1(a)
Check for periodicity of the following signals. Also find the new period.
(i) x(t)=3cos(15πt)+4cos(35πt−π4)+8sin(55πt)
(ii) x(n)=3cos2(π6n)+2cos2(π4n)
(i) x(t)=3cos(15πt)+4cos(35πt−π4)+8sin(55πt)
(ii) x(n)=3cos2(π6n)+2cos2(π4n)
4 M
1(b)
Determine whether the given signal is energy or power signal. Hence obtain its energy power accordingly.
\( (i)\ x(t)=4\sin t-\infty
(ii) x(n)=(37)nu(n)
\( (i)\ x(t)=4\sin t-\infty
(ii) x(n)=(37)nu(n)
4 M
1(c)
Plot x(t) = u(t) ' r(t) + r(t-1). Hence plot its even and odd parts also.
4 M
1(d)
Prove time shifting of Z-transform.
4 M
1(e)
Check for Dynamicity, Linearity, Time variance, causality of the system.
(i) y(t) = t x(t) + x (t-1)
(ii) y(n) = 3x (-n) + 4.
(i) y(t) = t x(t) + x (t-1)
(ii) y(n) = 3x (-n) + 4.
4 M
2(a)
Obtain inverse Z-transform for all possible ROC's. Also comment on Causality and Stability in each case. H(z)=z(3z−7)(z−14)(z+2)
10 M
2(b)
State and prove Time Shifting and Convolution property of Continous Time Fourier Transform.
10 M
3(a)
Obtain graphical concolution of following two signals.
10 M
3(b)
Obtain exponential Fourier series of the following signal.
10 M
4(a)
Determine h(t) for all possible ROC's.
If T.F.=H(s)=2s+7(s+2)(s−3)
Also comment on Causality and Stability of the system for each case.
If T.F.=H(s)=2s+7(s+2)(s−3)
Also comment on Causality and Stability of the system for each case.
10 M
4(b)
A causal DT LTI system is described as
y(n) = 3y(n-2) + 4y(n-1) +x(n)
Obtain:
(1) T.F. of system
(2) Obtain step response
(3) Obtain response if input x(n)=(12)nu(n)
(4) Also plot pole's and zeros of the T.F. and comment on causality and stability.
y(n) = 3y(n-2) + 4y(n-1) +x(n)
Obtain:
(1) T.F. of system
(2) Obtain step response
(3) Obtain response if input x(n)=(12)nu(n)
(4) Also plot pole's and zeros of the T.F. and comment on causality and stability.
10 M
5(a)
Determine Impluse response and step response of a CT LTI system. d2y(t)dt2+7dy(t)dt+12y(t)=x(t)
10 M
5(b)
Obtain auto-correlation of following signals
(i) x(t)=3e−2tu(t)
(ii) x(n)=(34)nu(n)
(i) x(t)=3e−2tu(t)
(ii) x(n)=(34)nu(n)
10 M
6(a)
Obtain DT Fourier Transform of following signal h(n) = [2 1 2] plot its magnitude and phase spectrum.
10 M
6(b)
Obtain :
(i) Z- transform of x(n)=n(34)nu(n)+u(n−1)
(ii) Laplace transform of x(t) = t . e-3t u(t) + t u (t-1)
Use properties of transform only.
(i) Z- transform of x(n)=n(34)nu(n)+u(n−1)
(ii) Laplace transform of x(t) = t . e-3t u(t) + t u (t-1)
Use properties of transform only.
10 M
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