Enhanced frequency analysis using wavelets

Abstract

An enhanced frequency analysis method is introduced, using a phase shift wavelet representation, to analyse individual frequency components and to reveal features of a given signal. The frequency representation provides details at each time location without the loss, caused by local orthogonality between the wavelet basis functions and the given signal, which occurs when a normal wavelet decomposition is employed. Movement of the local orthogonality locations, corresponding to the phase shift of the wavelet basis functions, are studied and it is shown that these movements are important and can be used to reveal features of the signal in the frequency domain, such as continuities, smoothness, and trends. Several examples are presented to illustrate the method and an application to a permanent magnet synchronous drive system is provided to demonstrate the approach.