Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 238

EXAMPLE 7.7
a. Design a lowpass FIR filter with 25 taps using the MATLAB program listed in the “MATLAB Programs” section
at the end of this chapter. The cutoff frequency of the filter is 2,000 Hz, assuming a sampling frequency of
8,000 Hz. The rectangular window and Hamming window functions are used for each design.
b. Plot the frequency responses along with those obtained using the rectangular window and Hamming window for
comparison.
c. List the FIR filter coefficients for each window design method.
Solution:
a. With a given sampling rate of 8,000 Hz, the normalized cutoff frequency can be found as

U c ¼ 2; 000 2p
8; 000

¼ 0:5p radians

Now we are ready to design FIR filters via the MATLAB program. The function firwd(N, Ftype, WnL, WnH, Wtype)
listed in the “MATLAB Programs” section at the end of this chapter, has five input parameters, which are described
as follows:
• “N” is the number of specified filter coefficients (the number of filter taps).

• “Ftype” denotes the filter type, that is, input “1” for the lowpass filter design, input “2” for the highpass filter

design, input “3” for the bandpass filter design, and input “4” for the band reject filter design.

0

-50

-100

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

0

-500

-1000

-1500

-2000

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

FIGURE 7.12

Frequency responses using the rectangular and Hamming windows.