5. The figure below shows a system consisting of a continous-time LTI system followed by a sampler ( p(t) = ER=8(t – nT)), conversion to a sequence ( y(n) = E y. (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: k=+o, + 2dy.(t) dt d²yc(t) + yc(t) = xc(t). dt2 The input x.(t) is a unit impulse 8(t). a. Determine y.(t). Determine the frequency response H(el") and the impulse response h(n) such that w(n) = 8(n). x(t) Ye (t) Conversion y(n) of w(n) LTI LTI impulse train to a sequence H(ew) P(t)

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5. The figure below shows a system consisting of a continous-time LTI system followed by a
sampler ( p(t) = EE(t – nT)), conversion to a sequence ( y(n) = E y. (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 :
+ 2dy.(t)
+ yc(t) = x.(t).
dt2
dt
The input x-(t) is a unit impulse 8 (t).
a. Determine y.(t).
Determine the frequency response H(el") and the impulse response h(n) such that w(n) =
8 (n).
b.
Conversion y(n)
of
impulse train
to
a sequence
*-(t)
Ye(t)
w(n)
LTI
LTI
H(ew)
p(t)
Transcribed Image Text:5. The figure below shows a system consisting of a continous-time LTI system followed by a sampler ( p(t) = EE(t – nT)), conversion to a sequence ( y(n) = E y. (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 : + 2dy.(t) + yc(t) = x.(t). dt2 dt The input x-(t) is a unit impulse 8 (t). a. Determine y.(t). Determine the frequency response H(el") and the impulse response h(n) such that w(n) = 8 (n). b. Conversion y(n) of impulse train to a sequence *-(t) Ye(t) w(n) LTI LTI H(ew) p(t)
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