1 (a)
Determine whether the signals are power or energy signals.
(i) x(t)=0.9e-3t u(t)
(ii) x[n]=u[n]
(i) x(t)=0.9e-3t u(t)
(ii) x[n]=u[n]
4 M
1 (b)
Convolve h[n] = n+1; 0 ≤ n ≤ 3 with
x[n] = n2; 0 ≤ n ≤ 2.
x[n] = n2; 0 ≤ n ≤ 2.
4 M
1 (c)
Given Equation: y(t)=2r(t)-2r(t-1)-2u(t-3)
Sketch y(t) and odd part of y(t).
Sketch y(t) and odd part of y(t).
4 M
1 (d)
Determine whether each of the signals is periodic. If so find its fundamental period-
4 M
1 (e)
Check Dynamicity, Linearity, Time variance and Causality of
y[n] = x[n] + x[n+2]
y[n] = x[n] + x[n+2]
4 M
2 (a)
Determine the exponential Fourier Series of the signal x(t).
10 M
2 (b)
Perform convolution of :
(i) 2u(t) with u(t) (2 marks)
(ii) e2t u(t) with e-5t u(t) (4 marks)
(iii) tu(t) with e-5t u(t) (4 marks)
(i) 2u(t) with u(t) (2 marks)
(ii) e2t u(t) with e-5t u(t) (4 marks)
(iii) tu(t) with e-5t u(t) (4 marks)
10 M
3 (a)
Sketch
x(t) = t ; 0= 1 ; 1= 3-t ; 2Then sketch
(i) x(2-t)
(ii) x(t-3)
(iii) x(2t)
(iv) 0.5x(-t)
x(t) = t ; 0
(i) x(2-t)
(ii) x(t-3)
(iii) x(2t)
(iv) 0.5x(-t)
10 M
3 (b)
Consider an analog signal:
x(t) = 5cos(50πt) + 2sin(200πt) - 2cos(100πt)
(i) Determine Nyquist Sampling Rate. (2 marks)
(ii) If the given x(t) is sampled at the rate of 200Hz, what is the discrete time signal obtained after sampling? (3 marks)
x(t) = 5cos(50πt) + 2sin(200πt) - 2cos(100πt)
(i) Determine Nyquist Sampling Rate. (2 marks)
(ii) If the given x(t) is sampled at the rate of 200Hz, what is the discrete time signal obtained after sampling? (3 marks)
5 M
3 (c)
Find the DTFT of x[n] = {2,1,2} and compute its magnitude at ω = 0 and ω = π/2.
5 M
4 (a)
Find the Z-Transform
(i) x[n] = (0.1)nu[n] + (0.3)nu[-n-1]
(ii) x[n]=(0.5)n[u[n] - u[n-2]].
(i) x[n] = (0.1)nu[n] + (0.3)nu[-n-1]
(ii) x[n]=(0.5)n[u[n] - u[n-2]].
5 M
4 (b)
Prove convolution property of Z-Transform.
5 M
4 (c)
Determine the response of an LTI discrete time system governed by the difference equation
y[n] - 2y[n-1] - 3y[n-2] = x[n] + 4x[n-1] for the input
x[n]=2nu[n] with initial conditions
y[-2] = 0, y[-1] = 5.
y[n] - 2y[n-1] - 3y[n-2] = x[n] + 4x[n-1] for the input
x[n]=2nu[n] with initial conditions
y[-2] = 0, y[-1] = 5.
10 M
5 (a)
(i) Using Laplace Transform, determine the total response of the system described by the equation
y''(t) + 5y'(t) + 4y(t) = x'(t).
The initial conditions are y(0)=0 and y'(0)=1. The input to the system is x(t)=e-2tu(t). (6 marks)
(ii) Also find the Impulse Response of the above system assuming initial conditions = 0. (4 marks)
y''(t) + 5y'(t) + 4y(t) = x'(t).
The initial conditions are y(0)=0 and y'(0)=1. The input to the system is x(t)=e-2tu(t). (6 marks)
(ii) Also find the Impulse Response of the above system assuming initial conditions = 0. (4 marks)
10 M
5 (b)
Realize Direct Form I, Direct Form II first order cascade and first order parallel structures
10 M
6 (a)
Find x[n] if
![](data:image/png;base64,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)
(i) ROC: |z|> 1/3
(ii) ROC: 1/4 < |z| < 1/3
(iii) ROC: |z|< 1/4
(i) ROC: |z|> 1/3
(ii) ROC: 1/4 < |z| < 1/3
(iii) ROC: |z|< 1/4
10 M
6 (b)
Prove time shifting property of Fourier Transform.
5 M
6 (c)
Determine the unit step response of the system whose impulse response is given as h(t) = 3u(t).
5 M
7 (a)
The state space representation of a discrete time system is given as-
![](data:image/png;base64,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)
Derive the transfer function H(z) of the system.
Derive the transfer function H(z) of the system.
10 M
7 (b)
Using suitable method obtain the state transition matrix φ(t) for the system matrix.
10 M
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