In this paper a robust, single carrier, multi-user, DSP-based implementation of an OFDM, differential phase shift keying (DPSK) block demodulator is suggested. It is shown that a direct, DSP-based implementation of the above system using a single FFT symbol is highly susceptible to artifacts induced by symbol timing errors (symbol synchronization jitter, SSJ). A dual symbol, FFT-based implementation is suggested to alleviate the effect of timing error on the demodulation process, even eliminate some of the SSJ-induced artifacts. The countermeasures used in the implementation do not assume any statistical model of SSJ nor are they dependant on a symbol synchronization scheme. Also a dual version of the demodulator is derived for an important, but less known, modulation technique called symmetric DPSK (SDPSK).

A class of discrete dynamical systems with nonlinear feedback is considered. These systems generalize various maps arising in connection with chaotic dynamical systems, topological dynamics, and linear systems theory. We give a complete characterization of this class of systems.

Spatial reasoning is an important component in pictorial retrieval systems. There are two approaches to handling spatial relationships: the well-known one is to use algorithms on which most earlier work such as [13, 17, 21] is based, and the recent one [30] is to construct deductive rules that allow spatial relationships to be deduced. Sistla et al. [30] developed a system of rules $\cal R$ on reasoning about basic spatial relationships that are of common interest in pictorial databases. In this paper, we consider the following two problems with that system of rules $\cal R$: the deduction problem (that is, to deduce new spatial relationships from a given set $F$ of spatial relationships) and the reduction problem (that is, to eliminate redundant spatial relationships from $F$. We use the mathematically simple matrix representation approach to show that these two problems can be solved by efficient (i.e., polynomial-time) algorithms. The time required by both of them is at most a constant multiple of the time to compute the transitive reduction of a directed graph with $n$ vertices or to compute the transitive closure of a directed graph with $n$ vertices or to perform $n\times n$ Boolean matrix multiplication, and thus is always bounded by time complexity $O(n^3)$ (and space complexity $O(n^2)$), where $n$ is the number of all involved objects.

In this paper we investigate the consistency problem for spatial relationships in content-based image database systems. We use the mathematically simple matrix representation approach to present an efficient (i.e., polynomial-time) algorithm for consistency checking of spatial relationships in an image.

It is shown that, there exists an efficient algorithm to detect whether, given a set $SR$ of absolute spatial relationships, the maximal set of $SR$ under $\cal R$ contains one pair of contradictory spatial relationships. The time required by it is at most a constant multiple of the time to compute the transitive reduction of a graph or to compute the transitive closure of a graph or to perform Boolean matrix multiplication, and thus is always bounded by time complexity $O(n^{3})$ (and space complexity $O(n^{2})$), where $n $ is the number of all involved objects. As a corollary, this detection algorithm can completely answer whether a given set of three-dimensional absolute spatial relationships is consistent.