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 mentionedI 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

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

1.	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 mentionedI 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» RIGHT answer is (a) \(\frac{\Omega_P}{(10^{-K_P/10}-1)^{1/2N}}\) Explanation: We know that, \([\frac{Ω_P}{Ω_C}]^{2N} = 10^{-K_P/10}-1\) => \(Ω_C = \frac{Ω_P}{(10^{-K_P/10}-1)^{1/2N}}\).

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