Proceedings Article | 5 April 2000
Proc. SPIE. 4056, Wavelet Applications VII
KEYWORDS: Modulation, Wavelets, Receivers, Multiplexing, Signal processing, Electronic filtering, Data communications, Binary data, Filtering (signal processing), Information operations
In the past decade, wavelet filters have been widely applied to signal processing. In effect, wavelet filters are perfect reconstruction filter banks (PRFBs). However, in most researches, the filterbanks and wavelets operate on real- valued or complex-valued signals. In this paper, PRFBs operating over integer quotient rings (IQRs) are introduced. We denote an IQR as Z/(q). Algorithms for constructing such filter banks are proposed. The PRFB design can be carried out either in the time or the frequency domain. We demonstrate that some classical or well known filter tap coefficients can even be transformed into values over Z/(q) in a simple and straightforward way. Here we emphasize that to achieve perfect reconstruction (PR), the filters need not to work on elements in fields. In fact, operating on elements in IQRs can achieve PR with proper choices of a ring and filter tap coefficients. The designed filter banks can be orthogonal or biorthogonal. Based ona PRFB over an IQR, to which we refer as an IQR-PRFB, a perfect reconstruction transmultiplexer (PRTM), to which we refer as an IQR-PRTM, can be derived. Through the utilization of the IQR-PRTM multiplexing and multiple access in a multi-user digital communication system can be realized. The IQR-PRTM effectively decomposes the communication signal space into several orthogonal subspaces, where each multiplexed user sends his message in one of them. If some of the orthogonal subspaces are preserved for parity check, then error correction at the receiving end can be performed. In the proposed schemes, the data to be transmitted must be represented with elements of Z/(q), which can be done easily. A modulation and demodulation/detection scheme, in conjunction with the IQR-PRTM is proposed.
