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

## 4pSP4. A first approximation to wavelet transform.

**Jose Romero
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Salvador Cerda
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**
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*Laboratorio de Acustica, Departamento de Fisica Aplicada, Facultad de
Ciencias Fisicas, c/ Doctor Moliner, Burjasot 46100, Spain
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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.