Digital Signal Processing Reference
In-Depth Information
FIR f
i
lter using Kaiser window
optimal FIR filter
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(a)
(b)
(1) The stop-band ripples in Fig. 15.21(a) have a uniform peak value of roughly
70 dB, which is about 20 dB less than the maximum stop-band ripple
value in Fig. 15.21(b). The stop-band attenuation of the optimal FIR fil-
ter is therefore higher than that for the filter obtained from the Kaiser
window.
(2) As illustrated in Fig. 15.22(a), where the magnitude response of the optimal
FIR filter is plotted on a linear scale, there are noticeable pass-band ripples
in the magnitude response of the optimal FIR filter. Figure 15.22(b) plots
the magnitude response of the FIR filter obtained from the Kaiser window,
where the pass-band ripples are negligible. The improvement in the stop-
band attenuation of the optimal FIR filter can therefore be attributed to the
pass-band ripples that the optimal filter has incorporated. The optimal FIR
filter distributes the distortion between the pass and stop bands. The FIR
filter obtained from the Kaiser window has most distortion concentrated in
the stop band, which leads to higher ripples (or lesser attenuation) within
its stop band.
(3) Finally, we observe that the transition bands in the two FIR filters are
roughly of the same width.
Fig. 15.22. Same as Fig. 15.21
except the frequency responses
are plotted on a linear scale.
15.7 Summary
This chapter presented techniques for designing causal FIR filters. The ideal
frequency-selective filters presented in Chapter 14 are physically unrealizable
because of strict constraints on the pass- and stop-band gains of the filter and
also because of a sharp transition between the pass and stop bands. Practi-
cal implementations of the ideal filters are obtained by allowing acceptable
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