Accession Number : ADA131208

Title :   Analysis of a Delayed Delta Modulator.

Descriptive Note : Technical rept.,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Gerr,Neil L ; Cambanis,Stamatis

PDF Url : ADA131208

Report Date : May 1983

Pagination or Media Count : 49

Abstract : Delayed Delta Modulation (DDM) uses a second feedback loop in addition to the standard DM loop. While the standard loop compares the current predictive estimate of the input to the current sample, the new loop compares it to the upcoming sample so as to detect and anticipate slope overloading. Since this future sample must be available before the present output is determined and the estimate updated, delay is introduced at the encoding. The performance of DDM with perfect integration and step-function reconstruction is analyzed for each of three inputs. In every case, the stochastic stability of the system is established. For a discrete time i.i.d input, the (limiting) joint distribution of input and output is derived, and the (asymptotic) mean square sample point error MSE(SP) is computed when the input is Gaussian. For a Wiener input, the joint distribution of the sample point and predictive errors is derived, and MSE(SP) and the time-averaged MSE (MSE(TA)) are computed. For a stationary, first-order Gauss-Markov input, the joint distribution of input and output is derived, and MSE(SP) and MSE(TA) computed. Graphs of the MSE's illustrate the improvement attainable by using DDM instead of DM. With optimal setting of parameters, MSE(SP) (MSE(TA) is reduced about 15% (35%). (Author)

Descriptors :   *Mathematical prediction, *Delta modulation, *Stochastic processes, Delay, Loops, Feedback, Input, Output, Parameters, Optimization, Stability, Integration, Distribution functions, Linear systems, Stationary, Convergence, Computations, Slope, Overload

Subject Categories : Statistics and Probability
      Radiofrequency Wave Propagation

Distribution Statement : APPROVED FOR PUBLIC RELEASE