1.

Which of the following equation is True?(a) \([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}+1\)(b) \([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{K_S/10}+1\)(c) \([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}-1\)(d) None of the mentionedThe question was asked in an international level competition.The question is from Design of Low Pass Butterworth Filters topic in section Digital Filters Design of Digital Signal Processing

Answer»

The correct answer is (b) \([\FRAC{\Omega_S}{\Omega_C} ]^{2N} = 10^{K_S/10}+1\)

To EXPLAIN I WOULD say: We KNOW that,

KP=-10 \(log⁡[1+(\frac{\Omega_S}{\Omega_C})^{2N}]\)

=>\([\frac{Ω_S}{Ω_C}]^{2N} = 10^{\frac{-K_S}{10}}-1\)



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