2. (1) Filter is lowpass.(2) Filter is passive.(3) Passband transition frequency is 4.79. Stopband transition frequency is 20.88.(4) Roll-off ratio is 4.36. Consider a linear time-invariant system such as [H(jw)|=120,000/ 160,000 + 16w^4. Assume the passband attenuationlevel is 95% of peak & the stopband attenuation level is 5% ofpeak.A) characterize the filter as lowpass, highpass, bandpass, orbandstop.B) characterize the filter as active or passive.C) determine the passband and stopband transition frequency/frequencies.D) determine the roll-off ratio/ratios.

Answered: Consider a linear time-invariant system…

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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2. (1) Filter is lowpass.
(2) Filter is passive.
(3) Passband transition frequency is 4.79. Stopband transition frequency is 20.88.
(4) Roll-off ratio is 4.36.

Consider a linear time-invariant system such as [H(jw)|=
120,000/ 160,000 + 16w^4. Assume the passband attenuation
level is 95% of peak & the stopband attenuation level is 5% of
peak.
A) characterize the filter as lowpass, highpass, bandpass, or
bandstop.
B) characterize the filter as active or passive.
C) determine the passband and stopband transition frequency/
frequencies.
D) determine the roll-off ratio/ratios.

Expert Solution

Step 1

$|H (j ω)| = \frac{120000}{160000 + 16 ω^{4}}$

To characterize whether the given filter is low pass, high pass or band pass or band stop; Compute the gain at the frequencies shown below;

$A t ω = 0; {|H (j ω)|}_{ω = 0} = \frac{120000}{160000 + 16 {(0)}^{4}} = \frac{3}{4} A t ω = \infty; {|H (j ω)|}_{ω = 0} = \frac{120000}{160000 + 16 {(\frac{1}{0})}^{4}} = 0$

It is observed that the gain is finite at low frequency and it drops to zero as the frequency approaches infinity. The filter can therefore be classified to be a low pass filter, since gain exists for lower values of frequencies.

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