(2) Consider a LTI system with the following transfer function H.(s) = N,(s)/D.(*), where D.(s) = + (12/Q)s + Na(*) = k(12o/Q)*), %3D k= 5, Q= 4, and flo 4000x rad./see. (a) Derive expresesions for the magnitude and phase responses. Hence, plot it in order to determine the type of filter. What is it? (b) Find the poles and zeros of the filter. Is the filter stable? Why? (c) Determine the frequency at which the magnitude response is maximum.

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(2) Consider a LTI system with the following transfer function
H.(s) = Na(s)/D.(s),
where
D.(s) = + (2/Q)x +.
N(s) = k((!lo/Q)s),
k = 5, Q = 4, and flo = 4000x rad./see.
(a) Derive expressions for the magnitude and phase responses. Hence, plot it in order to
determine the type of filter. What is it?
(b) Find the poles and zeros of the filter. Is the filter stable? Why?
(c) Determine the frequency at which the magnitude response is maximum.
(d) Plot the magnitude response in dB, hence find the 3-dB band-width in Hz.
Transcribed Image Text:(2) Consider a LTI system with the following transfer function H.(s) = Na(s)/D.(s), where D.(s) = + (2/Q)x +. N(s) = k((!lo/Q)s), k = 5, Q = 4, and flo = 4000x rad./see. (a) Derive expressions for the magnitude and phase responses. Hence, plot it in order to determine the type of filter. What is it? (b) Find the poles and zeros of the filter. Is the filter stable? Why? (c) Determine the frequency at which the magnitude response is maximum. (d) Plot the magnitude response in dB, hence find the 3-dB band-width in Hz.
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