Applying Markov chains to calculate the probability of saturation in digital IIR filters

We propose a new method to model the effect of finite-precision arithmetic in infinite impulse response (IIR) digital filters. As an application, we use the proposed model to compute the probability of saturation or overflow in IIR filters implemented in fixed-point arithmetic. The transition from the current filter output to the next output is modeled as a firstorder Markov chain. The Markov chain transition probability matrix is then used to evaluate the probabilities of saturation or overflow for first and second-order IIR filters.