Chair: J. Kovacevic, AT&T Bell Laboratories (USA)
Ton Kalker, University of California (USA)
Hyungju Park, University of California (USA)
Martin Vetterli, University of California (USA)
The Euclidean algorithm is a frequently used tool in the analysis of one- dimensional 1D multirate systems. This tool is however not available for multidimensional MD multirate systems. In this paper we discuss how Groebner basis techniques can fill this gap. After presenting the relevant facts about Groebner bases, we will show in three examples how this technique can contribute to MD multirate systems theory. The first example addresses the completion of partly given perfect reconstruction filter banks; the second example investigates invertible sample rate conversion schemes; the third one, which is mentioned only very briefly, deals with oversampled perfect reconstruction filter banks.
Jelena Kovacevic, AT&T Bell Laboratories (USA)
We construct two-dimensional local cosine bases in discrete and continuous time. Solutions are offered both for rectangular and nonrectangular lattices. In the case of nonrectangular lattices, the problem is solved by mapping it into a one-dimensional equivalent problem.
H. Safiri, University of Windsor (CANADA)
M. Ahmadi, University of Windsor (CANADA)
In this paper, a structure consisting of only all-pass subsystems for the design of n-dimensional IIR digital filters with arbitrary cutoff boundaries is presented. It is shown that all-pass filter is a universal building block for multidimensional digital filters. Utilization of the proposed structure for n=2, and 3 is given in more details.
Srikanth Pokala, Wright State University (USA)
Arnab K. Shaw, Wright State University (USA)
A least-squares technique is presented for designing quarter-plane separable-denominator 2-D IIR filters to best approximate prescribed frequency domain (FD) specification. It is shown that the FD error vector is linearly related to the 2-D numerator coefficients, whereas the relationship with the 2-D denominators is quasi-linear. Furthermore, the numerator and denominator estimation problems are theoretically decoupled. The quasi-linear relationship is used to formulate an algorithm for iterative estimation of the denominator. The numerator is found in one step using the estimated denominator. Computer simulations show the effectiveness of the proposed method and its superior performance compared to several existing methods.
Stephane Coulombe, Universite du Quebec (CANADA)
Eric Dubois, Universite du Quebec (CANADA)
This research addresses the frequency multiplexing of multidimensional signals, having different bandwidths or defined on different lattices, with perfect or near perfect reconstruction, i.e., zero or low crosstalk between signals and zero or low distortion of individual signals. The paper discusses important issues such as: what are the valid modulating frequencies, how to manage quadrature modulation, what are the conditions for perfect reconstruction, how many signals can be transmitted perfectly, when and why linear periodically time-varying (LPTV) filters must be used in the system, structure of filters to preserve compatibility with conventional frequency multiplexers, and design procedures.