01-04-2014, 11:37 AM
The LNM Institute of Information Technology, NJaipur, Rajasthan Mid Semester Exam
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1) a) Consider a continuous-time linear time-invariant (LTI) system whose response to the signal
x1 (t) in Figure 1(a) is the signal y1 (t) illustrated in Figure 1(b). Determine and sketch the
response of the system to the input x2 (t) depicted in Figure 1©.
b) Determine the energy for each of the following continuous-time signals:
i) x1 (t) = u(t + 3) − u(t − 3), where u(·) denotes the continuous-time unit step function.
1 (t)
ii) x2 (t) = d x
2) Consider a continuous-time LTI system with input x(t) and output y(t) related through the equation
t
y(t) =
e−(t−θ) x(θ − 2)dθ.
−∞
a) Determine the impulse response h(t) for this system.
b) Determine the step response s(t) for this system.
c) Determine the response of the system when the input x(t) = u(t + 1) − u(t − 2), where u(·)
denotes the continuous-time unit step function.
[3+3+4=10 marks]
3) a) A discrete-time periodic signal x[n] is real valued and has a fundamental period N = 5. The
jπ/6
nonzero Fourier series (FS) coefficients for x[n] are a0 = 2, a2 = a∗
, a4 = a∗
−2 = 2e
−4 =
∞
jπ/3
e
. Express x[n] in the form x[n] = A0 + k=1 Ak sin(ωk n + φk ).
b) Consider a discrete-time LTI system with impulse response h[n] = −δ[n + 2] − δ[n + 1] +
δ[n] + δ[n − 1] + δ[n − 2], where δ(·) denotes the discrete-time unit impulse function.