STUPIDSID
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
(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-
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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