ANALYTICAL ESTIMATION OF SIGNAL TRANSITION ACTIVITY FROM WORD-LEVEL STATISTICS

Presented in this paper is a novel methodology to determine the averag e number of transitions in a signal from its word-level statistical de scription, The proposed methodology employs: 1) high-level signal stat istics, 2) a statistical signal generation model, and 3) the signal en coding (or number representation) to estimate the transition activity for that signal, In particular, the signal statistics employed are mea n (mu), variance (sigma(2)), and autocorrelation (rho). The signal gen eration models considered are autoregressive moving-average (ARMA) mod els, The signal encoding includes unsigned, one's complement, two's co mplement, and sign-magnitude representations. First, the following exa ct relation between the transition activity (t(i)), bit-level probabil ity (p(i)), and the bit-level autocorrelation (rho(i)) for a single bi t signal b(i) is derived t(i) = 2p(i)(1 - p(i))(1 - rho(i)). (1) Next, two techniques are presented which employ the word-level signal stati stics, the signal generation model, and the signal encoding to determi ne rho(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-bi t signals generated via ARMA models indicate that an error in T of les s 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 repres entation to have lower transition activity than unsigned, ones' comple ment, 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 operato rs such as adders, multipliers, multiplexers, and delays, and then the transition activity T is calculated, Simulation results with ARMA inp uts show that errors less than 4% are achievable in the estimation of the total transition activity in the filters, Furthermore, the transpo se form structure is shown to have fewer signal transitions as compare d to the direct form structure for the same input.