Question

Which of the following is the characteristic equation of a Chebyshev filter?

(a) 1+ϵ^2TN^2(s/j)=0

(b) 1-ϵ^2TN^2(s/j)=0

(c) 1+ϵ TN^2(s/j)=0

(d) None of the mentioned

I had been asked this question in an interview.

I'm obligated to ask this question of Chebyshev Filters in portion Digital Filters Design of Digital Signal Processing

Answer 1

Correct option is (a) 1+ϵ^2TN^2(s/j)=0

For explanation: We know that for a chebyshev filter, we have

|H(jΩ)|=\(\frac{1}{\sqrt{1+ϵ^2 T_N^2(\frac{Ω}{Ω_P})}}\)

=>|H(jΩ)|^2=\(\frac{1}{\sqrt{1+ϵ^2 T_N^2(\frac{Ω}{Ω_P})}}\)

By replacing jΩ by s and consequently Ω by s/j in the above equation, we get

=>|HN(s)|^2=\(\frac{1}{1+ϵ^2 T_N^2 (s/j)}\)

The poles of the above equation is given by the equation 1+ϵ^2TN^2(s/j)=0 which is called as the characteristic equation.