Free Printable EC 8352 SS

1.

When

\omega

=0 in the signal

x\left(t\right)=A\ e^{st\ },\

where

s=\alpha+j\omega

, the signal x(t) represents

a)

Exponential Signal

b)

Step SIgnal

c)

Ramp Signal

d)

Sinusoidal Signal

2.

The mathematical operation

\int_{-\infty}^{\infty\ }x\left(t\right)\ e^{-st}\ dt

is called

a)

Laplace TRansform

b)

Two sided Laplace Transfrom

c)

One sided Laplace Transform

d)

Generalized frequency domain transform

3.

The term

\omega

in

s=\sigma+j\omega

is called

a)

Frequency

b)

Real Frequency

c)

Complex Frequency

d)

Critical Frequency

4.

The Laplace transform will to ll transform a time domain signal

a)

s - domain

b)

Z- domain

5.

For a stable causal system ------------------should lie on left half of the s-plane

a)

Poles

b)

Zeros

6.

The Laplace transform is used to transform a frequency domain signal to complex frequency domain

a)

True

b)

False

7.

The inverse Laplace transform of the transfer function gives the impulse response

a)

True

b)

False

8.

The direct form - I structure uses less number of integrator than direct form II structure

a)

True

b)

False

9.

The ROC of a causal signal x(t) is

a)

entire s - plane

b)

region in between two abscissa of convergence

c)

right of abscissa of convergence

d)

left of abscissa of convergence

10.

The Laplace transform of the causal signal

t^n\ u\left(t\right)

is

a)

$\frac{n!}{s^n-1}$

b)

$\frac{n!}{s^n}$

c)

$\frac{n}{s}$

d)

none of the above

11.

If x(t) and X(s) are Laplace transform pairs, then Laplace transform of

e^{-at}\ x\left(t\right)

is

a)

$X\left(s-a\right)$

b)

$X\left(s+a\right)$

c)

$e^{as}\ X\left(s\right)$

d)

$e^{-as}\ X\left(s\right)$

12.

If x(t) and X(s) are Laplace transform pairs, then Laplace transform of

\frac{x\left(t\right)}{t}

is

a)

$\int_0^{\infty}X\left(s\right)\ ds$

b)

$\int_s^{\infty}X\left(s\right)\ ds$

c)

$\frac{1}{s}\int_0^{\infty}X\left(s\right)\ ds$

d)

$\frac{1}{s}\int_s^{\infty}X\left(s\right)\ ds$

13.

If x(t) and X(s) are Laplace transform pair, and X(s) is rational, then which of the following statements are true.

(i) poles and zeros are critical frequencies

(ii) the ROC of X(s) does not include poles

(iii) the number of finite zeros will be less than or equal to number of poles

a)

i and ii only

b)

i only

c)

ii only

d)

all the above

14.

If x(t) and X(s) are Laplace transform pair, and X(s) is rational, the which of the following statements are true regarding the ROC of X(s)

(i) The ROC is bounded by poles or extends to infinity

(ii) If x(t) is right sided, then ROC is right most pole.

(iii) If x(t) is left sided, then ROC is left of left most people.

a)

i only

b)

ii only

c)

ii and iii only

d)

all the above

15.

The inverse Laplace transform

X\left(s\right)=\frac{2}{s^2+2s+5}

is

a)

$x\left(t\right)=e^{-t}\cos2t$

b)

$x\left(t\right)=e^{-t}\sin2t$

c)

$x\left(t\right)=e^{-2t}\cos5t$

d)

$x\left(t\right)=e^{-2t}\sin5t$

16.

The inverse Laplace transform of

X\left(s\right)=\frac{4}{s+5}

for ROC

Re\left\{s\right\}>-4\ and\ Re\left\{s\right\}<-4

are respectively

a)

$4e^{-5t}u\left(t\right)\ and\ 4e^{-5t}u\left(-t\right)$

b)

$4e^{5t}u\left(t\right)\ and\ 4e^{5t}u\left(-t\right)$

c)

$4e^{-5t}u\left(t\right)\ and\ -4e^{-5t}u\left(-t\right)$

d)

$-4e^{-5t}u\left(t\right)\ and\ -4e^{-5t}u\left(-t\right)$

17.

For a continuous time LTI system which of the following statements are true

(i) The transfer function is ration of Laplace transform of output and input

(ii) The transfer function is ratio of Laplace transform of input and output

(iii) The transfer function is Laplace transform of impulse response

a)

i only

b)

i and iii only

c)

ii only

d)

iii only

18.

If x(t), y(t) are input, output and impulse response of LTI continuous time system respectively then,

a)

$h\left(t\right)\ =\ x\left(t\right)\ \cdot\ y\left(t\right)$

b)

$x\left(t\right)\ =\ y\left(t\right)\ \cdot\ h\left(t\right)$

c)

$y\left(t\right)\ =\ x\left(t\right)\ \cdot\ h\left(t\right)$

d)

$y\left(t\right)\ =\ h\left(t\right)\ \cdot\ h\left(t\right)$

19.

The convolution of u(t) with u(t) will be equal to,

a)

$\delta\left(t\right)$

b)

$u\left(t\right)$

c)

$t\ u\left(t\right)$

d)

$t^2u\left(t\right)$

20.

The convolution of $e^{-at}\ u\left(t\right)\ with\ e^{-at}\ u\left(t\right)$ will be a equal

a)

$t\ u\left(t\right)$

b)

$e^{-at}\ u\left(t\right)$

c)

$e^{-2at}\ u\left(t\right)\$

d)

$t\ e^{-at}\ u\left(t\right)\$

21.

Fourier series is useful for frequency domain analysis of ---------- signals

a)

Periodic

b)

Aperiodic

c)

Linear

d)

Nonlinear

22.

The ratio of Fourier transform of output and input of a system is called------------------

a)

Transfer Function

b)

Impulse response

c)

output response

d)

input response

23.

The Fourier transform of impulse response will be equal to -------------------------

a)

Transfer function

b)

output

c)

input

d)

none of the above

24.

The magnitude line spectrum is symmetric and phase line spectrum is anti symmetric

a)

True

b)

False

25.

For waveform with even spectrum , the Fourier coefficient is always zero

a)

True

b)

False

26.

For waveforms with odd symmetry, the Fourier Coefficients are always zero

a)

True

b)

False

27.

An alternating waveform will always have even harmonic only

a)

True

b)

False

28.

An even signal with halfwave symmetry will always have been harmonics of cosine terms

a)

True

b)

False

29.

An odd signal with halfwave symmetry will always have been harmonics of sine terms

a)

True

b)

False

30.

The shifting of vertical axis of a waveform , will not affect the even/ odd symmetry

a)

True

b)

False

31.

In frequency spectrum using Fourier transform, the magnitude spectrum will have even symmetry and phase spectrum will have odd symmetry

a)

True

b)

False

32.

The fourier transform of a periodic signal will be summation of impulse

a)

True

b)

False

33.

The total average power in a periodic signal is equal to the sum of power in all of its harmonic

a)

True

b)

False

34.

Fourier transform is useful for frequency domain analysis of both periodic and non periodic signal

a)

True

b)

False

35.

Laplace transform is a generalized transform and Fourier transform is particular transform

a)

True

b)

False

36.

The value of

e^{-\infty}

is------------------

(a)

37.

The value of

e^{\infty}

is------------------

(a)

38.

The value of cos 0 is------------------

(a)

39.

The value of sin 0 is------------------

(a)

40.

Which of the following is the Analysis Equation of Fourier Transform?

a)

$F\left(w\right)=\int_{-\infty}^{\infty}f\left(t\right)e^{jwt\ }dt$

b)

$F\left(w\right)=\int_0^{\infty}f\left(t\right)e^{jwt}dt$

c)

$F\left(w\right)=\int_0^{\infty}f\left(t\right)e^{-jwt}dt$

d)

$F\left(w\right)=\int_{-\infty}^{\infty}f\left(t\right)e^{-jwt}dt$

41.

Find the Fourier Transform of an Exponential signal

f\left(t\right)=e^{-at}u\left(t\right),a>0

a)

$\frac{1}{a+jw}$

b)

$\frac{1}{a-jw}$

c)

$\frac{1}{-a+jw}$

d)

$\frac{1}{-a-jw}$

42.

The Fourier Transform of a function

X\left(t\right)\ is\ X\left(w\right).

what will be the fourier transform of

\frac{\text{d}X\left(t\right)}{\text{d}t}

?

a)

$\frac{X\left(f\right)}{jf}$

b)

$j2\pi fX\left(f\right)$

c)

$\frac{\text{d}X\left(f\right)}{\text{d}t}$

d)

$jfX\left(f\right)$

43.

Find the Inverse Fourier transform of $\delta\left(w\right)$

a)

$\frac{1}{2\pi}$

b)

$2\pi$

c)

$\frac{1}{\pi}$

d)

$\pi$

44.

Find the inverse Fourier Transform of $f\left(t\right)=1$

a)

$u\left(t\right)$

b)

$\delta\left(t\right)$

c)

$e^{-t}$

d)

$\frac{1}{jw}$

45.

$f\left(x\right)=1,\ \ \ 0<x<\infty\$ cannot be represented by a Fourier Integral

a)

True

b)

False

46.

Find the convolution of the signals $X_1\left(t\right)=e^{-2t}u\left(t\right)$ and $X_2\left(t\right)=e^{-3t}u\left(t\right)$

a)

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

b)

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

c)

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

d)

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

47.

Which one is the correct definition of Laplace Transform?

a)

$F\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt$

b)

$F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)$

48.

What is the Laplace Transform for $f\left(t\right)=t^3$ ?

a)

$\frac{1}{s^3}$

b)

$\frac{2}{s^3}$

c)

$\frac{6}{s^4}$

d)

$\frac{3}{s^3}$

49.

What is Laplace Transform for $e^{-2t}$ ?

a)

$\frac{1}{s-2}$

b)

$\frac{1}{s+2}$

c)

$\frac{2}{s}$

d)

$\frac{1}{s^2}$

50.

What is Laplace Transform for $\sin\ 2t$ ?

a)

$\frac{2}{s^2+2}$

b)

$\frac{s}{s^2+2}$

c)

$\frac{2}{s^2+4}$

d)

$\frac{s}{s^2+4}$

EC 8352 SS - IAT#2

Total questions: 50

Worksheet time: 50mins

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