• Digital FIR filters are designed such that they have linear phase characteristics in the pass band, if FIR filters are realized using Direct Form realization in linear phase is maintained even when quantization of the filter is done.

  • Quantization does not affect the phase characteristics of FIR filter, but it affects the magnitude response.

  • To avoid this affect, the cascade form realization should be used and 12 to 14 beats should be used to represent the coefficients.

  • Similarly the number of bits for coefficient must be increased to maintain the same and in the frequency response of characteristics of the filter.

  • Let us consider each filter coefficient is rounded to (b + 1) bits, then the maximum error in the coefficient value is bounded as:

$-2^{(b+1)} \lt e_h(n)\lt2^{-(b+1)}$

The error in the frequency response is given by,

$E_M (ω)=∑_{n=0}^{M-1}e_h (n) e^{-jωn}$