IIR filters using stochastic arithmetic

We consider the design of IIR filters operating on oversampled sigma-delta modulated bit streams using stochastic arithmetic. Conventional digital filters process multi-bit data at the Nyquist rate using multi-bit multipliers and adders. High resolution ADCs based on the sigma-delta modulation generate random bits at an oversampled rate as intermediate data. We propose to filter the sigma-delta modulated bit streams directly and present first and second order low pass IIR filters based on the stochastic integrator. Experimental results show a significant reduction in hardware area by using stochastic filters.