STUPIDSID
1 (a)
Determine whether the following signals are energy signals or power signals? Calculate their energy of power [ i) x(t)=Acos (2pi f_0 t+ heta) \ ii) x(n)=left ( dfrac {1}{4} ight )^n u(n) ]
5 M
1 (b)
Let x(n)=u(n+1)-u(n-5). Find and sketch even and odd parts of x(n).
5 M
1 (c)
Mention and explain the conditions for the system to be called as IIR.
5 M
1 (d)
State and explain Gibbs phenomenon.
5 M
2 (a)
i) plot the signals with respect to time.
x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)+u(t-4)-2u(t-5)
ii) Find the even and odd parts of the signal.
x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)+u(t-4)-2u(t-5)
ii) Find the even and odd parts of the signal.
10 M
2 (b)
State and prove the following properties of the Fourier transformation
i) Frequency Differentiation and time integration.
i) Frequency Differentiation and time integration.
10 M
3 (a)
An analog signal x(t) is given by x(t)=2cos(2000π)+3sin(6000πt)+8cos(12000πt)
i) Calculate Nyquist sampling rate.
ii) if x(t) is sampled at the rate F(s)=5KHz. What is the discrete time signal obtained after sampling.
iii) What is the analog signal y(t) we can reconstruct from the samples if the ideal interpolation is used.
i) Calculate Nyquist sampling rate.
ii) if x(t) is sampled at the rate F(s)=5KHz. What is the discrete time signal obtained after sampling.
iii) What is the analog signal y(t) we can reconstruct from the samples if the ideal interpolation is used.
10 M
3 (b)
Find the Laplace Transform of the signals shown below.
10 M
4 (a)
Obtain the transfer function of the system defined by the following state space equations [ egin{bmatrix}x1(t)\x2(t) \x3(t) end{bmatrix} = egin{bmatrix}-1 &1 &-1 \0 &-2 &1 \0 &0 &-3
end{bmatrix} egin{bmatrix}x1(t)\x2(t) \x3(t)
end{bmatrix}+ egin{bmatrix} 1 &0 \0 &1 \1 &0
end{bmatrix} egin{bmatrix}u1(t)\u2(t)
end{bmatrix} egin{bmatrix}y1(t)\y2(t)
end{bmatrix}= egin{bmatrix}1 &1 &1 \0 &1 &1
end{bmatrix}egin{bmatrix}x1(t)\x2(t) \x3(t)
end{bmatrix} ]
10 M
4 (b)
Find the state equation and output equation for the system given by [ G(s)=dfrac {1}{s^3+4s^2+3s+3} ]
10 M
5 (a)
Find the Fourier series for the function x(t) defined by [ x(t)= egin{Bmatrix} 0 &dfrac {-T}{2}
10 M
5 (b)
Obtain the Fourier transform of rectangular pulse of duration 2 second and having a magnitude of 10 volts.
10 M
6 (a)
Develop cascade and parallel realization structure for [ H(z)= dfrac {frac {z}{6}+ frac {5}{24}z^{-1}+ frac {1}{24}z^{-2}}{1-frac {1}{2}z^{-1}+ frac {1}{4}z^{-2}} ]
10 M
6 (b)
Determine the system function, unit sample response and pole zero plot of the system described by the difference equation y(n)-1/2 y(n-1)=2x(n) and also comment on type of the system.
10 M
7 (a)
Explain the relationship between the Laplace transform and Fourier transform.
7 M
7 (b)
State properties of state transition matrix.
6 M
7 (c)
State and discuss the properties of the region of convergence for Z-transform.
7 M
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