Digital Signal Processing Systems, Basic Filtering Types, and Digital Filter Realizations - Digital Signal Processing: Fundamentals and Applications - page 206

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FIGURE 6.33

Notch filter frequency responses.

filter with a notch frequency of 60 Hz where the digital system has a sampling frequency of 500 Hz. We
obtain a notch filter (details can be found in Chapter 8) as follows:

1 1 : 4579 z 1 þ z 2

HðzÞ¼ (6.45)

1 1 : 3850 z 1 þ 0 : 9025 z 2

The DSP difference equation is expressed as
yðnÞ¼xðnÞ 1 : 4579 xðn 1 Þþ 1 : 3850 yðn 1 Þ 0 : 9025 yðn 2 Þ

(6.46)

The frequency responses are computed and plotted in Figure 6.33 . Comparisons of the raw ECG signal
corrupted by 60-Hz interference with the enhanced ECG signal for both the time domain and
frequency domain are displayed in Figures 6.34 and 6.35 , respectively. As we can see, the notch filter
completely removes the 60-Hz interference.

6.8 SUMMARY
1. The digital filter (DSP system) is represented by a difference equation, which is linear and time
invariant.
2. The filter output depends on the filter current input, past input(s), and past output(s) in general.
Given arbitrary inputs and nonzero or zero initial conditions, operating the difference equation
can generate the filter output recursively.