The computational complexity of time-frequency distributions

Abstract

A number of lower bounds on the communication and multiplicative complexity are derived. The (Area)*(Time)/sup 2/ (AT/sup 2/) bound for the discrete short time Fourier transform, the discrete Wigner-Ville distribution, the discrete ambiguity function and the discrete Gabor transform is shown to be AT/sup 2/= Omega (N/sup 3/ log/sup 2/ N), where N/sup 2/ is the number of output points. The lower bound on multiplicative complexity for these is shown to be Omega (N/sup 2/). For the N-point discrete wavelet transform a lower bound of AT/sup 2/= Omega (N/sup 2/ log/sup 2/ N) and a multiplicative complexity of Omega (N) are the same as the lower bounds for the DFT.<>