Multidimensional mapping techniques for convolution

It is shown that the Winograd approach, nesting algorithms, and multidimensional interpolation methods for circular convolution are conveniently described using similarity transforms and companion matrices. Using the notion of similarity, it is further shown that the one-dimensional to multidimensional mapping techniques employed by the nesting algorithms can be extended to some noncircular convolutions. This increases the flexibility in the design of algorithms which employ both the Chinese remainder theorem and the multidimensional techniques. The use of multidimensional mappings for noncircular convolutions in multidimensional interpolation methods is also described.<>