1.

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 mentionedI 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»

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.


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