Question

What is the value of magnitude frequency response of a Butterworth low pass filter at Ω=0?

(a) 0

(b) 1

(c) 1/√2

(d) None of the mentioned

I got this question during an online interview.

This key question is from Butterworth Filters in section Digital Filters Design of Digital Signal Processing

Answer 1

The correct answer is (b) 1

Easiest explanation: The magnitude frequency response of a Butterworth low pass filter is given as

|H(jΩ)|=\(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)

At Ω=0 => |H(jΩ)|=1 for all N.