What is the factor to be multiplied to the dc gain of the filter to obtain filter magnitude at cutoff frequency?(a) 1(b) √2(c) 1/√2(d) 1/2I got this question in an online interview.I would like to ask this question from Butterworth Filters in chapter Digital Filters Design of Digital Signal Processing

What is the factor to be multiplied to the dc gain of the filter to ob

1.	What is the factor to be multiplied to the dc gain of the filter to obtain filter magnitude at cutoff frequency?(a) 1(b) √2(c) 1/√2(d) 1/2I got this question in an online interview.I would like to ask this question from Butterworth Filters in chapter Digital Filters Design of Digital Signal Processing
Answer» CORRECT ANSWER is (C) 1/√2 The best I can explain: The dc gain of the filter is the filter magnitude at Ω=0. We know that the filter magnitude is given by the equation \|H(jΩ)\|=\(\frac{1}{\SQRT{1+(\frac{Ω}{Ω_C})^{2N}}}\) At Ω=ΩC, \|H(jΩC)\|=1/√2=1/√2(\|H(jΩ)\|) THUS the filter magnitude at the cutoff frequency is 1/√2 times the dc gain.

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