Question

If δ1 represents the ripple in the pass band for a chebyshev filter, then which of the following conditions is true?

(a) 1-δ1 ≤ Hr(ω) ≤ 1+δ1; |ω|≤ωP

(b) 1+δ1 ≤ Hr(ω) ≤ 1-δ1; |ω|≥ωP

(c) 1+δ1 ≤ Hr(ω) ≤ 1-δ1; |ω|≤ωP

(d) 1-δ1 ≤ Hr(ω) ≤ 1+δ1; |ω|≥ωP

I got this question during an online interview.

The question is from Design of Optimum Equi Ripple Linear Phase FIR Filters topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Correct option is (a) 1-δ1 ≤ Hr(ω) ≤ 1+δ1; |ω|≤ωP

Best explanation: Let us consider the design of a low pass filter with the pass band edge frequency ωP and the ripple in the pass band is δ1, then from the general specifications of the chebyshev filter, in the pass band the filter frequency response should satisfy the condition

1- δ1 ≤ Hr(ω) ≤ 1+δ1; |ω|≤ωP