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JNTUWORLD
Code No-: R21044
II B. Tech I Semester, Supplementary Examinations, May - 2012
SIGNALS & SYSTEMS (Com. to ECE, EIE, ECC, BME)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
~~~~~~~~~~~~~~~~~~~~~~~~
1. a) Discuss orthogonal vector space and orthogonal signal space and its importance in signal
analysis.
b) Find the expression for mean square error using the expression of a function using
orthogonal signal space.
2. a) Write Drichlet’s conditions to obtain Fourier series representation of any signal.
b) Find the Trigonometric Fourier series for the periodic ware from shown below and draw its
magnitude spectra.
3. a) State and prove differentiation property of Fourier transforms.
b) Find the fourier transform of following waveform using the property of Fourier transform.
1 of 2
SET - 1 R10
1
0.5
1 3 2 4 5
t
f(t)
-2T -T/2 T
V
2T
Time
-T T/2
-V
f(t)
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Code No-: R21044
4. a) Explain the properties of a Linear Time Invariant (LT I) systems.
b) Clearly discuss the filter characteristics of linear systems and Mention conditions for
distortion less transmission of a signal through the system.
5. a) Explain Energy Density Spectrum of a signal and also explain about energy densities of the
input and the response of a system.
b) Obtain the relationship between auto correlation and Energy Density Spectrum of a signal.
6. a) State and Prove sampling theorem for low pass signals. Also, explain the recovery of
original signal from its sampled signal. Draw neat diagrams wherever necessary.
b) Obtain the Nyquist rate of the signal,
.5000cos2010000sin102000cos)( ttttx πππ ++=
7.
a) Find the Laplace Transform of the signal .)()(.)( 32tuetuetx
tt+=
− Also draw its region of
convergence.
b) Find the inverse Laplace transform of the following, )52()1(
1)(
2+++
−=
sss
ssX
8. a) Explain briefly ROC and its important properties with regards to Z-Transform.
b) Find Z-transforms of the following sequences and give their region of convergence.
( ) )()( nuin
−21 ( ) ( ){ } )()( nuii
nn−+ 4
121
2 of 2
SET - 1 R10
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JNTUWORLD
Code No-: R21044
II B. Tech I Semester, Supplementary Examinations, May - 2012
SIGNALS & SYSTEMS (Com. to ECE, EIE, ECC, BME)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
~~~~~~~~~~~~~~~~~~~~~~~~
1. a) Define orthogonal signal space and approximate a function by a set of mutually orthogonal
functions.
b) Derive expression for mean square error using the expression obtained above.
2. a) Explain the symmetry of waveform and comment on Fourier co-efficient
b) Obtain the trigonometric Fourier series for the waveform shown below.
3. a) State and prove time convolution property of Fourier transforms
b) Find the Fourier Transform of the function below.
4. a) Explain filter characteristics of linear systems and what are the conditions to obtain
distortion less transmission through the linear systems.
b) Obtain relationship between rise time and band width of a low pass filter when unit step
signal is applied.
1 of 2
SET - 2 R10
- π
x(t)
A
t -2π π 2π 3 π
2
π−
2
π
A
t
f(t)
A cos t
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Code No-: R21044
5. a) A two port network has an impulse response h(t) given by h(t)= e-t u(t). The input to the
network is a pulse of unit amplitude extending from t=0 to t=2 sec. Using convolution,
determine the output.
b) State and Prove Parseval’s theorem for energy signals.
6. a) State and Prove sampling theorem. Also, show using neat diagrams the effect of Aliasing
due to under sampling.
b) Calculate the Nyquist rate of the function.
ttttx πππ 5000cos2010000sin102000cos)( ++=
7. a) Find the Laplace transform of the following, ).1(2cos...3)( 4−=
−ttetf
t
b) Obtain inverse Laplace Transform, .)52()23(
27223)(
22
2
++++
++=
ssss
sssX
8. a) Find Z- Transforms of the following sequences and give their Region of convergences.
i) )(2
1nu
n
−
ii) )(4
1
2
1nu
nn
+
b) Find Inverse Z- transform for the following transform2
1;
2
11
1)(
1
<
+
=−
z
z
zX .
2 of 2
SET - 2 R10
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JNTUWORLD
Code No-: R21044
II B. Tech I Semester, Supplementary Examinations, May - 2012
SIGNALS & SYSTEMS
(Com. to ECE, EIE, ECC, BME)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
~~~~~~~~~~~~~~~~~~~~~~~~
1. a) Explain how vector analogy with signal is useful for spectral or signal analysis.
b) Explain how a function can be represented by a closed or a complete set of mutually
orthogonal functions.
2. a) State strong and weak Drichlet’s conditions.
b) Find the Fourier series expansion of the half wave rectified sine wave shown below.
3. a) State and prove Frequency translation property of Fourier Transform
b) Using convolution theorem find the Fourier transform F(ω) of the following function
)(.sin)( tutwetf o
at−=
4. a) Obtain the condition for distortionless transmission of signal through linear system.
b) Define causality and physical realisability of a system. Also, explain about Paley-Wiener
criterion for physical realisalbltity of system.
5. a) Define correlation. Explain auto correlation, cross-correlation and give their properties.
b) Prove that the power spectral density and the correlation function of a periodic waveform
Forms a Fourier transform pair.
1 of 2
SET - 3 R10
-π
x(t)
t
π 2π 3π
A
0 -2π
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JNTUWORLD
Code No-: R21044
6. a) State uniform sampling theorem and prove both graphically and analytically. Also, mention
all the results used.
b) Explain reconstruction of signal from its sampled signal.
7. a) Find the Laplace transform of the following function
<<
=
−
otherwise
Ttetx
at
0
0)(
Plot its region of convergence
b) Find inverse Laplace Transform of
+
+=
bs
assX ln)(
8. a) Find z-transform of [ ] )1(.1−=
−nuanx
n
b) Obtain Inverse z- transform of X(z) using the properties.
.2;2
3)( >
−= z
zzX
2 of 2
SET - 3 R10
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JNTUWORLD
Code No-: R21044
II B. Tech I Semester, Supplementary Examinations, May - 2012
SIGNALS & SYSTEMS
(Com. to ECE, EIE, ECC, BME)
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry Equal Marks
~~~~~~~~~~~~~~~~~~~~~~~~
1. a) Derive the condition for two signals f1(t) and f2(2) to be orthogonal to each other.
b) Define impulse function and explain clearly how impulse function can be used for analyzing
any system.
2. a) Obtain the relations between the coefficients of trigonometric Fourier series and Exponential
Fourier series.
b) Find the exponential Fourier series for the periodic waveform shown below and draw its
spectrum.
3. a) State and prove time scaling property of Fourier transforms.
b) Using the properties of Fourier transform, find the Fourier transform of the following.
)2()( 3−=
−tuetx
t atetg
−=)(
4. a) Derive the transfer function of a LTI system and hence explain filter characteristics of linear
system.
b) When a unit step signal is applied to a low pass filter, obtain the relationship between the
Rise time and band width of the filter.
5. a) State and prove frequency convolution theorem.
b) Determine the auto correlation Rg(τ) for )(.)( tuetgat−
= and hence prove that Rg(τ) exhibits
conjugate property what is the significance of Rg(0).
1 of 2
SET - 4 R10
-8
t
-4 -2 2 4 8
1
f(t)
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JNTUWORLD
Code No-: R21044
6. a) State uniform sampling theorem and prove both graphically and analytically. Mention all
the results used.
b) Explain reconstruction of the signal from its sampled signal.
7. a) State and prove Differentiation Theorem for Laplace Transforms.
b) Find Laplace Transform of x(t) & Sketch Pole-Zero plot with ROC
)()(.)( 23tuetuetx
tt−+=
−
8. a) Find Z-transform of x[n] & Sketch Pole-Zero plot with ROC
)1(2
1)(
3
1][ −−
+
= nunuxx
nn
b) Find the inverse Z-Transform of ;43
)(21
1
−−
−
+−=
ZZ
ZzX R O C 1>Z .
2 of 2
SET - 4 R10
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