Quantized Filter Analysis - Introduction to Digital Signal Processing and Filter Design - page 375

Figure 7.14 Coefficients of reference filter and quantized filter with format [8 7] in a

lattice-coupled allpass structure.

7.6 QUANTIZATION ANALYSIS OF FIR FILTERS

Next we decide to investigate whether the alternative of designing a quantized
FIR filter would give us a better result. Choosing the same frequency-domain
specifications as for the IIR lowpass elliptic filter, we design an FIR lowpass filter
with an equiripple passband and stopband. The reference filter with infinite
precision uses the remez algorithm and yields a linear phase FIR (type I)
filter of order 16. The magnitude response of this filter is shown in Figure 7.15.
When we select the sign magnitude, fixed-point 7 bit wordlength and the 8 bit
wordlength, the results are as shown in Figures 7.16 and 7.17, respectively.
It is apparent that there is not a significant difference between the two filters
with 7 and 8 bit wordlength. In Figure 7.18 we plot a magnified magnitude
in decibels in the passband of the FIR filter with 8 bits for the wordlength. The
maximum deviation from the specified passband ripple of 0 . 3dBis ∼ 0 . 1dB.The
coefficients of the reference filter and the quantized filter are listed in Figure 7.19.
It is noted that several coefficients of the quantized filter have an underflow as
indicated by the digit 0 in the first column and have been rounded to zero.
Finally we compare the quantization effects on the IIR with the effect on the
FIR filter by comparing the magnitude responses shown in Figures 7.18 and 7.13.
It is easy to notice that the FIR filter has a lower sensitivity to quantization than
does the IIR filter that we chose above. The IIR filter in the form of the lattice-
coupled allpass structure and the FIR filter in the direct form have a wordlength