The well-known Whittaker-Kotel 'nikov-Shannon sampling theorem for frequency-bandlimited functions of time is extended to functions of multidimensional arguments. It is shown that a function whose spectrum is restricted to a finite region of wave-number space may be reconstructed from its sampIes taken over a periodic lattice having suitably small repetition vectors. The most efficient lattice ...

We consider the relative stability of time-invariant and time-varying unnormalized lattice filters. First, we consider a set of lattice filters whose reflection parameters i obey j ij i and provide necessary and sufficient conditions on the i that guarantee that each time-invariant lattice in the set has poles inside a circle of prescribed radius 1= < 1, i.e., is relatively stable with degree o...

This study presents a tap-leakage adjustment algorithm to control the tap drifting problem in an adaptive echo canceller. A nonrecursive transversal filter structure and stochastic gradient adaptation algorithm are first studied. On the basis of these studies, the effect of tap drift when the input spectrum does not cover the full band is presented. The tap-leakage algorithm, which has been use...

Designing optimal filer banks for subband coding applications has recently attracted considerable attention [1]-[5]. In particular, the authors have developed an adaptive algorithm based on stochastic gradient descent (SGD) that enables one to optimize two channel paraunitary filter banks in an on-line fashion [3]. The idea has also been extended to the case of tree-structured filter banks [4]....

Among the earliest publications of Evelyn Nelson are four papers which appeared in 1971—Nelson [1971a, 1971b] and Burris and Nelson [1971/72, 1971]. These papers contributed to our understanding of the intricate structural diversity of the lattice of equational theories. In particular, these papers revealed that large partition lattices occur as intervals in the lattice of equational theories o...

The aim of this paper is further to develop the filter theory on residuated lattices. The concept of interval valued intuitionistic (T, S)-fuzzy filters on residuated lattices is introduced by linking the intuitionistic fuzzy set, t-norm, s-norm and filter theory of residuated lattices; The properties and equivalent characterizations of Interval valued intuitionistic (T, S)-fuzzy filters are in...

In this paper, we present a new class of linear-phase cosinemodulated filter banks. In contrast to the 2M band structure of the linear-phase DCT-II filter bank derived by Lin and Vaidyanathan, our filter bank has M bands and requires different prototype filters for the analysis and synthesis. Given the PR constraints of the bank, we derive a non-orthogonal lattice structure for implementing the...

This correspondence discusses the design and factorization of FIR paraunitary filter banks where several analysis filters are given. A lattice factorization-based algorithm is presented that provides complete and minimal characterization for nonlinear-phase and balanced linear-phase systems. As a result, the design problem can be formulated as an unconstrained optimization of the lattice coeffi...

In this paper, we develop structures for FIR perfect-reconstruction QMF banks which cover a subclass of systems that yield linear-phase analysis filters for arbitrary M. The parameters of these structures can be optimized in order to design analysis filters with minimum stopband energy which a t the same time have linear-phase and satisfy the perfect-reconstruction property. If there are M subb...