Question

What is the equation for magnitude frequency response |H(jΩ)| of a low pass chebyshev-I filter?

(a) \(\frac{1}{\sqrt{1-ϵ T_N^2 (\frac{Ω}{Ω_P})}}\)

(b) \(\frac{1}{\sqrt{1+ϵ T_N^2 (\frac{Ω}{Ω_P})}}\)

(c) \(\frac{1}{\sqrt{1-ϵ^2 T_N^2 (\frac{Ω}{Ω_P})}}\)

(d) \(\frac{1}{\sqrt{1+ϵ^2 T_N^2 (\frac{Ω}{Ω_P})}}\)

This question was posed to me in unit test.

This interesting question is from Chebyshev Filters in chapter Digital Filters Design of Digital Signal Processing

Answer 1

The correct option is (d) \(\frac{1}{\sqrt{1+ϵ^2 T_N^2 (\frac{Ω}{Ω_P})}}\)

The explanation is: The magnitude frequency response of a low pass chebyshev-I filter is given by

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

where ϵ is a parameter of the filter related to the ripple in the pass band and TN(x) is the N^th order chebyshev polynomial.