sym=gabmulappr(T,a,M); sym=gabmulappr(T,g,a,M); sym=gabmulappr(T,ga,gs,a,M); [sym,lowb,upb]=gabmulappr( ... );
| T | matrix to be approximated |
| g | analysis/synthesis window |
| ga | analysis window |
| gs | synthesis window |
| a | Length of time shift. |
| M | Number of channels. |
| 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.
M. Dörfler and B. Torrésani. 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. [ http ]
P. Balazs. Basic definition and properties of Bessel multipliers. Journal of Mathematical Analysis and Applications, 325(1):571--585, January 2007. [ http ]
H. G. Feichtinger, M. Hampejs, and G. Kracher. Approximation of matrices by Gabor multipliers. IEEE Signal Procesing Letters, 11(11):883--886, 2004.