Download VTU BE 2020 Jan [folder1] 4th Sem 17EC42 Signals and Systems Question Paper

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Time: 3 hrs.
Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Explain with an example :

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i) Even and odd signal
ii) Energy and power signal
iii) Time shifting
iv) Time scaling
v) Prescenduce rule.

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b. Sketch the following :
y(t) = r(t + 2) - r(t + 1) - r(t - 1) + r(t - 2)
c. Given the signal x(t) as shown in the Fig.1(c) sketch the following :
i) x(2t + 2) and ii) x(t/2 - 1).
O

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Fig.1(c)
OR
2 a. Find the even the odd components of the following signals :
i) x(t) = cost + sin t + sin t ? cos t
ii) x(n) {-3, 1, 2, -4, 2} .

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b. For the signal shown in Fig.Q2(b), find the total energy.
7.C-L)
(10Marks)
(02Marks)
(08Marks)

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(06 Marks)
(08 Marks)
-4. -- 3
-
2 ^1 0 1

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2 3 It S
Fig.Q2(b)
c.
Verify the following system for linearity and time invariance :
i) y(t) = t?x(t) ii) y(n) = x[n] + n. (06 Marks)

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Module-2
3 a. What do you mean by impulse response of an LTI system? Starting from fundamentals,
deduce the equation for the response of an LT1 system if the input sequences x(n) and the
impulse response h(n) are given. (08 Marks)
b. Determine the output of an LTI system for an input x(t) = u(t) - u(t - 2) and impulse

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response h(t) = u(t) - u(t - 2).
,, (06 Marks)
c. An LTI system is characterized by an impulse response h(n) = (3/4)
n
..004,:find the response

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of the system when the input x(n) = u(n). Also evaluate the output aniie system at n = + 5
and n =- - -5. (06 Marks)
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17EC42
USN
Fourth Semester B.E. Degree Examination, Dee.2019/Jan.2020
Signals and Systems
Time: 3 hrs.

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Max. Marks: 100
Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Explain with an example :
i) Even and odd signal

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ii) Energy and power signal
iii) Time shifting
iv) Time scaling
v) Prescenduce rule.
b. Sketch the following :

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y(t) = r(t + 2) - r(t + 1) - r(t - 1) + r(t - 2)
c. Given the signal x(t) as shown in the Fig.1(c) sketch the following :
i) x(2t + 2) and ii) x(t/2 - 1).
O
Fig.1(c)

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OR
2 a. Find the even the odd components of the following signals :
i) x(t) = cost + sin t + sin t ? cos t
ii) x(n) {-3, 1, 2, -4, 2} .
b. For the signal shown in Fig.Q2(b), find the total energy.

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7.C-L)
(10Marks)
(02Marks)
(08Marks)
(06 Marks)

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(08 Marks)
-4. -- 3
-
2 ^1 0 1
2 3 It S

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Fig.Q2(b)
c.
Verify the following system for linearity and time invariance :
i) y(t) = t?x(t) ii) y(n) = x[n] + n. (06 Marks)
Module-2

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3 a. What do you mean by impulse response of an LTI system? Starting from fundamentals,
deduce the equation for the response of an LT1 system if the input sequences x(n) and the
impulse response h(n) are given. (08 Marks)
b. Determine the output of an LTI system for an input x(t) = u(t) - u(t - 2) and impulse
response h(t) = u(t) - u(t - 2).

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,, (06 Marks)
c. An LTI system is characterized by an impulse response h(n) = (3/4)
n
..004,:find the response
of the system when the input x(n) = u(n). Also evaluate the output aniie system at n = + 5

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and n =- - -5. (06 Marks)
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4 a. LT1 system has an impulse response :
1 ; n = +/ -1
h(n)= 2 ; n = 0

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0 ; otherwise
OR
Determine
x(n)=
the output of this system in response to the input :

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2 ; n = 0
3 ; n = I
-2 ; n = 2
0 ; otherwise
(06 Marks)

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b. Determine the discrete time convolution of input x(n) u(n) and impulse response
h(n) = u(n - 3). Assume magnitude of 13 to be less than 1. (08 Marks)
c.
Prove [x(n) * hi(n)] * h2(n) = x(n) * [hi(n) * h2(n)]. (06 Marks)
Module-3

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5 al Evaluate
i) h(n)
the step response for the following impulse responses
= u(n)
ii) h(t) = u(t + 1) - u(t - 1). (08 Marks)

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b. Check for the following impulse responses memoryless, causal and stable.
i) h(t)
=
e
2t

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u(t 1)

ii) h(n) = (1)
n
u(n). (06 Marks)

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c. Evaluate the DTFS representation for the signal :
x[n]= si rin
10
n ?ni+ cos[
g

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n]+1
21 21
Sketch magnitudes and phase spectra. (06 Marks)
OR
6 a. An inter connection of LT1 system is shown in Fig.Q6(a). The impulse responses are

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h
i
(n) =(1)
n
u(n+2), h2(n) = 5(n) and h3(n) = u(n-1). Find the impulse response h(n) of the

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overall system. (06 Marks)
Fig.Q6(a)
b. State the following properties of continuous time Fourier series
i) Convolution ii) Time shift iii) Linearity iv) Differential in time domain. (04 Marks)
c.

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Find the complex Fourier coefficient for the periodic waveform
Fig.Q6(c). Also draw the amplitude and phase spectra.
AAA
Fig.Q6(c)
2 of 3

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x(t) as shown in the
(10 Marks)
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17EC42

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USN
Fourth Semester B.E. Degree Examination, Dee.2019/Jan.2020
Signals and Systems
Time: 3 hrs.
Max. Marks: 100

--- Content provided by‌ FirstRanker.com ---

Note: Answer any FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Explain with an example :
i) Even and odd signal
ii) Energy and power signal

--- Content provided by‌ FirstRanker.com ---

iii) Time shifting
iv) Time scaling
v) Prescenduce rule.
b. Sketch the following :
y(t) = r(t + 2) - r(t + 1) - r(t - 1) + r(t - 2)

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c. Given the signal x(t) as shown in the Fig.1(c) sketch the following :
i) x(2t + 2) and ii) x(t/2 - 1).
O
Fig.1(c)
OR

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2 a. Find the even the odd components of the following signals :
i) x(t) = cost + sin t + sin t ? cos t
ii) x(n) {-3, 1, 2, -4, 2} .
b. For the signal shown in Fig.Q2(b), find the total energy.
7.C-L)

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(10Marks)
(02Marks)
(08Marks)
(06 Marks)
(08 Marks)

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-4. -- 3
-
2 ^1 0 1
2 3 It S
Fig.Q2(b)

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c.
Verify the following system for linearity and time invariance :
i) y(t) = t?x(t) ii) y(n) = x[n] + n. (06 Marks)
Module-2
3 a. What do you mean by impulse response of an LTI system? Starting from fundamentals,

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deduce the equation for the response of an LT1 system if the input sequences x(n) and the
impulse response h(n) are given. (08 Marks)
b. Determine the output of an LTI system for an input x(t) = u(t) - u(t - 2) and impulse
response h(t) = u(t) - u(t - 2).
,, (06 Marks)

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c. An LTI system is characterized by an impulse response h(n) = (3/4)
n
..004,:find the response
of the system when the input x(n) = u(n). Also evaluate the output aniie system at n = + 5
and n =- - -5. (06 Marks)

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1 of 3
4 a. LT1 system has an impulse response :
1 ; n = +/ -1
h(n)= 2 ; n = 0
0 ; otherwise

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OR
Determine
x(n)=
the output of this system in response to the input :
2 ; n = 0

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3 ; n = I
-2 ; n = 2
0 ; otherwise
(06 Marks)
b. Determine the discrete time convolution of input x(n) u(n) and impulse response

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h(n) = u(n - 3). Assume magnitude of 13 to be less than 1. (08 Marks)
c.
Prove [x(n) * hi(n)] * h2(n) = x(n) * [hi(n) * h2(n)]. (06 Marks)
Module-3
5 al Evaluate

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i) h(n)
the step response for the following impulse responses
= u(n)
ii) h(t) = u(t + 1) - u(t - 1). (08 Marks)
b. Check for the following impulse responses memoryless, causal and stable.

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i) h(t)
=
e
2t
u(t 1)

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ii) h(n) = (1)
n
u(n). (06 Marks)
c. Evaluate the DTFS representation for the signal :

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x[n]= si rin
10
n ?ni+ cos[
g
n]+1

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21 21
Sketch magnitudes and phase spectra. (06 Marks)
OR
6 a. An inter connection of LT1 system is shown in Fig.Q6(a). The impulse responses are
h

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i
(n) =(1)
n
u(n+2), h2(n) = 5(n) and h3(n) = u(n-1). Find the impulse response h(n) of the
overall system. (06 Marks)

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Fig.Q6(a)
b. State the following properties of continuous time Fourier series
i) Convolution ii) Time shift iii) Linearity iv) Differential in time domain. (04 Marks)
c.
Find the complex Fourier coefficient for the periodic waveform

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Fig.Q6(c). Also draw the amplitude and phase spectra.
AAA
Fig.Q6(c)
2 of 3
x(t) as shown in the

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(10 Marks)
7 a.
b.
c.
(

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L. 7
17EC42
Iltte
1
1

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?
e`
Module-4v:: r?;
s.
Find the Fourier transform of the signal x(t) = sk,etch magnitude and phase

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spectra. -
? ..-
(08 Marks)
State and prove the following properties of discrete time rciurier transform.
i) Convolution

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ii) Frequency differentiation. (08 Marks)
Find the DTFT of the signal x[n] = u[n] - u[n - 6]. (04 Marks)
OR
8 a. Obtain the DTFT of the rectangular pulse is defined as :
x[n]=1

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=0;Inl>M
b. Specify the Nyquist rate for the following signals
i) x(t) = cos (5irt) + 0.5 cos (107a)
ii) x(t) = sin c (200t).
c. Using properties of Fourier transform, find the Fourier transform of the signal :

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x(t) = dt {te
-2
` sin u(t)].
(08 Marks)
(04 Marks)

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(08 Marks)
Module-5
9 a. Determine the Z-transform of the signal x[n] = a
n
u[n]. Indicate the ROC and locations of

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poles and zeros of X(z) in the z-plane. (06 Marks)
b. Find the Z-transform and the ROC of the discrete sinusoid signal x(n) = sin [en) u(n).
(08 Marks)
1/
7

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-1
4
-

C. Find the inverse Z-transform of x(z) = ROC z I >1. (06 Marks)

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12
z"-')(1?
_
4z
-

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i)
OR
10 a. Find the impulse response for the following difference equation :
y(n) - 4y(n - 1) + 3y(n - 2) = x(n) + 2x(n - 1). (08 Marks)
b. Find the Z -transform and ROC of x(n) = a

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l
u(n - 1) using properties of Z-transforms.
(06 Marks)
c. Using Z-transform find the convolution of the following two sequences :
h[n]

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Y
2
r; 0 n 2
0
; otherwise

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And x[n] = 8[n] + 8[n- 1] + 8[n - 2]. (06 Marks)
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