Summary: The paper explores novel techniques involving number theoretic concepts to perform real-time digital signal processing for high bandwidth data stream applications in Digital Signal Processing. For most data stream signal processing algorithms, the arithmetic manipulations are simple in form (cascades of additions and multiplications in a well defined 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 the circuitry and by allowing the construction of very benign architectures, down to the individual cells. Such architectures can be used in aggressive VLSI/ULSI implementations. We restrict ourselves to the computation of linear filter and transform algorithms, with the inner product form, which probably account for the vast majority of digital signal processing functions implemented commercially.