PCONV - Periodic convolution

Usage

h=pconv(f,g)
h=pconv(f,g,ftype);

Description

pconv(f,g) computes the periodic convolution of f and g. The convolution is given by

\begin{equation*} h\left(l+1\right)=\sum_{k=0}^{L-1}f\left(k+1\right)g\left(l-k+1\right) \end{equation*}

pconv(f,g,'r') computes the convolution where g is reversed (involuted) given by

\begin{equation*} h\left(l+1\right)=\sum_{k=0}^{L-1}f\left(k+1\right)\overline{g\left(k-l+1\right)} \end{equation*}

This type of convolution is also known as cross-correlation.

pconv(f,g,'rr') computes the alternative where both f and g are reversed given by

\begin{equation*} h\left(l+1\right)=\sum_{k=0}^{L-1}f\left(-k+1\right)g\left(l-k+1\right) \end{equation*}

In the above formulas, \(l-k\), \(k-l\) and \(-k\) are computed modulo \(L\).

The input arrays f and g can be 1D vectors or one of them can be a multidimensional array. In either case, the convolution is performed along columns with row vectors transformed to columns.