UNSDGT Uniform Non-stationary Discrete Gabor transform
Usage: c=unsdgt(f,g,a,M);
[c,Ls]=unsdgt(f,g,a,M);
Input parameters:
f : Input signal.
g : Cell array of window functions.
a : Vector of time positions of windows.
M : Numbers of frequency channels.
Output parameters:
c : Cell array of coefficients.
Ls : Length of input signal.
UNSDGT(f,g,a,M) computes the uniform non-stationary Gabor coefficients
of the input signal f. The signal f can be a multichannel signal,
given in the form of a 2D matrix of size Ls xW, with Ls being
the signal length and W the number of signal channels.
The non-stationary Gabor theory extends standard Gabor theory by
enabling the evolution of the window over time. It is therefore necessary
to specify a set of windows instead of a single window. This is done by
using a cell array for g. In this cell array, the n'th element g{n}
is a row vector specifying the n'th window. However, the uniformity
means that the number of channels is fixed.
The resulting coefficients is stored as a M xN xW
array. c(m,n,w) is thus the value of the coefficient for time index n,
frequency index m and signal channel w.
The variable a contains the distance in samples between two consecutive
blocks of coefficients. a is a vectors of integers. The variables g and
a must have the same length.
The time positions of the coefficients blocks can be obtained by the
following code. A value of 0 correspond to the first sample of the
signal:
timepos = cumsum(a)-a(1);
[c,Ls]=nsdgt(f,g,a,M) additionally returns the length Ls of the input
signal f. This is handy for reconstruction:
[c,Ls]=unsdgt(f,g,a,M);
fr=iunsdgt(c,gd,a,Ls);
will reconstruct the signal f no matter what the length of f is,
provided that gd are dual windows of g.
Notes:
------
UNSDGT uses circular border conditions, that is to say that the signal is
considered as periodic for windows overlapping the beginning or the
end of the signal.
The phaselocking convention used in UNSDGT is different from the
convention used in the DGT function. UNSDGT results are phaselocked
(a phase reference moving with the window is used), whereas DGT results
are not phaselocked (a fixed phase reference corresponding to time 0 of
the signal is used). See the help on PHASELOCK for more details on
phaselocking conventions.
References:
P. Balazs, M. Doerfler, F. Jaillet, N. Holighaus, and G. A. Velasco.
Theory, implementation and applications of nonstationary Gabor frames.
J. Comput. Appl. Math., 236(6):1481--1496, 2011.
Url: http://ltfat.github.io/doc/nonstatgab/unsdgt.html
See also: insdgt, nsgabdual, nsgabtight, phaselock, demo_nsdgt.
Package: ltfat