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88<br />

Signals and Spectra Chap. 2<br />

0 dB<br />

dB 0<br />

–5<br />

|H(f)| dB<br />

3 dB<br />

–10<br />

–15<br />

|H(f)| dB<br />

=–10 log [1+(f/f 0 ) 2 ]<br />

–3f 0 –2f 0 –f 0 f 0 2f 0<br />

(a) Magnitude Response<br />

3f 0<br />

f<br />

Degrees<br />

90°<br />

45°<br />

¨(f)<br />

¨(f) = –tan –1<br />

(<br />

f<br />

–––<br />

f 0<br />

(<br />

–3f 0 –2f 0 –f 0 f 0 2f 0 3f 0<br />

–3f 0 –2f 0 –f 0 f 0 2f 0 3f 0<br />

f<br />

–45°<br />

–90°<br />

360<br />

( –––––<br />

2∏f 0<br />

f degrees<br />

(b) Phase Response<br />

T d (f)<br />

Sec<br />

1<br />

T d (f) = –––– tan –1 f<br />

(–––<br />

2∏f f 0<br />

1<br />

–––––<br />

2∏f 0<br />

f<br />

(<br />

(<br />

(c) Time Delay<br />

Figure 2–16<br />

Distortion caused by an RC low-pass filter.

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