Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 254

The 500 Hz signal with noise and its spectrum are plotted in Figure 7.22 , from which it is obvious that
the digital sine wave contains noise. The spectrum is also displayed to give a better understanding of
the noise frequency level. We can see that noise is broadband, existing from 0 Hz to the folding
frequency of 4,000 Hz. Assuming that the desired signal has a frequency range of only 0 to 800 Hz, we
can filter noise from 800 Hz and beyond. A lowpass filter would complete such a task. Then we
develop the filter specifications:

Passband frequency range: 0 Hz to 800 Hz with the passband ripple less than 0.02 dB
Stopband frequency range: 1 kHz to 4 kHz with 50 dB attenuation

As we will see, lowpass filtering will remove noise in the range 1,000 Hz to 4,000 Hz , and hence the
signal to noise power ratio will be improved.
Based on the specifications, we design an FIR filter with the Hamming window, a cutoff frequency
of 900 Hz, and an estimated filter length of 133 taps. The enhanced signal is depicted in Figure 7.23 ,
where the clean signal can be observed. The amplitude spectrum for the enhanced signal is also
plotted. As shown in the spectral plot, the noise level is negligible between 1 and 4 kHz. Notice that
since we use the higher-order FIR filter, the signal experiences a linear phase delay of 66 samples, as is
expected. We also see some transient response effects. However, the transient response effects will end
after the first 132 samples due to the length of the FIR filter. MATLAB implementation is given in
Program 7.7.

4

2

0

-2

-4

0 50 100 150 200 250

Number of samples

1.5

1

0.5

0

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

FIGURE 7.22
Signal with noise and its spectrum.