The figure below shows a system consisting of a continous-time LTI system followed by a sampler ( p(t) = E 8(t – nT)), conversion to a sequence ( y(n) = E=yc (k)8(n – k) ), and an LTI discrete-time system. The continous-time LTI system is causal and satisfies the linear, constant-coefficient differential equation : - d?yc(t) dt2 + 2dyc(t) dt + y.(t) = xc(t). The input x(t) is a unit impulse 8(t). a. Determine y.(t).

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Determine the frequency response H(el®) and the impulse response h(n) such that w(n) =
8(n).
b.
Conversion y(n)
of
x,(t)
Ye(t)
w(n)
LTI
LTI
impulse train
to
a sequence
H(ejw)
P(t)
Transcribed Image Text:Determine the frequency response H(el®) and the impulse response h(n) such that w(n) = 8(n). b. Conversion y(n) of x,(t) Ye(t) w(n) LTI LTI impulse train to a sequence H(ejw) P(t)
5. The figure below shows a system consisting of a continous-time LTI system followed by a
sampler ( p(t) = E 8(t – nT)), conversion to a sequence ( y(n) = EEyc (k)8(n –
k) ), and an LTI discrete-time system. The continous-time LTI system is causal and satisfies the
linear, constant-coefficient differential equation :
d?yc(t)
+ 2"
dt
dyc(t)
+ yc(t) =
xc(t).
dt2
The input x.(t) is a unit impulse 8 (t).
a. Determine y.(t).
Transcribed Image Text:5. The figure below shows a system consisting of a continous-time LTI system followed by a sampler ( p(t) = E 8(t – nT)), conversion to a sequence ( y(n) = EEyc (k)8(n – k) ), and an LTI discrete-time system. The continous-time LTI system is causal and satisfies the linear, constant-coefficient differential equation : d?yc(t) + 2" dt dyc(t) + yc(t) = xc(t). dt2 The input x.(t) is a unit impulse 8 (t). a. Determine y.(t).
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