct the phase of 'greasy', use the following:

% Setup the problem and the coefficients
f=greasy;
g='gauss';
a=20; M=200;
c=dgt(f,g,a,M);
s=abs(c).^2;
theta=angle(c);

% Reconstruct and get spectrogram and angle
r=isgram(s,g,a);
c_r=dgt(r,g,a,M);
s_r=abs(c_r).^2;
theta_r=angle(c_r);

% Compute the angular difference
d1=abs(theta-theta_r);
d2=2*pi-d1;
anglediff=min(d1,d2);

% Plot the difference in spectrogram and phase
figure(1);
plotdgt(s./s_r,a,16000,'clim',[-10,10]);
colormap([bone;flipud(bone)])
title('Relative difference in spectrogram');

figure(2);
plotdgt(anglediff,a,16000,'lin');
colormap(bone);
title('Difference in angle');