Wavelets have received considerable attention in recent general signal processing, image processing, and pattern recognition literature, as a new method of signal analysis. This marks a transition in wavelet study from theoretical investigation to application-driven research. In this paper, wavelets and wavelet transformations are presented in a context intended to be appropriate as a first exposure to the engineer. The wavelet transform, more specifically the discrete wavelet transform, and its relationship to multiresolution analysis is then explored in a framework familiar to those versed in multirate digital signal processing concepts. Elements of the perspective offered by wavelet analysis, in contrast to the features of more conventional Fourier techniques, are examined. General procedures for wavelet-based signal processing applications are discussed and the specific application of reducing noise in audio signals examined. Within the context of this application, considerations unique to wavelet analysis are revealed and trade-offs analyzed. Finally, the results obtained from implementing the noise reduction system are presented and extensions to the technique proposed. / Master of Science