Fast Hopping Discrete Sine Transform

Discrete sine transform (DST) is widely used in digital signal processing such as image coding, spectral analysis, feature extraction, and filtering. This is because the discrete sine transform is close to the optimal Karhunen-Loeve transform for first-order Markov stationary signals with low correlation coefficients. Short-time (hopping) discrete sine transform can be employed for time-frequency analysis and adaptive processing quasi-stationary data such as speech, biomedical, radar and communication signals. Hopping transform refers to a transform computed on the signal of a fixed-size window that slides over the signal with an integer hop step. In this paper, we first derive a second-order recursive equation between DST spectra in equidistant signal windows, and then propose two fast algorithms for computing the hopping DST based on the recursive relationship and input-pruned DST algorithm. The performance of the proposed algorithms with respect to computational costs and execution time is compared with that of conventional sliding and fast DST algorithms. The computational complexity of the developed algorithms is lower than any of the existing algorithms, resulting in significant time savings.