Free Printable SS - REVISION 5

1.

Inverse Laplace transform, transform

a)

$f\left(t\right)\ to\ F\left(s\right)$

b)

$F\left(s\right)\ to\ f\left(t\right)$

c)

$f'\left(t\ \right)\ to\ f\left(t\right)$

d)

$f\left(t\right)\ to\ f'\left(t\right)$

2.

Find $L^{-1}\left(\frac{1}{s^2+1}\right)$

a)

sin t

b)

sin 5t

c)

cos t

3.

The $L^{-1}\left(\frac{4}{\left(s^2+9\right)}\right)$ is $a\ \sin\ 3t$ . What is a?

a)

$\frac{2}{3}$

b)

$\frac{4}{3}$

c)

$3$

4.

$L^{-1}\left(\frac{4}{s^{\left(3\right)}}\right)$

a)

$4t^3$

b)

$2t^2$

c)

$2t^3$

5.

$L^{-1}\left(\frac{1}{\left(s-3\right)^2}\right)$

a)

$e^{2t}t$

b)

$e^tt^2$

c)

$e^{3t}t$

6.

$L^{-1}\left(\frac{3s}{\left(s+2\right)^4}\right)$

a)

$\frac{1}{2}e^{-t}\left(3t^2-t^{\left(3\right)}\right)$

b)

$e^{-2t}\left(\frac{3}{2}t^2-t^{\left(3\right)}\right)$

c)

$e^{-t}\left(\frac{3}{2}t^2-t^{\left(3\right)}\right)$

7.

$L^{-1}\left(\frac{s}{\left(s-4\right)^2+16}\right)$

a)

$e^{4t}\left(\cos\ 4t+\sin\ 4t\right)$

b)

$e^{2t}\left(\cos\ 2t+\sin\ 2t\right)$

c)

$e^{2t}\left(4\cos\ t+4\sin\ t\right)$

8.

$L^{-1}\left(\frac{\left(s+2\right)}{s^2+2s+5}\right)$

a)

$f(t)=e^{-t}\sin(2t)+e^{-t}\cos(2t)$

b)

$f(t)=\frac{1}{2}e^{-t}\sin(2t)+e^{-t}\cos(2t)$

c)

$f(t)=e^{-t}\sin(2t)+\frac{1}{2}e^{-t}\cos(2t)$

9.

By convolution theorem, find Inverse Laplace Transform for $X\left(s\right)=\frac{1}{s\left(s^2+4\right)}$

a)

$\frac{1}{2\ }\sin\ 2t$

b)

$\frac{1}{4}\cos\ 2t-4$

c)

$\frac{1}{4}\left(1-\cos\ 2t\right)$

10.

By convolution theorem, find F(s) and G(s) $X\left(s\right)=\frac{1}{s\left(s^2+4\right)}$

a)

$F\left(s\right)=\frac{1}{s};G\left(s\right)=\frac{1}{s^2+4}$

b)

$F\left(s\right)=\frac{1}{s^{ }};G\left(s\right)=\frac{1}{s^3+4s}$

c)

$F\left(s\right)=\frac{1}{s^2+4};G\left(s\right)=\frac{1}{s^{ }}$

11.

The z-transform of a signal X(n) whose definition is given by X(z)=

\sum_{n=0}^{\infty}x\left(n\right)z^{-n}

is known as

a)

Unilateral Z-transform

b)

Bilateral Z-transform

c)

Rational Z-transform

d)

None of the above

12.

For what kind of signals one sided Z-transfrom is unique

a)

All signals

b)

Anti-causal signal

c)

Causal signal

d)

None of the above

13.

Z-transform is linear

a)

True

b)

False

14.

The Z-transform of

\delta\left(n+k\right)>0

is

a)

$z^{-k,\ }z\ne0$

b)

$z^k,z\ne0$

c)

$z^{-k},\ all\ z$

d)

$z^k,all\ z$

15.

Z-transform of the sequence $\left\{2^k\right\},k\ge0\ is\ \frac{z}{z-2}$

a)

True

b)

False

16.

$Z-transform\ of\ the\ sequence\ \left\{\frac{a^k}{k!}\right\},k\ge0=e^{\frac{a}{z}}$

a)

True

b)

False

17.

$Z-transform\ of\ the\ sequence\ \left\{nc_r\right\},\left(0\le r\le n\right)\ is\ \left(1+z\right)^n$

a)

True

b)

False

18.

$The\ value\ of\ the\ Radius\ of\ convergence\ of\ f\left(n\right)=2^n,n<0\ is$

a)

0< $\left|z\right|$ <1

b)

-2< $\left|z\right|$

c)

$\left|z\right|$ <2

d)

z-plane

19.

$The\ ROC\ of\ u\left(n\right)=4^n,for\ n<0;2^n,for\ n\ge0\ is$

a)

0<z<1

b)

z<4

c)

2<z

d)

2<z<4

20.

$If\ Z\left(u_n\right)=u\left(z\right),\ then\ \lim_{n\rightarrow\infty}u_n=\lim_{n\rightarrow\infty}\left(z-1\right)u\left(z\right)$

a)

True

b)

False

21.

$The\ Inverse\ Z-transform\ of\frac{z}{\left(z+1\right)^2}is$

a)

$\left(-1\right)^{n+1}$

b)

$n\left(-1\right)^{n-1}$

c)

$\left(-1\right)^{n-1}$

d)

$n\left(-1\right)^{n+1}$

22.

$The\ value\ of\ inverse\ z-transform\ of\ \log\left(\frac{z}{z+1}\right)is$

a)

$\frac{\left(-1\right)^n}{n}for\ n=0;\ \ 0\ otherwise$

b)

$\frac{\left(-1\right)^n}{n}$

c)

$0,\ for\ n=0;\ \ \frac{\left(-1\right)^n}{n},otherwise$

d)

$0$

23.

Find the Z-transform of δ(n+3).

a)

1

b)

z

c)

z²

d)

z³

24.

a)

a

b)

c

c)

d

d)

b

25.

For causal sequences, the ROC is the exterior of a circle of radius r.

a)

True

b)

False

26.

a)

a

b)

b

c)

c

d)

d

27.

For a right hand sequence, the ROC is entire z-plane.

a)

False

b)

True

28.

The type of systems which are characterized by input and the output quantized at certain levels are called as

a)

analog

b)

discrete

c)

continuous

d)

digital

29.

The type of systems which are characterized by input and the output capable of taking any value in a particular set of values are called as

a)

Analog

b)

Discrete

c)

Digital

d)

Continuous

30.

A system is said to be defined as non causal, when

a)

the output at the present depends on the input at an earlier time

b)

the output at the present does not depend on the factor of time at all

c)

the output at the present depends on the input at the current time

d)

the output at the present depends on the input at a time instant in the future

31.

What is the other name of a Continuous Time Unit Impulse Function?

a)

Dirac delta function

b)

Unit function

c)

Area function

d)

Direct delta function

32.

Why is the impulse duration important?

a)

It is zero

b)

It changes with time

c)

It approaches zero

d)

It depends on the situation

33.

Which among the following are the stable discrete time systems? 1. y(n) = x(4n) 2. y(n) = x(-n) 3. y(n) = ax (n) + 8 4. y(n) = cos x(n)

a)

1 & 3

b)

2 & 4

c)

1, 3 & 4

d)

1,2,3 & 4

34.

Which one of the following is the correct statement ? The system characterized by the equation y(t) = ax(t) + b is

a)

linear for any value of b

b)

linear if b > 0

c)

linear if b < 0

d)

non-linear

35.

Which one of the following systems described by the following input-output relations is non-linear ?

a)

y(n) = n x(2n)

b)

y(n) = x (n2)

c)

y(n) = n2x(n)

d)

y(n) = x2(n)

36.

A function of one more variables which conveys information on the nature of physical phenomenon is called

a)

Noise

b)

Interference

c)

System

d)

Signal

37.

Which one of the following is correct ? Energy of a power signal is

a)

Finite

b)

Zero

c)

Infinite

d)

Between 1 And 2

38.

Which one of the following is correct ? A system can be completely described by a transfer function if it is

a)

Non-Linear And Continuous

b)

Linear And Time-Varying

c)

Non-Linear And Time-Invariant

d)

Linear And Time Invariant

39.

Convolution of two sequences X1 Z[n] and X2 [n] is represented as

a)

X1(z)* X2(z)

b)

X1(z) X2 (z)

c)

X1 (z) + X2(z)

d)

X1(z)/X2(z)

40.

Laplace transforms of f(t) and g(t) are F(s) and G(s), respectively. Which one of the following expressions gives the inverse Laplace transform of F(s) G(s) ?

a)

f(t) g(t)

b)

f(t) /g(t)

c)

f(t) + g(t)

d)

f(t) *g(t)

41.

The lengths of two discrete time sequence x1(n) and x2(n) are 5 and 7, respectively. What is the maximum length of a sequence x1(n)*x2(n) ?

a)

5

b)

6

c)

7

d)

11

42.

If the response of a system to an input does not depend on the future values of the input.Then which one of the following is true for the system ?

a)

It Is Aperiodic

b)

It Is Causal

c)

It Is Anticipator

d)

It Is Discrete

43.

What is the number of roots of the polynomial F(z) = 4z3 – 8z2 –z + 2, lying outside the unit circle ?

a)

0

b)

1

c)

2

d)

3

44.

Which condition determines the causality of the LTI system in terms of its impulse response ?

a)

Only if the value of an impulse response is zero for all negative values of time

b)

Only if the value of an impulse response is unity for all negative values of time

c)

Only if the value of an impulse response is infinity for all negative values of time

d)

Only if the value of an impulse response is negative for all negative values of time

45.

The spectrum of the sampled signal may be obtained without overlapping only if

a)

fs ≥ 2fm

b)

fs < fm

c)

fs < 2fm

d)

fs > fm

46.

What is the disadvantage of exponential Fourier series?

a)

It is tough to calculate

b)

It is not easily visualized

c)

It cannot be easily visualized as sinusoids

d)

It is hard for manipulation

47.

Which are the fourier coefficients in the following?

a)

a0, an and bn

b)

an

c)

bn

d)

an and bn

48.

What is the fundamental period of the signal : ejwt?

a)

2π/w

b)

2π/w2

c)

2π/w3

d)

4π/w

49.

All real time systems concerned with the concept of causality are

a)

non causal

b)

causal

c)

neither causal nor non causal

d)

memoryless

50.

How does Fourier series make it easier to represent periodic signals?

a)

Harmonically related

b)

Periodically related

c)

Sinusoidally related

d)

Exponentially related

SS - REVISION 5

Total questions: 50

Worksheet time: 25mins

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