Tensor product algebra as a tool for VLSI implementation of the discrete Fourier transform

Abstract

A tool to aid in the automated VLSI implementation of the discrete Fourier transform (DFT) is described. This tool is tensor product algebra, a branch of finite-dimensional multilinear algebra. Tensor product formulations of fast fourier transform (FFT) algorithms to compute the DFT are presented. These mathematical formulations are manipulated, using properties of tensor product algebra, to obtain variants that adapt to performance constraints in a VLSI implementation process. The possibility of automating this procedure by processing these mathematical formulations or expressions in a behavioral synthesis environment of a silicon compilation system is discussed. A transformation technique between a symbolic computation environment and a behavioral synthesis environment for the transferring of functional primitives is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>