The computational complexity of time-frequency distributions

A number of lower bounds on the communication and multiplicative complexity are derived. The (Area)×(Time)² (AT 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 AT²=Ω(N³ log² N), where N² is the number of output points. The lower bound on multiplicative complexity for these is shown to be Ω(N²). For the N-point discrete wavelet transform a lower bound of AT²=Ω(N ² log² N) and a multiplicative complexity of Ω(N) are the same as the lower bounds for the DFT