Quantization and roundoff noises in fixed-point FIR digital filters

The errors in a fixed-point finite impulse response (FIR) filter due to quantization (analog-to-digital conversion) and roundoff are considered. Expressions for the exact moments of the filter output noise are derived. It is well known that, when the input signal satisfies certain conditions, the popular additive white noise model can be valid in describing the quantization noise. The characteristics of multiplicative roundoff noises, however, differ from what this model predicts, even under conditions where the roundoff noises are white. Hence the additive white noise model does not provide accurate results on the characteristics of the output error in an FIR filter. Using the exact formulas for the moments, the author computes the exact power spectrum of the filter output error. These results agree well with those obtained from simulation