TCONV - Twisted convolution

Usage

h=tconv(f,g);

Description

tconv(f,g) computes the twisted convolution of the square matrices f and g.

Let h=tconv(f,g) for f,g being \(L \times L\) matrices. Then h is given by

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

where \(m-k\) and \(n-l\) are computed modulo L.

If both f and g are of class sparse then h will also be a sparse matrix. The number of non-zero elements of h is usually much larger than the numbers for f and g. Unless f and g are very sparse, it can be faster to convert them to full matrices before calling tconv.

The routine spreadinv can be used to calculate an inverse convolution. Define h and r by:

h=tconv(f,g);
r=tconv(spreadinv(f),h);

then r is equal to g.