Fixed-point error analysis of two-channel perfect reconstruction filter banks with perfect alias cancellation

This paper studies the effects of fixed-point arithmetic in two-channel perfect reconstruction (PR) filter banks. Practical implementations of filter banks often require scaling of coefficients and differing binary word sizes to maintain dynamic range. When scaling is used with fixed precision arithmetic, the perfect alias cancellation (PAC) and PR constraints no longer hold. The main contribution of this paper is the derivation of constraints whereby PAC is maintained, even when coefficients are scaled and when the analysis and synthesis filter banks use different binary word lengths. Once PAC is established, the fixed-point effects on PR properties can be analyzed using standard methods. The theory is verified by comparing predicted and actual reconstruction signal-to-noise ratios resulting from simulating a symmetric wavelet transform.