A comparison of fast orthogonal search, Fourier transform, and wavelet transform approaches in nonstationary signal analysis

The problem of representing redundancies in nonstationary signals is important in such signal processing applications as speech and image compression, coding, feature extraction, recognition, and video. Transformation techniques have been recognized to be a promising analysis tool in the merging of signal processing and human perception theories (JAY92). Orthogonal transformations such as the discrete Fourier transform (DFT), discrete wavelet transform (DWT), and very recently, generalizations on the DWT, have found widespread use in the analysis of nonstationary signals. In this thesis the fast orthogonal search (FOS) algorithm developed by Korenberg (KOR87) is applied to the analysis of speech signals, and compared with corresponding analyses by the discrete Fourier and generalized wavelet transforms.; The FOS algorithm is applied in both a single resolution block transform analysis and a multiresolution block transform analysis. The latter approach is made in an attempt to reflect the nature of typical nonstationary signals for which high frequency events occur for short duration and low frequency events occur for longer duration.; The two FOS approaches are compared to a block transform DFT analysis, and a generalized wavelet packet analysis that has recently been introduced by Coifman et al (COI92). The newly released software due to Coifman et al (COI91b) was chosen so that the analysis employed would be current and represent a good measure of the present capabilities of wavelet transform techniques. The comparisons of compression performance are made on a set of five digitized speech recordings, for a mean square error (MSE) criterion. The results for each of the five signals show that FOS clearly outperforms the DFT and wavelet approaches in both data compression and accuracy of representation.