On the problem of designing IIR digital filters with short coefficient word lengths

The paper presents an algorithm for designing IIR digital filters with short coefficient word lengths. The algorithm has the flexibility of obtaining a better design at the expense of investing more computational time. It was found that, by incorporating Crochiere's idea of equalizing passband and stopband statistical word lengths before applying the algorithm, we are capable of obtaining a further reduction in the overall word length when compared with that obtained by applying the algorithm alone. The principle of the algorithm and the concept of statistical word lengths equalization for further word length reduction applies to all IIR digital filters of different structures and passbands, with and without their transfer functions expressed in a closed form.