GABMULAPPR Best Approximation by a Gabor multiplier
Usage: sym=gabmulappr(T,a,M);
sym=gabmulappr(T,g,a,M);
sym=gabmulappr(T,ga,gs,a,M);
[sym,lowb,upb]=gabmulappr( ... );
Input parameters:
T : matrix to be approximated
g : analysis/synthesis window
ga : analysis window
gs : synthesis window
a : Length of time shift.
M : Number of channels.
Output parameters:
sym : symbol
sym=GABMULAPPR(T,g,a,M) calculates the best approximation of the given
matrix T in the Frobenius norm by a Gabor multiplier determined by the
symbol sym over the rectangular time-frequency lattice determined by
a and M. The window g will be used for both analysis and
synthesis.
GABMULAPPR(T,a,M) does the same using an optimally concentrated, tight
Gaussian as window function.
GABMULAPPR(T,gs,ga,a) does the same using the window ga for analysis
and gs for synthesis.
[sym,lowb,upb]=GABMULAPPR(...) additionally returns the lower and
upper Riesz bounds of the rank one operators, the projections resulting
from the tensor products of the analysis and synthesis frames.
References:
M. Doerfler and B. Torresani. Representation of operators in the
time-frequency domain and generalized Gabor multipliers. J. Fourier
Anal. Appl., 16(2):261--293, April 2010.
P. Balazs. Hilbert-Schmidt operators and frames - classification, best
approximation by multipliers and algorithms. International Journal of
Wavelets, Multiresolution and Information Processing, 6:315 -- 330,
2008.
P. Balazs. Basic definition and properties of Bessel multipliers.
Journal of Mathematical Analysis and Applications, 325(1):571--585,
January 2007.
H. G. Feichtinger, M. Hampejs, and G. Kracher. Approximation of
matrices by Gabor multipliers. IEEE Signal Procesing Letters,
11(11):883--886, 2004.
Url: http://ltfat.github.io/doc/operators/gabmulappr.html
See also: framemulappr, demo_gabmulappr.
Package: ltfat