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 low pass filter with a pass band 10 rad/sec?

(a) \(\frac{100}{s^2+10s+100}\)

(b) \(\frac{s^2}{s^2+s+1}\)

(c) \(\frac{s^2}{s^2+10s+100}\)

(d) None of the mentioned

The question was posed to me by my college director while I was bunking the class.

My doubt stems from Design of Low Pass Butterworth Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

The correct option is (a) \(\frac{100}{s^2+10s+100}\)

The best explanation: The low pass-to-low pass transformation is

s→s/Ωu

Hence the required low pass filter is

Ha(s)=H(s)|s→s/10

=\(\frac{100}{s^2+10s+100}\).