Fast Wavelet Transform/Inverse Transform and Data Reduction for Signal Reconstruction

Abstract

Wavelet transform, WT, is a representative method of time-frequency analysis of a non-stationary signal. The original time series is obtained from the two-dimensional distribution by applying an inverse wavelet transform, IWT. However, fast Fourier transform, FFT, algorithm can not be applied to fast WT/IWT calculations because the base function of a WT is nonsinusoidal, while the algorithm can be used for fast computation of a short-time Fourier transform, STFT. For fast computation of a WT/IWT, a particular algorithm has been used in a time-domain calculation. In this study, a new fast WT/IWT algorithm, which is applied in the frequency domain, is proposed. Since the amount of data needed to represent a time frequency two-dimensional distribution is very large, a data reduction technique is required to enable fast computation of an IWT. An algorithm which can be used for redundancy elimination of WT data is introduced into the fast IWT analysis. Calculation times of this new fast WT/IWT algorithm are compared with those of traditional ones, for the analysis of both simulated signals and measured voices. From the comparisons, it is clear that the new method markedly speeds up the computation.