Fast Recursive Computation of Sliding DHT with Arbitrary Step

Abstract

Short-time (sliding) transform based on discrete Hartley transform (DHT) is often used to estimate the power spectrum of a quasi-stationary process such as speech, audio, radar, communication, and biomedical signals. Sliding transform calculates the transform coefficients of the signal in a fixed-size moving window. In order to speed up the spectral analysis of signals with slowly changing spectra, the window can slide along the signal with a step of more than one. A fast algorithm for computing the discrete Hartley transform in windows that are equidistant from each other is proposed. The algorithm is based on a second-order recursive relation between subsequent equidistant local transform spectra. The performance of the proposed algorithm with respect to computational complexity is compared with the performance of known fast Hartley transform and sliding algorithms.