VLSI IMPLEMENTATIONS OF NUMBER-THEORETIC TECHNIQUES IN SIGNAL-PROCESSING

This paper explores novel techniques involving number theoretic concep ts to perform real-time digital signal processing for high bandwidth d ata stream applications in Digital Signal Processing. For most data st ream signal processing algorithms, the arithmetic manipulations are si mple in form (cascades of additions and multiplications in a well defi ned structure) but the numbers of operations that have to be computed every second can be large. This paper discusses ways in which recently introduced number theoretic mapping techniques can be used to perform DSP operations by both reducing the amount of hardware involved in th e circuitry and by allowing the construction of very benign architectu res, down.to the individual cells. Such architectures can be used in a ggressive VLSI/ULSI implementations. We restrict ourselves to the comp utation of linear filter and transform algorithms, with the inner prod uct form, which probably account for the vast majority of digital sign al processing functions implemented commercially.