Fast and memory-efficient algorithms for computing quadratic time–frequency distributions

Abstract Algorithms for computing time–frequency distributions (TFDs) limit computation time by reducing numerical operations. But these fast algorithms do not reduce the memory load. This article presents four TFD algorithms to minimise both the computation and memory loads. Each algorithm is optimised for a specific kernel category. Three algorithms reduce memory by computing an exact TFD without oversampling; the fourth algorithm, for the nonseparable kernel, reduces memory by computing a decimated TFD. The separable-kernel algorithm, using a biomedical signal as an example, computes an exact TFD with only 12% of the computation load and 1% of the memory required by conventional algorithms.