Signal analysis and coherence using the continuous wavelet transform

This research paper was completed and submitted at Nipissing University, and is made freely accessible through the University of Toronto’s TSpace repositoryThis Major Research Paper (MRP) explores methods of time-frequency decomposition of continuous time series, with a brief explanation of the historical development of these methods. A focus is placed on wavelet analysis and the Continuous Wavelet Transform(CWT). A variation of the CWT that applies the basic concepts of Fourier analysis (by using a sinusoidal mother wavelet to obtain good frequency resolution) is discussed. The relationship between Fourier period and wavelet scale is explored, and an analytical derivation of this relationship for the Morlet mother wavelet is presented. This MRP analyzes methods used to compare two signals. Although the Cross Wavelet Transform (XWT) is explained, a specific focus is placed on Wavelet Coherence, which uses the CWT to compare two signals and extract meaningful data about how they are linearly related. Statistical methods are developed to determine significant values of the CWT and wavelet coherence. These methods are assessed using simulated signals and real human experimental data