Digital Signal Processing Systems, Basic Filtering Types, and Digital Filter Realizations - Digital Signal Processing: Fundamentals and Applications - page 203

6.7.2 Bandpass Filtering of Speech
Bandpass filtering plays an important role in DSP applications. It can be used to pass the signals
according to the specified frequency passband and reject the frequency other than the passband
specification. Then the filtered signal can be further used for the signal feature extraction. Filtering can
also be applied to perform applications such as noise reduction, frequency boosting, digital audio
equalizing, and digital crossover, among others.
Let us consider the following digital fourth-order bandpass Butterworth filter with a lower cutoff
frequency of 1,000 Hz, an upper cutoff frequency of 1,400 Hz (that is, the bandwidth is 400 Hz), and
a sampling rate of 8,000 Hz:

0 : 0201 0 : 0402 z 2 þ 0 : 0201 z 4

HðzÞ¼

(6.43)

1 2 : 1192 z 1 þ 2 : 6952 z 2 1 : 6924 z 3 þ 0 : 6414 z 4

Converting the z-transfer function into the DSP difference equation yields
yðnÞ¼ 0 : 0201 xðnÞ 0 : 0402 xðn 2 Þþ 0 : 0201 xðn 4 Þ
þ 2 : 1192 yðn 1 Þ 2 : 6952 yðn 2 Þþ 1 : 6924 yðn 3 Þ 0 : 6414 yðn 4 Þ

(6.44)

The filter frequency responses are computed and plotted in Figure 6.32A with MATLAB. Figure 6.32B
shows the original speech and filtered speech, while Figure 6.32C displays the spectral plots for the
original speech and filtered speech.

0

-10

-20

-30

-40

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

200

100

0

-100

-200

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

FIGURE 6.32A

Frequency responses of the designed bandpass filter.