What is the expression for cutoff frequency in terms of stop band gain?(a) \(\frac{\Omega_S}{(10^{-K_S/10}-1)^{1/2N}}\)(b) \(\frac{\Omega_S}{(10^{-K_S/10}+1)^{1/2N}}\)(c) \(\frac{\Omega_S}{(10^{K_S/10}-1)^{1/2N}}\)(d) None of the mentionedI have been asked this question by my school principal while I was bunking the class.My query is from Design of Low Pass Butterworth Filters in division Digital Filters Design of Digital Signal Processing

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

1.	What is the expression for cutoff frequency in terms of stop band gain?(a) \(\frac{\Omega_S}{(10^{-K_S/10}-1)^{1/2N}}\)(b) \(\frac{\Omega_S}{(10^{-K_S/10}+1)^{1/2N}}\)(c) \(\frac{\Omega_S}{(10^{K_S/10}-1)^{1/2N}}\)(d) None of the mentionedI have been asked this question by my school principal while I was bunking the class.My query is from Design of Low Pass Butterworth Filters in division Digital Filters Design of Digital Signal Processing
Answer» The CORRECT answer is (C) \(\frac{\Omega_S}{(10^{K_S/10}-1)^{1/2N}}\) The explanation is: We know that, \([\frac{Ω_S}{Ω_C}]^{2N} = 10^{-K_S/10}-1\) => \(Ω_C = \frac{Ω_S}{(10^{-K_S/10}-1)^{1/2N}}\).

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