Relationships among Scaling and Wavelet Coefficients, Filter Banks and Nyquist Sampling for Multiuser Communications

摘要

Necessary conditions are given on the coefficients of the basic recursion equation for scaling functions for the existence and orthogonality of their integer translations. For tree-structured wavelet packet filter bank synthesis-analysis pairs used as multiplexer-demultiplexer pairs for multi-user communications, the conditions for orthogonality lead to spectrum efficient coverage of the entire frequency axis around the unit circle by magnitude frequency responses of multiplexer channels. These conditions are also used to study a wideband VSB synthesis filter bank pair with real inputs, followed by a matching analysis filter bank pair. It is shown that input sequences are recovered with. no crosstalk by Nyquist sampling of the imaginary coefficients of the odd powers of the output sequences. Further insights into Nyquist sampling for filter banks are also provided.