What is the magnitude frequency response of a Butterworth filter of order N and cutoff frequency ΩC?(a) \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)(b) \(1+(\frac{Ω}{Ω_C})^{2N}\)(c) \(\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}\)(d) None of the mentionedThis question was posed to me by my college professor while I was bunking the class.My doubt stems from Butterworth Filters topic in section Digital Filters Design of Digital Signal Processing

What is the magnitude frequency response of a Butterworth filter of or

1.	What is the magnitude frequency response of a Butterworth filter of order N and cutoff frequency ΩC?(a) \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)(b) \(1+(\frac{Ω}{Ω_C})^{2N}\)(c) \(\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}\)(d) None of the mentionedThis question was posed to me by my college professor while I was bunking the class.My doubt stems from Butterworth Filters topic in section Digital Filters Design of Digital Signal Processing
Answer» Right CHOICE is (a) \(\FRAC{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\) To elaborate: A BUTTERWORTH is characterized by the magnitude frequency response \|H(jΩ)\|=\(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\) where N is the order of the filter and ΩC is defined as the cutoff frequency.

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