Wavelets and its application in cardiology

Abstract

Wavelet theory is associated with building a model for a signal or a system with a set of special signals called wavelets. Wavelets are "small waves" which are oscillatory with fast decaying to zero in nature. Fourier Transform is a kind of signal representation which makes use of infinitely supported sinusoidal signals where the time localization of the signal is not achieved. Short Time Fourier Transform (STFT) or a windowed Fourier Transform provides some degree of localization in time, but the resolution is fixed. But wavelet transform provides time and frequency localization at various levels. Here wavelets are used to approximate a signal. Each element in a wavelet set is constructed from a single function called the "mother wavelet". Each element is a scaled and translated version of the mother wavelet. Thus the given signal is broken down into scaled and translated forms of wavelet, the process being called wavelet decomposition or wavelet transformation [1-4]. The reconstructi on of the signal from the Wavelet transform is the Inverse Wavelet Transform. Such an analysis and representation is useful in the processing of seismicsignals, image processing, signal compression, acoustics, control systems, biosignal analysis etc. where time localization is essential. This chapter deals with a brief theory of the wavelet transforms and a few applications specific to the analysis of ECG signals.