CFS: Time-frequency representations of acoustic signals based on redundant wavelet methodologies

In this dissertation, we develop high quality representations for acoustic signals based on wavelet methodologies. These representations, the Cardinal Framelet Synthesis (CFS) representations , use wavelets in a redundant context to improve the ability to localize signal information and to suppress time-dependent artifacts that are typical of non-redundant, e.g., orthogonal, representations. The basic building blocks of the CFS representations are redundant wavelet constructions, known in the literature as framelets, which we have generalized to the framelet-packet setting. We have developed for this purpose new framelet systems based on interpolating refinable functions.; A significant component is the development of CFS based algorithms for acoustic signal denoising. We present the results of extensive numerical experimentation in CFS denoising with respect to a large collection of acoustic signals from a variety of sources. The CFS denoising algorithms tend to exhibit fewer artifacts and distortions in the recovered signals compared to orthogonal-based denoising methods.