Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 256

xlabel( ' Number of samples ' );ylabel( ' Sample value ' );grid;
subplot(2,1,2);plot(f,Ayk(1:N/2 þ 1)); axis([0 fs/2 0 1.5]);
xlabel( ' Frequency (Hz) ' ); ylabel( ' Amplitude

j Y(f) j ' );grid;

7.4.2 Speech Noise Reduction
In a speech recording system, we digitally record speech in a noisy environment at a sampling rate of
8,000 Hz. Assuming the recorded speech contains information within 1,800 Hz, we can design
a lowpass filter to remove the noise between 1,800 Hz and the Nyquist limit (the folding frequency of
4,000 Hz). The filter specifications are listed below:
Filter type: lowpass FIR filter
Passband frequency range: 0-1,800 Hz
Passband ripple: 0.02 dB
Stopband frequency range: 2,000-4,000 Hz
Stopband attenuation: 50 dB

According to these specifications, we can determine the following parameters for filter design:
Window type ¼ Hamming window
Number of filter taps ¼ 133
Lowpass cutoff frequency ¼ 1,900 Hz

1 x 10 4

0.5

0

-0.5

-1

0 0.05 0.1 0.15 0.2 0.25

Number of samples

800

600

400

200

0

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

FIGURE 7.24A
Noisy speech and its spectrum.