Question

What is the order of a low pass Butterworth filter that has a -3dB bandwidth of 500Hz and an attenuation of 40dB at 1000Hz?

(a) 4

(b) 5

(c) 6

(d) 7

This question was posed to me in an interview for internship.

Asked question is from Characteristics of Commonly Used Analog Filters in portion Digital Filters Design of Digital Signal Processing

Answer 1

The correct option is (d) 7

To explain: Given Ωc=1000π and Ωs=2000π

For an attenuation of 40dB, δ2=0.01. We know that

N=\(\frac{log⁡[(\frac{1}{δ_2^2})-1]}{2log⁡[\frac{Ω_s}{Ω_s}]}\)

Thus by substituting the corresponding values in the above equation, we get N=6.64

To meet the desired specifications, we select N=7.