ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

4pSP4. A first approximation to wavelet transform.

Jose Romero

Salvador Cerda

Laboratorio de Acustica, Departamento de Fisica Aplicada, Facultad de Ciencias Fisicas, c/ Doctor Moliner, Burjasot 46100, Spain

The wavelet transform is a tool usually used to analyze time-varying spectrum signals. In this work a simple algorithm was presented to evaluate the integrals involved in wavelet transform. In the analysis of time-varying spectrum signals different methods are used. One of them is the short-time Fourier transform (STFT). This method was presented and its problems were mentioned. To solve them, the discrete wavelet transform (DWT) and the Weyl--Heisenberg wavelet transform (WHT) were introduced. To compute the DWT an algorithm was presented that replaced the integrals by a sum in analogy to the case of FT, and also permitted computation of the WHT. Some signals were analyzed using three functions as the mother wavelet: the Haar function, the Mexican hat function, and the Morlet function. The analyzed signals were a 1860-Hz tone, a sweep simulated with cos(at[sup 2]+b), an impulsive signal, and an example on FFT which did not work correctly. Results were graphically represented and comments on every case were realized. It was found that in different cases, it was best to use the mother wavelet functions.