Analysis of quantization errors in the direct form for finite impulse response digital filters

An analysis of the three possible types of quantization effects in the direct form realization of finite impulse response (FIR) digital filters is presented. These quantization effects include roundoff noise, A-D noise, and filter frequency response errors due to coefficient quantization. Since the analysis of roundoff noise and A-D noise for the direct form is straightforward, this paper concentrates on an analysis of the effects of quantized coefficients on the resulting filter frequency response. Based on this analysis, statistical bounds on the error incurred in the frequency response of a filter due to coefficient quantization are developed and verified by extensive experimental data. Using these bounds, a procedure for applying known techniques for FIR filter design to the design of filters with finite word length coefficients is presented. On the whole, the direct form is shown to be a very attractive structure for realizing FIR filters.