Staggered parallel short-time Fourier transform

Abstract

In this paper, we present the staggered parallel short-time Fourier transform, an algorithm that uses a quasi-parallel procedure to compute exact STFT coefficients of 1D signals. The algorithm leverages parallelism with the capacity of feedforward STFT algorithms to re-use prior computations. It performs this by carefully organizing input signals and collecting past computations into 2D memory buffers. Re-using stored information in memory enables fast computation of up to N/2 FFTs in parallel. The algorithm's time complexity is at O[6T] under an abstract circuit implementation – achieving a complexity measure that is independent of sample complexity N. Its time complexity is asymptotically equivalent with the best possible exact algorithm of O[T] time complexity, with a constant efficiency at O[1] relative to the best known sequential algorithm. Its efficiency property holds whether in an abstract circuit implementation or in a CPU implementation with limited number of cores. In general, the algorithm consumes less processors than other parallel STFT algorithms but can potentially require more memory. To test the algorithm's properties, we implement several STFT algorithms in a CPU with varying numbers of cores. These algorithms use either FFT, iterative, or feedforward schemes to capture the range of existing STFT algorithms for comparison. From our experimental results, our proposed algorithm has the least running time among exact STFT algorithms, while consuming less CPU processors than other forms of parallel implementations.