Fast Generalized Sliding Sinusoidal Transforms

Discrete cosine and sine transforms closely approximate the Karhunen-Loeve transform for first-order Markov stationary signals with high and low correlation coefficients, respectively. Discrete sinusoidal transforms can be used in data compression, digital filtering, spectral analysis and pattern recognition. Short-time transforms based on discrete sinusoidal transforms are suitable for the adaptive processing and time-frequency analysis of quasi-stationary data. The generalized sliding discrete transform is a type of short-time transform, that is, a fixed-length windowed transform that slides over a signal with an arbitrary integer step. In this paper, eight fast algorithms for calculating various sliding sinusoidal transforms based on a generalized solution of a second-order linear nonhomogeneous difference equation and pruned discrete sine transforms are proposed. The performances of the algorithms in terms of computational complexity and execution time were compared with those of recursive sliding and fast discrete sinusoidal algorithms. The low complexity of the proposed algorithms resulted in significant time savings.

Automated summary

This paper introduces the applications of discrete cosine and sine transforms in first-order Markov stationary signals and proposes fast algorithms based on a generalized solution and pruned discrete sine transforms. The performances of the algorithms are compared with other algorithms, demonstrating low complexity and fast execution time.