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extc sem4 ss assignments .pdf

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Signal &amp; System (SS) Assignments
 Assignment No. 1
1. Determine whether the following signals are periodic or not. If periodic determine the
fundamental period.
(1) 10sin(12πt)+4sin(18πt)
(2) 4sin(πn)
(3) 7sin(n)
(4) 3sin(t)
(5) 5sin(5πt).sin(18πt)
2. Find the energy and power of following signals
(1) X(t)= Acos(2πft+δ)
(2) X(t)=rect(t/T0)
3. X(n)=(0.5)n u(n). State whether it is an energy or power signal. Justify.
4. Sketch x(t)= u(t)+r(t-1)-2u(t
2u(t-3)+u(t-5).
5. Determine whether the following systems are time invariant or not.
(1) Y(t)=x(t)-3u(t).
(2) Y(n)=x(2n+2)+x(n).
(3) Y(n)=x2(n).
6. Find impulse response of the system described by the following equation.
2y’(t)+3y(t)=x(t).

Update

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 2
1. State and prove all the properties of LTI system.
2. Determine the output of the LTI system given
X(t)= u(t) &amp; h(t)= u(t-2).
u(t
3. A discrete –time
time signal is shown below: sketch and label carefully each of the
following signal:
a) X[n-4]
b) X[3-n].
c) X[3n]
d) X[3n+1]
e) X[n-2]δ[n-2].
f) X[(n-1)2]
4. Continuous time system with input x(t) and output y(t) related by
Y((t)=x(sin(t))
(1) Is this system causal?
(2) Is this system time-invariant?
5. Express each complex no. in polar form: a) 1+j

(b) (1-j)2 (c) (1+j)/(1
(1+j)/(1-j)

Update

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 3
1. Explain Dirichlet’s condition for the existence of Fourier series.
2. Obtain the quadrature Fourier series for the rectangular Fourier series shown below:
3. Obtain the Fourier series of the unit impulse train shown below. Also plot the
amplitude and phase spectrum for the same.
4. State and prove all the properties of the Fourier series.
5. Obtain thee Fourier series of the saw tooth waveform shown below. Obtain its
spectrum.

 Assignment No. 4
1. State and prove all the properties all the properties of Fourier transform.
2. Obtain the Fourier transform of a cosine wave having frequency f0 and peak amplitude
of unity and plot its spectrum.
3. Obtain the Fourier transform of the signal shown below and obtain its amplitude
4. For the sinc function obtain the Fourier transform and plot the spectrum.
5. Explain the Parseval’s
arseval’s theorem for the energy signal.
6. Find the Fourier transform of the impulse train shown below:

Update

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 5
1. State and prove all the properties
prope
of the Laplace transform.
2. Using shifting property find the Laplace transform of sin wt and cos wt.
3. Find Laplace transform of x(t)=(t-3)
x(t)=(t 2.
4. If x(t)=δ(t)-δ(t-2)
2) then find Laplace transform of signal d2x(t)/dt2.
5. Find the Laplace transform of x(t)=cos(3t+π/4) u(t). Draw its ROC.
6. State and prove initial and final value theorem.
7. Find initial and final value of
X(s)=2(s2+1)/s(s+1)(s+5)
8. Specify all possible ROCs for the function X(s) given below. Also find x(t) in each
case
X(s)=4s/(s+2)(s+4)
=4s/(s+2)(s+4)

Update

Nilesh Deokar
9821540802

Bhushan Borole
9892703175

8097260574

 Assignment No. 6
1. State and prove all the properties of z-transform.
z
2. Determine z-transform
transform and ROC of signal:
X(n)=[ 3(4n)-5(3n)] u(n).
3. Find the z-transform
transform of the following function along with ROC
X(n)=anu(n)+δ(n--5).
4. Determine Z-transform
transform of:
X(n)=sinw0n u(n).
It is given that x1(n) = {1, 2, 3, 4, 0, 1}
5. Using time shifting property find Z transform of x2(n) where:
X2(n) {1, 2, 3, 4, 0, 1}
6. Obtain z transform of x(n)= anu(n) using scaling property.

Update

Nilesh Deokar
9821540802

Bhushan Borole
9892703175