The frequency variation of response errors in fixed and floating point FIR filters

The form of the expected variations in frequency response errors due to coefficient quantisation have been derived for both fixed and floating point coefficient representations. Deviations from the otherwise constant `white´ error response occur because of symmetries in the impulse response. The deviations take the form of peaks or nulls at low or high limits of the frequency range depending on filter order and the type of symmetry. Quantitative information on the height, location and frequency domain extent of these deviations is provided. Awareness of these phenomena can be of interest to the filter designer when assessing the wordlength suitability of a processor architecture for implementing a given filter specification without prior knowledge of the filter coefficients