Function: gabmulappr
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