Joseph D. Lakey
Appl. Res. Labs, Univ. of Texas, P.O. Box 8029, Austin, TX 78713-8029
Dept. of Math., Univ. of Texas, P.O. Box 8029, Austin, TX 78712
Texas A&M Univ., College Station, TX 77843
Motivated by the human auditory system, a new signal transform is presented which models the way humans hear. Cochlear processing acts like a constant bandwidth bank of filters in the low frequency range but is of proportional bandwidth at higher frequencies. This new transform, which we call the composite wavelet transform, is better able to model this process than standard signal processing techniques such as the short-time Fourier transform (STFT) and the continuous wavelet transform (CWT). The composite wavelet transform in fact provides a signal analysis tool that is able to examine signals with competing signal structures whereas the STFT and the CWT do not. In order to insure stable signal recovery, the theory of frames is examined. An overview of the theory of frames will be given and wavelet and Gabor frames will be discussed. Recent work on frames for the composite wavelet transform will also be presented. Finally, some applications of frames, especially to speech signal processing will be considered.