Application of the Wavelet Transform to Signal Analysis
Like the Fourier Transform, the Wavelet Transform decomposes signals as a superposition of simple units from which the original signals can be reconstructed. The Fourier Transform decomposes signals into sine and cosine functions of different frequencies, while the Wavelet Transform decomposes signals into wavelets. Since the Fourier Transform is a global integration transform and there is no time factor in it, it cannot effectively analyze non-stationary signals whose statistical properties change with time. In order to analyze non-stationary signals, we need to decompose signals into units that are localized in both the time and frequency domains. Using the Wavelet Transform with the B-wavelet, we wrote a program package in Mathematica to implement the decomposition and reconstruction algorithms for signal processing. A data acquisition system developed in another project is used to acquire both the synthesized signals and real voice signals. Application of the Wavelet Transform on these signals will be presented.