Question

What is the transfer function of Butterworth low pass filter of order 2?

(a) \(\frac{1}{s^2+\sqrt{2} s+1}\)

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

(c) \(s^2-\sqrt{2} s+1\)

(d) \(s^2+\sqrt{2} s+1\)

The question was asked in a job interview.

Query is from Butterworth Filters topic in division Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (a) \(\frac{1}{s^2+\sqrt{2} s+1}\)

Explanation: We know that the Butterworth polynomial of a 2^nd order low pass filter is

B2(s)=s^2+√2 s+1

Thus the transfer function is given as \(\frac{1}{s^2+\sqrt{2} s+1}\).