Question

What is the Butterworth polynomial of order 1?

(a) s-1

(b) s+1

(c) s

(d) none of the mentioned

This question was addressed to me during an online exam.

Query is from Butterworth Filters in section Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (b) s+1

Explanation: Given that the order of the Butterworth low pass filter is 1.

Therefore, for N=1 Butterworth polynomial is given as B3(s)=(s-s0).

We know that, sk=\(e^{jπ(\frac{2k+1}{2N})} e^{jπ/2}\)

=> s0=-1

=> B1(s)=s-(-1)=s+1.