1.

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/secI 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»

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.



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