One and two-dimensional digital mutirate systems with applications in sub-sampling and bandlimited signal reconstruction

Citation

Liu, Vincent Cheng-Teh (1990) One and two-dimensional digital mutirate systems with applications in sub-sampling and bandlimited signal reconstruction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/cvbb-m844. https://resolver.caltech.edu/CaltechETD:etd-05092007-130540

Abstract

This thesis deals with the two-dimensional (2D) multirate quadrature mirror filter (QMF) bank and new applications of 1D and 2D multirate filter bank concepts to the periodic nonuniform sampling and reconstruction of bandlimited signals. The potential use of multirate filter banks in the statistically optimal estimation of signals in the presence of wide-sense cyclostationary noise is also examined. The two-dimensional QMF bank is free from aliasing if and only if a certain polyphase matrix product related to the filter bank possesses the 2D pseudo-circulant property. A 2D FIR filter bank can be designed with the perfect reconstruction property if the polyphase matrix of its analysis filter bank is constrained to be a 2D lossless matrix. A design example is included. The losslessness constraint is satisfied by imposing a cascaded structure of first-degree lossless sections on the polyphase matrix. A limited factroization theorem is derived for 2D FIR lossless systems where the order in one of the two dimensions is limited to unity. In the area of nonuniform sampling of multiband bandlimited signals, the filter bank approach is utilized to derive a computationally efficient method for reconstructing bandlimited signals. The above scheme can also be viewed as a mean of compressing and reconstructing an oversampled bandlimited signal. It is shown that such a scheme has lower computational complexity than traditional methods of sampling rate alteration. The results can be extended to nonuniform sampling in two-dimensions using integer lattices. A further application of the multirate filter bank is in signal estimation in the presence of cyclostationary noise. The necessary and sufficient condition for the filter bank to preserve the wide-sense stationarity of the input is derived. Several applications where cyclostationary noise is present are indicated, and through the use of simulations the performance of the optimal filter bank can be compared with the conventional scalar optimal filter. The roundoff noise in orthogonal matrix building blocks is analyzed, since these building blocks are commonly present in filter bank implementations.

Thesis Files