<title>Mixed-radix approach to incremental DFT refinement</title>

Abstract

Incremental refinement algorithms can quickly produce approximate results and may then improve the quality of those results in subsequent stages of computation. They offer promise for the development of real-time systems whose performance degrades gracefully under diminishing hard deadlines. We present a new class of incremental refinement algorithms which employ mixed-radix signal representations for the calculation of successive approximations to the DFT. This class includes algorithms with a wide range of cost/quality tradeoff characteristics. This work generalizes a previously reported class of algorithms which employ binary signal representations only. The mixed-radix formulation allows solutions of a given level of quality to be achieved using significantly fewer arithmetic operations in many instances. Under certain restrictions, these algorithms can also be implemented with no computational overhead using fixed-point binary hardware.