A Multidigit Adaptive Delta Modulation (ADM) System

Abstract

A multidigit adaptive delta modulation (ADM) system has been proposed where the error signal, between the input and the approximated signal produced by ADM coder, is coded in an auxiliary encoder. The error in the auxiliary coder is processed by another ADM and so on. The bit rate of each of these coders is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f_{r}/N</tex> where f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> is the overall transmission rate and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is the number of coders used. The bit streams are interleaved for transmission and at the receiver they are separated and decoded, and these signals are added and filtered. It is shown that for a given transmission rate, each coder operates at a basic sampling rate of f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rB</inf> such that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_{opt} = f_{r}/f_{rB}</tex> gives the optimum number of coders to be used for maximum signal-to-noise ratio (SNR). A bound is derived for the maximum SNR of such a system and is compared with the bounds derived for other predictive coders. The experimental results of a two-digit ADM are presented. An average SNR of 30 dB is obtained with a dynamic range of 32 dB at f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> = 32 kbits/s for band-limited noise signals. The SNR increases with the sampling rate at 15 dB/octave, as against 9 dB for a single-digit ADM. The frequency response is good and the variation of SNR with the message frequency of the delta coding system has been improved. The effect of channel errors has also been studied and the performance of the system is found satisfactory.