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 generalized 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.