WAVELET METHODS FOR TIME SERIES ANALYSIS

WAVELET METHODS FOR

TIME SERIES ANALYSIS

Curso: ANÁLISIS DE SISTEMAS DINÁMICOS NO LINEALES:

APLICACIÓN A LOS SISTEMAS NATURALES

Prof. JOSE FCO. GOMEZ GLEZ. jfcgomez@ull.es.

1. Introduction



The first recorded mention of what we now call a ‘wavelet’ seems to

be in 1909 in a thesis by Alfred Haar.



The concept of wavelets in its present theoretical form was first



Such research is particularly active in the United States, where it is

spearheaded by the work of scientists such as Ingrid Daubechies,

Ronald Coifman, and Victor Wichkerhauser.



Wavelets are a relatively new way of analyzing time series or images.

Wavelet analysis is in some cases complementary to existing

analysis techniques (e.g., correlation and spectral analysis) and in

other cases capable of solving problems for which little progress had

been made prior to the introduction of wavelets.

2. Summary of Fourier Theory

3. Why Wavelet analysis?



The results of the Fourier transform are the Fourier coefficients A(f),

which when are multiplied by a sinusoid of frequency f yield the

constituent sinusoidal components of the original signal.

 To study Non-stationary Signals, in which their frequency

frequency.