Question

What is the cutoff frequency of the Butterworth filter with a pass band gain KP=-1 dB at ΩP=4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS=8 rad/sec?

(a) 3.5787 rad/sec

(b) 1.069 rad/sec

(c) 6 rad/sec

(d) 4.5787 rad/sec

I got this question during an interview.

The origin of the question is Design of Low Pass Butterworth Filters in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (d) 4.5787 rad/sec

The explanation: We know that the equation for the cutoff frequency of a Butterworth filter is given as

ΩC = \(\frac{\Omega_P}{(10^{-K_P/10}-1)^{1/2N}}\)

We know that KP=-1 dB, ΩP=4 rad/sec and N=5

Upon substituting the values in the above equation, we get

ΩC=4.5787 rad/sec.