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It is well-known that the discrete Fourier transform (DFT) of a finite length discrete-time signal samples the discrete-time Fourier transform (DTFT) of the same signal at equidistant points on the unit circle. Hence, as the signal length goes to infinity, the DFT approaches the DTFT. Associated with the DFT are circular convolution and a periodic signal extension. In this paper we identify a large...
We derive the Haar filter bank for 1-D space signals, based on our recently introduced framework for 1-D space signal processing, termed this way since it is built on a symmetric space shift operation in contrast to the directed time shift operation. The framework includes the proper notions of signal and filter spaces, "z-transform," convolution, and Fourier transform, each of which is...
We present a domain-specific approach to generate high-performance hardware-software partitioned implementations of the discrete Fourier transform (DFT) in fixed point precision. The partitioning strategy is a heuristic based on the DFT's divide-and-conquer algorithmic structure and fine tuned by the feedback-driven exploration of candidate designs. We have integrated this approach in the Spiral linear-transform...
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