Ahmed H. Tewfik
Dept. of Elec. Eng., Univ. of Minnesota, Minneapolis, MN 55455
Wavelets are a family of basis functions for the space of finite energy signals. In a wavelet decomposition, a signal is expanded in terms of translates and dilates of a single function. Wavelets provide a flexible decomposition of signals. This flexibility is the foundation of a new generation of advanced low-bit-rate, high-quality audio coding procedures. By adaptively choosing the wavelet representations of consecutive segments of the audio signal one can optimally exploit the masking effect in human hearing. The performance of the resulting coding techniques surpasses that of known nonwavelet-based approaches. Another important property of wavelet decompositions is the fact that one can relate the structure of the wavelet coefficients of a given signal to the local time and frequency domain characteristics of the signal. In sonar processing, this fact has been exploited by a new class of robust direction of arrival estimation algorithms that can deal with background correlated noise of an unknown correlation structure. These algorithms separate signal from noise by analyzing the structure of the wavelet coefficients of the array outputs.