Incremental refinement of DFT and STFT approximations

We present a class of multistage algorithms for carrying out incremental refinement of DFT and STFT approximations. Each stage is designed to improve the previous stage's approximation in terms of frequency coverage, frequency resolution, and SNR. These algorithms rely almost exclusively on vector summation operations, and they can be designed to exhibit a variety of tradeoffs between improvement in approximation quality and computational cost per stage. The performance of incremental STFT refinement on real data serves to illustrate the relevance of such algorithms to application systems with dynamic real-time constraints.>