Question

What is the expression for cutoff frequency in terms of pass band gain?

(a) \(\frac{\Omega_P}{(10^{-K_P/10}-1)^{1/2N}}\)

(b) \(\frac{\Omega_P}{(10^{-K_P/10}+1)^{1/2N}}\)

(c) \(\frac{\Omega_P}{(10^{K_P/10}-1)^{1/2N}}\)

(d) None of the mentioned

I have been asked this question in examination.

This key question is from Design of Low Pass Butterworth Filters topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (a) \(\frac{\Omega_P}{(10^{-K_P/10}-1)^{1/2N}}\)

Explanation: We know that,

\([\frac{Ω_P}{Ω_C}]^{2N} = 10^{-K_P/10}-1\)

=> \(Ω_C = \frac{Ω_P}{(10^{-K_P/10}-1)^{1/2N}}\).