Continuous-time filters - Continuous and Discrete Time Signals and Systems - page 366

by enforcing the pass-band requirements. Repeat for the stop-band
requirements. Sketch the magnitude spectrum and confirm that the mag-
nitude spectrum satisfies the design specifications.

7.8 Repeat Problem 7.7 for the following specifications:

pass band (0 ≤ω≤ 50 radians/s) − 1 ≤ 20 log 10 H ( ω ) ≤ 0;

stop band ( ω > 65 radians/s) 20 log 10 H ( ω ) ≤− 25 .

7.9 Repeat (a) Problem 7.7 and (b) Problem 7.8 for the Type I Chebyshev
filter.

7.10 Repeat (a) Problem 7.7 and (b) Problem 7.8 for the Type II Chebyshev
filter.

7.11 Determine the order of the elliptic filters for the specifications included
in (a) Problem 7.7 and (b) Problem 7.8.

7.12 Using the results in Problems 7.7-7.11, compare the implementation
complexity of the Butterworth, Type I Chebyshev, Type II Chebyshev,
and elliptic filters for the specifications included in (a) Problem 7.7 and
(b) Problem 7.8.

7.13 By selecting the corner frequencies of the pass and stop bands, show that
the transformation

S = s ( ξ p2 − ξ p1 )
s 2 + ξ p1 ξ p2
maps a normalized lowpass filter into a bandstop filter.

7.14 Design a Butterworth highpass filter for the following specifications:

stop band (0 ≤ω≤ 15 radians/s) H ( ω ) ≤ 0 . 15;

pass band ( ω > 30 radians/s) 0 . 85 ≤ H ( ω ) ≤ 1 .

Sketch the magnitude spectrum and confirm that it satisfies the design
specifications.

7.15 Repeat Problem 7.14 for the Type I Chebyshev filter.

7.16 Repeat Problem 7.14 for the Type II Chebyshev filter.

7.17 Design a Butterworth bandpass filter for the following specifications:

stop band I (0 ≤ξ ≤ 100 radians/s) 20 log 10 H ( ω ) ≤− 15;

pass band (100 ≤ξ ≤ 150 radians/s) − 1 ≤ 20 log 10 H ( ω ) ≤ 0;

stop band II ( ξ ≥ 175 radians/s) 20 log 10 H ( ω ) ≤− 15 .

Sketch the magnitude spectrum and confirm that it satisfies the design
specifications.

7.18 Repeat Problem 7.17 for the Type I Chebyshev filter.