Analytical estimation of signal transition activity from word-level statistics

Presented in this paper is a novel methodology to determine the average number of transitions in a signal from its word-level statistical description. The proposed methodology employs: (1) high-level signal statistics, (2) a statistical signal generation model, and (3) the signal encoding (or number representation) to estimate the transition activity for that signal. In particular, the signal statistics employed are mean (μ), variance (σ²), and autocorrelation (ρ). The signal generation models considered are autoregressive moving-average (ARMA) models. The signal encoding includes unsigned, one´s complement, two´s complement, and sign-magnitude representations. First, the foilowing exact relation between the transition activity (t_i), bit-level probability (p_i), and the bit-level autocorrelation (ρ_i) for a single bit signal b_i is derived: t_i=2p_i (1-p_i)(1-ρ_i) (1). Next, two techniques are presented which employ the word-level signal statistics, the signal generation model, and the signal encoding to determine ρ_i (i=0, ···, B-1) in (1) for a B-bit signal. The word-level transition activity T is obtained as a summation over t_i (i=0,···, B-1); where t_i is obtained from (1). Simulation results for 16-bit signals generated via ARMA models indicate that an error in T of less than 2% can be achieved. Employing AR(1) and MA(10) models for audio and video signals, the proposed method results in errors of less than 10%. Both analysis and simulations indicate the sign-magnitude representation to have lower transition activity than unsigned, ones´ complement, or two´s complement. Finally, the proposed method is employed in estimation of transition activity in digital signal processing (DSP) hardware. Signal statistics are propagated through various DSP operators such as adders, multipliers, multiplexers, and delays, and then the transition activity T is calculated. Simulation results with ARMA inputs show that errors less than 4% are achievable in the estimation of the total transition activity in the filters. Furthermore, the transpose form structure is shown to have fewer signal transitions as compared to the direct form structure for the same input