VLSI Circuit Design of Digital Signal Processing Algorithms Using Tensor Product Formulation

Abstract Many important computation problems can be specified by block recursive algorithms. For example, matrix transposition and fast Fourier transform are block recursive algorithms. In this paper, we present a methodology of VLSI circuit design for block recursive algorithms based on the tensor product theory. Matrix transposition and fast Fourier transform algorithms are designed and implemented following this methodology. First, matrix transposition and fast Fourier transform algorithms are expressed as tensor product formulas. The tensor product formulas are modified to fit into interconnection networks, including the omega network and the hypercube network. The formulas are then used to generate high-level programming language code. Finally, a hardware description language, Verilog, is used to realize the algorithms according to the generated programs. The major goal of this paper is to provide an effective way to design VLSI circuits for block recursive algorithms.