Explain the effects of coefficient quantization in FIR filters

• Generally digital FIR filter are designed such that they have linear phase characteristic in the pass band. If FIR filter are realized using direct from realization then linear phase is maintained even when the quantization of filter co- efficients is done.

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

To avoid this effect , the cascade form realization should be used and 12 to 14 bits should be used to represent the co-efficients.

Similarly the number of bits per co-efficients must be increased to maintain the same error in the frequency response characteristic of the filter.

Let us say each filter coefficients is rounded to (b+1) bits. Then the maximum error in the co efficient value is bounded as,

- 2^{- (b + 1)} < e_{n} (n) < 2^{- (b + 1)}

The error in the frequency response can be given as,

E_{M} (w) = \sum_{n = 0}^{M - 1} e_{n} (n) . e^{- j w n}

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