Question

What is the Butterworth polynomial of order 3?

(a) (s^2+s+1)(s-1)

(b) (s^2-s+1)(s-1)

(c) (s^2-s+1)(s+1)

(d) (s^2+s+1)(s+1)

I got this question in an interview for job.

My question comes from Butterworth Filters in division Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (d) (s^2+s+1)(s+1)

The explanation is: Given that the order of the Butterworth low pass filter is 3.

Therefore, for N=3 Butterworth polynomial is given as B3(s)=(s-s0) (s-s1) (s-s2)

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

=> s0=(-1/2)+j(√3/2), s1= -1, s2=(-1/2)-j(√3/2)

=> B3(s)= (s2+s+1)(s+1).