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In this paper, a comprehensive overview of Computer Architecture for Digital Signal Processing is given. Such architectures are seen as the result of constraining influences from the nature of digital signal processing algorithms, architectural techniques including appropriate choice of primitive elements, the underlying digital system technology, and programming languages for digital signal processing. Following a consideration of these influences, several examples are given ranging from chips through board level processors, to attached support processors with very high throughput. Trends for the future are discussed throughout the paper.