SYMPHASE - Change Gabor coefficients to symmetric phase

Usage

c=symphase(c,a);

Description

symphase(c,a) alters the phase of the Gabor coefficients c so as if they were obtained from a Gabor transform based on symmetric time/frequency shifts. The coefficient must have been obtained from a dgt with parameter a.

Gabor coefficients with symmetric phase correspond to the following transform: Consider a signal f of length L and define \(N=L/a\). The output from c=symphase(dgt(f,g,a,M),a) is given by

\begin{equation*} c\left(m+1,n+1\right)=\sum_{l=0}^{L-1}f(l+1)e^{-2\pi im(l-na/2)/M}\overline{g(l-an+1)} \end{equation*}

where \(m=0,\ldots,M-1\) and \(n=0,\ldots,N-1\) and \(l-an\) is computed modulo L.

symphase(c,a,'lt',lt) does the same for a non-separable lattice specified by lt. Please see the help of matrix2latticetype for a precise description of the parameter lt.

References:

E. Chassande-Mottin, I. Daubechies, F. Auger, and P. Flandrin. Differential reassignment. Signal Processing Letters, IEEE, 4(10):293--294, 1997.