Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 287

5. Output the transfer function and check the frequency responses.
6. If the frequency specifications are satisfied, output the difference equation. If the frequency
specifications are not satisfied, increase the filter order and repeat beginning with step 4.
Table 7.19 shows the comparisons for the window, frequency sampling, and optimal methods. The
table can be used as a selection guide for each design method in this topic.
Example 7.20 describes the possible selection of the design method by a DSP engineer to solve
a real-world problem.

EXAMPLE 7.20
Determine the appropriate FIR filter design method for each of the following DSP applications.
a. A DSP engineer implements a digital two-band crossover system as described in Section 7.4.4 in this topic. He
selects the FIR filters to satisfy the following specifications:
Sampling rate ¼ 44,100 Hz
Crossover frequency ¼ 1,000 Hz (cutoff frequency)
Transition band ¼ 600 Hz to 1,400 Hz
Lowpass filter ¼ passband frequency range from 0 to 600 Hz with a ripple of 0.02 dB and stopband edge at 1,400
Hz with an attenuation of 50 dB.
Highpass filter ¼ passband frequency range from 1.4 to 44.1 kHz with a ripple of 0.02 dB and stopband edge at
600 Hz with an attenuation of 50 dB.

The engineer does not have the software routine for the Remez algorithm.
b. An audio engineer tries to equalize a speech signal sampled at 8,000Hz using a linear phase FIR filter based on the
magnitude specifications in Figure 7.43 . The engineer does not have the software routine for the Remez algorithm.
Solution:
a. The window design method is the first choice, since this formula is expressed in terms of the cutoff frequency
(crossover frequency), the filter order is based on the transient band, and the filter types are standard lowpass and
highpass. The ripple and stopband specifications can be satisfied by selecting the Hamming window. The optimal
design method will also do the job if the remez() algorithm is available. But there exists a challenge to satisfy the
combined unity gains at the crossover frequency of 1,000 Hz.
b. Since the magnitude frequency response is not a standard filter type such as lowpass, highpass, bandpass, or
bandstop, and the remez() algorithm is not available, the first choice should be the frequency sampling method.

Magnitude

2.0

1.0

0.0

0

fs/2=4000 Hz

FIGURE 7.43
Magnitude frequency response in Example 7.20(b).