مرکز منطقه ای اطلاع رساني علوم و فناوري - On the Delta Modulation of a First-Order Gauss-Markov Signal

Abstract :

Consider the delta-modulation (DM) of a first-order Gauss-Markov signal $X$ . Let the adjacent-sample correlation in $X$ be $c$ , and let the (first-order) DM predictor coefficient be $a$ . We express the quantizer input Qrin the form $[S_{r} - aE_{r - 1} + (c - a)X_{r - 1}]$ , where Sris an "innovations" term, $aE_{r - 1}$ denotes the effect of quantizationerror $(E)$ feedback and $(c - a)X_{r - 1}$ reflects the effect of using an $a \\neq c$ . For the important case of $c \\rightarrow 1$ (which models over-sampled DM inputs), we propose the simplifying assumption [7] of uncorrelated $X$ and $E$ ; with this assumption, our formalization of quantizer input leads very simply to interesting results in linear (LDM) and adaptive delta modulation (ADM). The LDM results are generalizations of known expressions for optimum values of $a$ , and the step-size Δ, and the value of signal-to-noise ratio SNR. For ADM, we derive optimum multiplier values for step-size adaptations with a one-bit memory, using the case of $c \\sim a = 1$ for simplicity. Our results depend on modeling instantaneous step-size adaptation as a mechanism for tracking the expected magnitude of $Q$ ; existing literature has formalized such adaptation models only for the case of multi-bit quantizers.