Wavelet transform-based digital signal processing

This study deals with applying the wavelet transform to mainly two different areas of signal processing: adaptive signal processing, and signal detection. It starts with background information on the theory of wavelets with an emphasis on the multiresolution representation of signals by the wavelet transform in Chapter 1. Chapter 2 begins with an overview of adaptive filtering in general and extends it to transform domain adaptive filtering. Later in the chapter, a novel adaptive filtering architecture using the wavelet transform is introduced. The performance of this new structure is evaluated by using the LMS algorithm with variations in step size. As a result of this study, the wavelet transform based adaptive filter is shown to reduce the eigenvalue ratio, or condition number, of the input signal. As a result, the new structure is shown to have faster convergence, implying an improvement in the ability to track rapidly changing signals. Chapter 3 deals with signal detection with the help of the wavelet transform. One scheme studies signal detection by projecting the input signal onto different scales. The relationship between this approach and that of matched filtering is established. Then the effect of different factors on signal detection with the wavelet transform is examined. It is found that the method is robust in the presence of white noise. Also, the wavelets are analyzed as eigenfunctions of a certain random process, and how this gives way to optimal receiver design is shown. It is further demonstrated that the design of an optimum receiver leads to the wavelet transform based adaptive filter structure described in Chapter 2.