Theoretical analysis of word-level switching activity in the presence of glitching and correlation

Abstract

This paper presents a novel analytical approach to compute the switching activity in digital circuits at the word level in the presence of glitching and correlation. The proposed approach makes use of signal statistics such as mean, variance, and autocorrelation. It is shown that the switching activity /spl alpha//sub f/ at the output node f of any arbitrary circuit in the presence of glitching and correlation is computed as /spl alpha//sub f/=/spl Sigma//sub i=1//sup S-1//spl alpha/(f/sub i,i+1/)=/spl Sigma//sub i=1//sup S-/ /sup 1/p(f/sub i+1/)(1-p(f/sub i/))(1-/spl rho/(f/sub i,i+1/)) (1) where /spl rho/(f/sub i,i+1/)=/spl rho/(f/sub i,i+1/)=(E[f/sub i/(Sn)f/sub i+1/(Sn)]- p(f/sub i/)p(f/sub i+1/))/(/spl radic/(p(f/sub i/)-p(f/sub i/)/sup 2/)(p(f/sub i+1/)- p(f/sub i+1//sup 2/))) (2). S number of time slots in a cycle; /spl rho/(f/sub i/,+1) time-slot autocorrelation coefficient; E[x]=expected value of x; p/sub x/=probability of the signal x being one. The switching activity analysis of a signal at the word level is computed by summing the activities of all the individual bits constituting the signal. It is also shown that if the correlation coefficient of the higher order bits of a normally distributed signal x is /spl rho/(x/sub c/), then the bit P/sub 0/ where the correlation begins and the correlation coefficient is related hy /spl rho/(x/sub c/)=erfc{(2(P/sub 0/-1)-1)/(/spl radic/2/spl sigma//sub x/)} where erfc(x)=complementary error function; /spl sigma//sub x/=variance of x. The proposed approach can estimate the switching activity in less than a second which is orders of magnitude faster than simulation-based approaches. Simulation results show that the errors using the proposed approach are about 6.1% on an average and that the approach is well suited even for highly correlated speech and music signals.