Question

If δ2 represents the ripple in the stop band for a chebyshev filter, then which of the following conditions is true?

(a) 1-δ2 ≤ Hr(ω) ≤ 1+δ2;|ω|≤ωs

(b) 1+δ2 ≤ Hr(ω) ≤ 1-δ2;|ω|≥ωs

(c) δ2 ≤ Hr(ω) ≤ δ2;|ω|≤ωs

(d) -δ2 ≤ Hr(ω) ≤ δ2;|ω|≥ωs

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Question is taken from Design of Optimum Equi Ripple Linear Phase FIR Filters in portion Digital Filters Design of Digital Signal Processing

Answer 1

The correct choice is (d) -δ2 ≤ Hr(ω) ≤ δ2;|ω|≥ωs

The explanation: Let us consider the design of a low pass filter with the stop band edge frequency ωs and the ripple in the stop band is δ2, then from the general specifications of the chebyshev filter, in the stop band the filter frequency response should satisfy the condition

-δ2 ≤ Hr(ω) ≤ δ2;|ω|≥ωs