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Figure 3.55 Cosine fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Figure 4.1 A first order low-pass filter . . . . . . . . . . . . . . . . . . . . . . . 186
Figure 4.2 Frequency response of the first order low-pass filter . . . . . . 186
Figure 4.3 A first order high-pass filter . . . . . . . . . . . . . . . . . . . . . . . 187
Figure 4.4 Frequency response of the first order high-pass filter . . . . . . 187
Figure 4.5 Response of the first order low-pass filter
to a square signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Figure 4.6 Response of the first order high–pass filter
to a square signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Figure 4.7 A desired low-pass frequency response . . . . . . . . . . . . . . . 191
Figure 4.8 A desired high-pass frequency response . . . . . . . . . . . . . . . 191
Figure 4.9 A desired band-pass frequency response. . . . . . . . . . . . . . . 192
Figure 4.10 A desired band-stop frequency respon se. . . . . . . . . . . . . . . 192
Figure 4.11 A desired frequency response: approximation and reality . . . 193
Figure 4.12 A filter structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Figure 4.13 Foster forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Figure 4.14 Cauer forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Figure 4.15 Radio tuning with an ideal filter . . . . . . . . . . . . . . . . . . . . 198
Figure 4.16 Specification of a low-pass filter . . . . . . . . . . . . . . . . . . . . 199
Figure 4.17 Frequency response of 5
th
order Butterworth filter. . . . . . . . 200
Figure 4.18 Poles of 5
th
order Butterworth filter. . . . . . . . . . . . . . . . . . 201
Figure 4.19 Step response of 5
th
order Butterworth filter . . . . . . . . . . . . 202
Figure 4.20 Effect of n on the frequency response of the Butterworth
filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Figure 4.21 Response of 5
th
order Butterworth filter
to a square wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Figure 4.22 Frequency response of 5
th
order Chebyshev 1 filter . . . . . . . 204
Figure 4.23 Poles of 5
th
order Chebyshev 1 filter . . . . . . . . . . . . . . . . . 205
Figure 4.24 Step response of 5
th
order Chebyshev 1 filter . . . . . . . . . . . 205
Figure 4.25 Effect of n on the frequency response of the Chebyshev
1 filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Figure 4.26 Response of 5
th
order Chebyshev 1 filter
to a square wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Figure 4.27 Frequency response of 5
th
order Chebyshev 2 filter . . . . . . . 208
Figure 4.28 Poles and zeros of 5
th
order Chebyshev 2 filter. . . . . . . . . . 209
Figure 4.29 Step response of 5
th
order Chebyshev 2 filter . . . . . . . . . . . 209
Figure 4.30 Effect of n on the frequency response
of the Chebyshev 2 filter . . . . . . . . . . . . . . . . . . . . . . . . . 210
Figure 4.31 Response of 5
th
order Chebyshev 2 filter
to a square wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Figure 4.32 Frequency response of 5
th
order elliptic filter . . . . . . . . . . . 212
Figure 4.33 Poles of 5
th
order elliptic filter . . . . . . . . . . . . . . . . . . . . . 212
Figure 4.34 Step response of 5
th
order elliptiic filter . . . . . . . . . . . . . . . 213
List of Figures xxi