Question

If H(s)=\(\frac{1}{s^2+s+1}\) represent the transfer function of a low pass filter (not Butterworth) with a pass band of 1 rad/sec, then what is the system function of a stop band filter with a stop band of 2 rad/sec and a center frequency of 10 rad/sec?

(a) \(\frac{(s^2+100)^2}{s^4+2s^3+204s^2+200s+10^4}\)

(b) \(\frac{(s^2+10)^2}{s^4+2s^3+204s^2+200s+10^4}\)

(c) \(\frac{(s^2+10)^2}{s^4+2s^3+400s^2+200s+10^4}\)

(d) None of the mentioned

This question was posed to me in semester exam.

This question is from Design of Low Pass Butterworth Filters topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Correct answer is (a) \(\frac{(s^2+100)^2}{s^4+2s^3+204s^2+200s+10^4}\)

Explanation: The low pass-to- band stop transformation is

\(s\rightarrow\frac{s(Ω_u-Ω_l)}{s^2+Ω_u Ω_l}\)

Hence the required band stop filter is

Ha(s)=\(\frac{(s^2+100)^2}{s^4+2s^3+204s^2+200s+10^4}\)