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SPREADOP - Spreading operator

Usage

h=spreadop(f,c);

Description

spreadop(f,c) applies the operator with spreading function c to the input f. c must be square.

spreadop(f,c) computes the following for c of size \(L \times L\):

\begin{equation*} h\left(l+1\right)=\sum_{n=0}^{L-1}\sum_{m=0}^{L-1}c\left(m+1,n+1\right)e^{2{\pi}ilm/L}f\left(l-n+1\right) \end{equation*}

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

The combined symbol of two spreading operators can be found by using tconv. Consider two symbols c1 and c2 and define f1 and f2 by:

h  = tconv(c1,c2)
f1 = spreadop(spreadop(f,c2),c1);
f2 = spreadop(f,h);

then f1 and f2 are equal.

References:

H. G. Feichtinger and W. Kozek. Operator quantization on LCA groups. In H. G. Feichtinger and T. Strohmer, editors, Gabor Analysis and Algorithms, chapter 7, pages 233--266. Birkhäuser, Boston, 1998.