A parallelized matching pursuit algorithm for the four-parameter chirplet decomposition

A four-parameter chirplet decomposition to expand signals in terms of the scaled, fractional Fourier transformed and time-frequency shifted Gaussians, has been developed. To reduce the required computational time of the decomposition to the level of a previously proposed three-parameter decomposition, a parallel decomposition algorithm is proposed. The parallel decomposition exploits the inherent rotational property of the four-parameter decomposition. In each of the rotation angles, a three-parameter matching pursuit algorithm is run over the discrete fractional Fourier transformed signal for that angle, and then based on the obtained results the component with the largest energy is selected as the optimal atom