Some results in the theory modulated filter banks and modulated wavelet tight frames
Perfect reconstruction filter banks, obtained by modulation of a linear-phase, low-pass, prototype filter, and the associated multichannel transmultiplexers are well documented in the engineering literature [\textit{N. J. Fliege}, Multirate digital signal processing: Multirate systems, filter banks, wavelets, Wiley (1995); \textit{R. A. Haddad}, \textit{T. W. Parsons}, Digital signal processing: Theory, applications, and hardware, Computer Science Press, New York, Oxford (1991); \textit{P. P. Vaidyanathan}, Multirate systems and filter banks, Prentice Hall (1993; Zbl 0784.93096); \textit{M. Vetterli} and \textit{J. Kovačević}, Wavelets and subband coding, Prentice Hall (1995)]. The filter bank techniques are of particular importance in speech analysis and synthesis by vocoder hardware which is remarkably immune to degradation from noise [\textit{R. A. Haddad} and \textit{T. W. Parsons} (loc. cit.)]. Another important application is in the field of high resolution radar imaging (SAR) and clinical magnetic resonance tomography [\textit{W. Schempp}, Wavelets in high resolution radar imaging and clinical magnetic resonance tomography. Cybern. Systems (to appear)]. Recently, perfect reconstruction modulated filter banks with the analysis and synthesis bank obtained from different prototypes have been reported. The paper under review describes a general form of modulation depending on an integer parameter, and presents a theory of modulated filter banks and associated wavelet bases including an efficient design procedure for unitary finite response modulated filter banks. Specifically, it deals with a parametrization of the unitary finite response modulated filter banks, and an associated parametrization of compactly supported modulated wavelet tight frames. A bewildering number of acronyms makes it hard to read the paper.
scientific article; zbMATH DE number 846190