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If NB and NC are the orders of the Butterworth and Chebyshev filters respectively to meet the same frequency specifications, then which of the following relation is true?

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If NB and NC are the orders of the Butterworth and Chebyshev filters respectively to meet the same frequency specifications, then which of the following relation is true?

(a) NC=NB

(b) NC<NB

(c) NC>NB

(d) Cannot be determined

This question was addressed to me in examination.

My doubt stems from Chebyshev Filters topic in chapter Digital Filters Design of Digital Signal Processing

1 Answer

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The correct choice is (b) NC<NB

Explanation: The equi-ripple property of the chebyshev filter yields a narrower transition band compared with that obtained when the magnitude response is monotone. As a consequence of this, the order of a chebyshev filter needed to achieve the given frequency domain specifications is usually lower than that of a Butterworth filter.

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