Free Printable EC8352-SS- Unit II-Part A

1.

The Fourier series is a combination of -----and ---- trigonometric terms

a)

sine and co secant

b)

tangent and cotangent

c)

sine and cosine

d)

cosine and secant

2.

The trigonometric Fourier series of an even function does not have

a)

Sine terms

b)

Cosine terms

c)

Constant term

d)

harmonic terms

3.

Which of the following functions cannot be expressed as a Fourier series ?

a)

tanx

b)

x

c)

xsinx

d)

cosx

4.

The incorrect statement from the following choices is

a)

The product of two even functions is an even function

b)

The product of two odd functions is an even function

c)

The product of an odd function and an even function is an even function

d)

The product of an odd function and an even function is an odd function

5.

The incorrect statement from the following choices is

a)

sinx is an odd function

b)

sin2x is an odd function

c)

sinx² is an odd function

d)

sinx² is an even function

6.

The trigonometric Fourier series of an even function does not have

a)

Sine terms

b)

Cosine terms

c)

Constant term

d)

harmonic terms

7.

The particular conditions that a function f(x) must fulfill in order that it may be expanded as a Fourier series is:

a)

Gibbs phenomenon

b)

Fourier–Mellin theorem

c)

Dirichlet conditions

d)

Convolution theorem

8.

A half range series consists of

a)

sine terms only

b)

cosine terms only

c)

both sine and cosine terms

d)

either only sine terms or only cosine terms

9.

For function $f\left(x\right)=\left\{x,\ -\pi<x<0\ \ \ and\ \ 0,\ \ 0<x<\pi\right\}$ , I have to determine

a)

$a_0\ and\ a_n.\ \ b_n=0$

b)

$b_{n\ }.\ \ a_0=0,\ a_n=0$

c)

$a_0\ ,\ a_n,\ \ and\ b_n$

d)

I am not sure, please help me!

10.

If\ b_n\ =\frac{4}{n\pi}\left\{1-\left(-1\right)^n\right\}\ ,\ What\ is\ the\ value\ of\ b_3\ ?

a)

$\frac{4}{n\pi}$

b)

$\frac{8}{n\pi}$

c)

$\frac{-8}{n\pi}$

d)

0

11.

The value of $a_0$ in the Fourier series of $f(x)=x$ in $(0,2π)$ is

a)

$2π$

b)

$π$

c)

$0$

d)

$-π$

12.

Pick out one of the conditions of Dirichlet’s condition.

a)

f\left(x\right)

is periodic, single-valued and finite

b)

$f\left(x\right)$ has infinite number of infinite discontinuous in any one period

c)

$f\left(x\right)$ is infinite valued function

d)

$f\left(x\right)$ has infinite number of maxima and minima

13.

What is the Fourier series expansion of the function f(x) in the interval (c, c+2π)?

a)

a0/2+∑∞n=1ancos(nx)+∑∞n=1bnsin(nx)

b)

a0+∑∞n=0ancos(nx)+∑∞n=0bnsin(nx)

c)

Eulers formula

d)

None of the above

14.

if $f\left(x\right)$ is an even function, then the value of $b_n$ in the Fourier series for $f\left(x\right)$ in $(-π,π)$ is

a)

$\left(2/π\right)∫_0^πf(x)\sin xdx$

b)

$π$

c)

$\left(1/π\right)\int_{-\pi}^{\pi}f(x)\sin xdx$

d)

$0$

15.

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)

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

16.

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

a)

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

b)

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

c)

$\frac{2}{s}$

d)

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

17.

Define this property: $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$

a)

Linearity Property

b)

First Shifting Property

c)

Convolution Theorem

d)

Second Shifting Property

18.

$L\left[f\left(t\right)\right]=F\left(s\right),\ then\ L\left[t^{n\ }f\left(t\right)\right]=$ If

a)

$\left(-1\right)\ \frac{d}{ds}\left\{F\left(s\right)\right\}$

b)

$\left(-1\right)^n\ \frac{d}{ds}\left\{F\left(s\right)\right\}$

c)

$\left(-1\right)\ \frac{d^n}{ds^n}\left\{F\left(s\right)\right\}$

d)

$\left(-1\right)^n\ \frac{d^n}{ds^n}\left\{F\left(s\right)\right\}$

19.

$\delta\left(t-a\right)\ is$

laplace Transform of

a)

$e^{\delta s}$

b)

$e^{as}$

c)

$e^{-as}$

d)

$e^{\delta t}$

20.

The Laplace transform of a unit impulse function is

a)

1/s

b)

1/s²

c)

1

d)

s

21.

The Fourier transform of a function is equal to its two-sided Laplace transform evaluated

a)

On the real axis of the s-plane

b)

On the line parallel to the real axis of the s-plane

c)

On the imaginary axis of the s-plane

d)

On the line parallel to the imaginary axis of the s-plane

22.

If the Fourier transform of f (t) is F (jω), then what is the Fourier transform of f (-t)?

a)

F (jω)

b)

F (-jω)

c)

-F (jω)

d)

Complex conjugate of F (jω)

23.

Fourier transform δ(t) is given as

a)

Zero

b)

1

c)

2 $\pi$ δ (ω)

d)

$\pi$ δ (ω)

24.

A signal x(t) has a Fourier transform X(ω). If x(t) is a real and odd function of t, them X(ω) is

a)

a real and even function of ω

b)

an imaginary and odd function of ω

c)

an imaginary and even function of ω

d)

a real and odd function of ω

25.

The Fourier transform of a conjugate symmetric function is always

a)

imaginary

b)

conjugate anti-symmetric

c)

real

d)

conjugate symmetric

EC8352-SS- Unit II-Part A

Total questions: 25

Worksheet time: 22mins

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