On the coefficient quantization of Multiplicative FIR filters

This paper analyzes the effects of coefficient quantization of Multiplicative Finite Impulse Response (MFIR) filters used to approximate the behavior of pole filters. Statistical analysis, zero displacement sensitivity and frequency domain analysis are used as measures of the filter performance for different coefficient lengths. A practical expression for determining the required number of bits for the coefficient quantization as a function of a predefined maximum deviation in the magnitude response is proposed in combination with an alternative method based on a time domain analysis. The time domain analysis allows, for a specific pole approximation, to investigate the sensitivity of the MFIR structure to coefficient variations. The paper concludes that, statistically, the MFIR pole approximation filter does not require a larger number of quantization bits for its coefficients than the corresponding Infinite Impulse Response (IIR) filter.