STUPIDSID
1 (a)
Determine the fundamental period of the following signals. x(t)=14+40cos(60πt)ii)x[n]=cos2[π4n]
4 M
1 (b)
Compare the nature of ROC of Z transform and Laplace transform.
4 M
1 (c)
For the given system, determine whether it is,
i) memory less
ii) causal
linear
iv) time-invariant.
y[n] = x[-n].
i) memory less
ii) causal
linear
iv) time-invariant.
y[n] = x[-n].
4 M
1 (d)
"Find out even and odd component of the following two signals. i) x(t)=cos2πt2ii)x(t)={t⋯⋯0≤t≤12−t⋯⋯1<2≤2"
4 M
1 (e)
Determine whether the signals are power or energy signals. Calculate energy / power accordingly.
i) x(t)=Ae-αtu(t)........... α>0.
ii) x[n]=u[n].
i) x(t)=Ae-αtu(t)........... α>0.
ii) x[n]=u[n].
4 M
2 (a)
Expand the periodic gate function as shown in the figure by the exponential Fourier Series. Also plot the Fourier spectrum (Magnitude and phase spectrum).
10 M
2 (b)
Find the inverse Laplace Transform of the following: i) X(S)=s−3s2+4s+13ii) X(S)=5s2−15−11(s+1)(s−2)3
10 M
3 (a)
Obtain inverse Laplace transform of the function X(s)=3S+7s2−2s−3 Write down and sketch possible ROCs. Find out inverse Laplace for all the possible ROCs.
10 M
3 (b)
Using the z transform method, solve the difference equation
y[n]-4y[n-1]+4y[n-2]=x[n]-x[n-1]
When y(-1)=y(-2)=0.
y[n]-4y[n-1]+4y[n-2]=x[n]-x[n-1]
When y(-1)=y(-2)=0.
10 M
4 (a)
Explain Gibbs phenomenon. Also explain conditions necessary for the convergence of Fourier Series.
5 M
4 (b)
Find out Fourier Transform of f(t)=10 δ(t-2). Sketch its amplitude and phase spectrum.
5 M
4 (c)
Perform convolution of
i) 2u(t) with u(t)
ii) e-2t u(t) with e-5t u(t)
iii) tu(t) with e-5t u(t).
i) 2u(t) with u(t)
ii) e-2t u(t) with e-5t u(t)
iii) tu(t) with e-5t u(t).
10 M
5 (a)
Convolve x[n]=(13)nu[n] with h[n]=(12)nu[n] using Fourier transform.
10 M
5 (b)
A system is described by the following difference equation. y[n]=34y[n−1]−18y[n−2]+x[n] Determine the following.
i) The system Transfer function H(2)
ii) Impulse response of the system h[n]
iii) Step response of the system s[n].
i) The system Transfer function H(2)
ii) Impulse response of the system h[n]
iii) Step response of the system s[n].
10 M
6 (a)
A discrete time signal is given by x[n]={,11,1,1,2} . Sketch the following signals.
i) x[n]
ii) x[n-2]
iii) x[n] ⋅ u[n-1]
iv) x[3-n]
v) x[n-1]⋅δ[n-1]
i) x[n]
ii) x[n-2]
iii) x[n] ⋅ u[n-1]
iv) x[3-n]
v) x[n-1]⋅δ[n-1]
10 M
6 (b)
For the periodic signal x[n] given below, find out Fourier series coefficient. x[n]=1+sin(2πN)n+3cos(2πN)n+cos(4πN+π2).
10 M
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