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Backexam Soln

The document contains the answers to multiple choice and numerical problems related to signals and systems. It includes identifying whether systems are linear, time-invariant, causal, and stable based on input-output relations. It also contains calculations of system functions in the z-domain and time-domain and sketches of frequency responses. The respondent provides short answers and calculations to problems addressing concepts like convolution, filtering, sampling, and the Fourier transform.

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Nguyen Duc Tai
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© Attribution Non-Commercial (BY-NC)
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Download as PDF, TXT or read online on Scribd
59 views4 pages

Backexam Soln

The document contains the answers to multiple choice and numerical problems related to signals and systems. It includes identifying whether systems are linear, time-invariant, causal, and stable based on input-output relations. It also contains calculations of system functions in the z-domain and time-domain and sketches of frequency responses. The respondent provides short answers and calculations to problems addressing concepts like convolution, filtering, sampling, and the Fourier transform.

Uploaded by

Nguyen Duc Tai
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1

Full Name:
Do not put any explanations or work in this answer sheet. Only your answers will be considered. Problem 1 (12%)

(a) y [n] = x[2n] Is the system: 1% (i) Linear? 1% (ii) Time-invariant? 1% (iii) Causal? 1% (iv) Stable? (b) y [n] = x[n] + x[n 1] Is the system: 1% (i) Linear? 1% (ii) Time-invariant? 1% (iii) Causal? 1% (iv) Stable? (c) y [n] = (x[|n|])2 Is the system: 1% (i) Linear? 1% (ii) Time-invariant? 1% (iii) Causal? 1% (iv) Stable? Problem 2 (6%)
1 1az 1

YES YES YES YES

NO NO NO NO

CANT TELL CANT TELL CANT TELL CANT TELL

YES YES YES YES

NO NO NO NO

CANT TELL CANT TELL CANT TELL CANT TELL

YES YES YES YES

NO NO NO NO

CANT TELL CANT TELL CANT TELL CANT TELL

Hxy (z ) = bz 1 + Hey (z ) = z 1

Please turn over

2 Problem 3 (7%)

3% (a) y [n] = x[n] + 1 2 x[n 1] + 2y [n 1] 2% (b) Stable? 2% (c) Causal? YES YES NO NO CANT TELL CANT TELL

Problem 4

(8%)

2% (a) h[n] = [n + 1] + [n 1] H (z ) = z + z 1 3% (b) yy [m] = [m + 2] + 2 [m] + [m 2] 3% (c) Pyy ( ) = 2(1 + cos(2 )) Problem 5 4% (a) H2 (z ) = (10%)
2(1 1 z 1 ) 2 1 1 z 1 3

3% (b) H2 (z ) unique? 3% (c) Hw (z ) = Problem 6 3% (a) T =


1 6000 z 1 1 1 3 z 1 1 1 2

YES

NO

(6%)

3% (b) Choice of T unique? NO. Specify another choice of T if answer is no: Problem 7 (9%)

T =

7 6000

4% (a) yc (t) = 6 cos(6t + 2 ) = 6 sin(6t) 5% (b) yc (t) = 6 cos(6t + 2) Problem 8 3% (a) H (z ) = (8%)
(1+jz 1 )(1jz 1 ) z 1 )(12z 1 ) (1 1 2

2% (b) Can system be causal and stable?

YES

NO YES NO

3% (c) If system is stable, h[n] = 0 n > m or n < m for nite integer m?

Please turn over

3 Problem 9 (10%) YES


1 2

2% (a) h[n] real-valued? 2% (b)


n= |h[n]| 2

NO

|H (ej )|2 d = 1

6% (c) Response of the system: y [n] = s[n] cos(c n 2) Problem 10 (7%)

5% (a) Sketch Yd (ej ) and Yc (j ):


Yd (e )
30000
j

/6

/6

Yc (j )
3

10 /6

10 /6

2% (b)

n= yd [n]

= Yd (ej 0 ) =

1 T1

= 3 104

4 Problem 11 (5%)

Output of the system: y [n] = s1 [n 39] cos( 34 n )

Problem 12 (Circle one) Problem 13

(3%) A (9%)
T

2% (a) H (j ) = ej 3 for || < 2% (b) (Circle one) 2% (c) yd [n] = yc (nT ) 3% (d) h[n] =
1 sin( (n 3 )) 1 (n 3 )

, 0 otherwise. C D E

Problem 14

(0%)

The best estimate of my grade is: 100

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