Piecewise Constant Signals Research Articles

Bandwidth necessary and sufficient for the determination of a periodic quantized signal

AbstractThe periodic quantized signal in this paper is defined as a piecewise constant signal which has a finite number of jumps in a period and has constant levels between adjacent jumping points. Periodic quantized signals are classified into four groups according to whether the jumping points and/or the height of jumps at the jumping points are, respectively, restricted to integer multiples of prescribed quantities or not.This paper considers the two groups among them: (1) the set of signals whose levels {aK} between adjacent jumping points are allowed to take arbitrary real values but the jumping points {tk} are restricted to integer multiples of T/N, where T is the time interval of a period and N is the number of jumping points in a period (signal set III); and (2) the set of signals whose levels aK} between adjacent jumping points and jumping points {tK} are restricted to integer multiples of a specified step size δ and respectively (signal set IV). We have studied the smallest amount of Fourier coefficients required for the determination of the original periodic quantized signal having N jumping points in a period. Our results assert that the Fourier coefficients necessary and sufficient for the determination of the original periodic quantized signal are given by: Up to the [N/2]th order for signals belonging to the signal set III, where [x] denotes the maximum integer not exceeding x. Up to the N0 ( N/p1)th order for signals belonging to the signal set IV, where p1 is the smallest prime factor of N.

On the detection of jumps in a Markovian piecewise-constant video-signal

A Markovian piecewise-constant signal which changes by abrupt jumps may serve as a model of many types of signals. In the video-signal a jump is equivalent to the contour in the image line. The maximum posterior probability estimation of jump distribution is used. Optimal method of estimating is based on dynamic programming with reducing the number of variants from 2 n−1 (full number of variants) to 1 6 n(n − 1)(n − 2) + n . The suboptimal iterative technique of jumps detection is suggested also, as well as the parallel scheme for its implementation. The lower boundaries of probabilities of edge missing and of false detection were obtained.

General synthesis procedure for computer control of single-loop and multiloop linear systems (an optimal sampling system)

This paper is concerned with the problem of designing optimal systems for the control of a plant governed by a linear differential equation with constant coefficients. Control is exerted by means of piecewise constant signals which can change only at the “sampling instants.” Optimality means here, as in some nonlinear problems, that the system achieves equilibrium with zero steady-state error from any initial state as quickly as possible.