Electronics and Communication Engineering - Signals and Systems

16. 

Let x(t) and y(t) with F.T. x(f) and y(f) respectively be related as shown in figure

Then y(f) is

A.
B.
C. -X(f/2)ej2pf
D. -X(f/2)e- j2pf

Answer: Option B

Explanation:

By applying time shifting and scaling property.


17. 

Which one is a linear system?

A. y[n] = x[n] x x[n - 1]
B. y[n] = x[n] + x[n - 10]
C. y[n] = x2[n]
D. (a) and (c)

Answer: Option B

Explanation:

For linearity

y1[n] = x1[n] + x2[n - 10] ...(1)

y2 = x2[n] + x2[n - 10] ...(2)

y1[n] = x1[n] + x2[n] + x2[n - 10] + x2[n - 10] ...(3)

Now find y1[n] + y2[n]

Corresponding to x1[n] + x2[n]

It is same as equation (3) hence linear.

But in part (c) y[n] = x2[n]

y1[n] = x21[n], y2[n] = x22[n]⇒ y1[n] + y2[n] = x22[n]...3

But y1[n] + y2[n]

Corresponing x1[n] + x2[n] is y1[n] + y2[n] = {x1[n] + x2[n]}2

= x12[n] + x22[n] + 2x1[n] x2[n]....4

Equations (3) and (4) are not same hence not linear.


18. 

Laplace transform of a pulse function of magnitude E and duration from t = 0 to t = a is

A. E / s
B.
C.
D.

Answer: Option C

Explanation:

.


19. 

The continuous time system with impulse response h(t) = is stable, for n is even, when

A. a = 0
B. a > 0
C. a < 0
D. a ≤ 0

Answer: Option C

Explanation:

For stable system exponential must be -ve so that a < 0.


20. 

If I (s) , initial value of i(t) is

A. 5A
B. 12.5 A
C. 0.05 A
D. 1250 A

Answer: Option A

Explanation:

.