What is the system function of the Butterworth filter with specifications as pass band gain KP= -1 dB at andOmega;P= 4 rad/sec and stop band attenuation greater than or equal to 20dB at andOmega;S= 8 rad/sec?a)b)c)d)None of the mentionedCorrect answer is option 'C'. Can you explain this answer? - EduRev Electrical Engineering (EE) Question

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What is the system function of the Butterworth filter with specifications as 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)
b)
c)
d)
None of the mentioned

Correct answer is option 'C'. Can you explain this answer?

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What is the system function of the Butterworth filter with specificati...

Explanation: From the given question,
KP= -1 dB, ΩP= 4 rad/sec, KS= -20 dB and ΩS= 8 rad/sec
We find out order as N=5 and Ω_C = 4.5787 rad/sec
We know that for a 5th order normalized low pass Butterworth filter, system equation is given as

The specified low pass filter is obtained by applying low pass-to-low pass transformation on the normalized low pass filter.
That is, Ha(s)=H5(s)|s→s/Ωc
= H5(s)|s→s/4.5787
upon calculating, we get option c.

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What is the system function of the Butterworth filter with specifications as 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)b)c)d)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?

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