Impulses and stochastic arithmetic for signal processing

The work described in this paper explores the use of Poisson point processes and stochastic arithmetic to perform signal processing functions. Our work is inspired by the asynchrony and fault tolerance of biological neural systems. The essence of our approach is to code the input signal as the rate parameter of a Poisson point process, perform stochastic computing operations on the signal in the arrival or “pulse” domain, and decode the output signal by estimating the rate of the resulting process. An analysis of the Poisson pulse frequency modulation encoding error is performed. Asynchronous, stochastic computing operations are applied to the impulse stream and analyzed. A special finite impulse response (FIR) filtering scheme is proposed that preserves the Poisson properties and allows filters to be cascaded without compromising the ideal signal statistics.