Free Printable 21EC5252_DSP_Unit 1

1.

The Fourier Transform of f(x) is $F[f(x)]=$

a)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ dx\ =\ F\left[s\right]$

b)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)e^{isx}\ dx\ =\ F\left[s\right]$

c)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ ds\ =\ F\left[s\right]$

d)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ \ \cos sx\ dx\ =\ F\left[s\right]$

2.

The inverse Fourier Transform of $F[f(x)]\$ is $f\left(x\right)\ =$

a)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\ F\left[s\right]\ dx\ =\ f\left(x\right)$

b)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}F\left[s\right]e^{isx}\ ds\ =f\left(x\right)$

c)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}F\left[s\right]\ e^{-isx}ds\ =f\left(x\right)$

d)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}F\left[s\right]\ \ \cos sx\ ds\ =\ f\left(x\right)$

3.

The complex form $e^{isx\ }$ and $e^{-isx}$ is

a)

$e^{isx\ }\ =\ \cos sx\ +\ \sin sx\ \ and\ e^{-isx\ }\ =\ \cos sx\ -\ \sin sx\ \$

b)

$e^{isx\ }\ =\ \cos sx\ +i\sin sx\ \ and\ e^{-isx\ }\ =\ \cos sx\ -i\sin sx\ \$

c)

$e^{isx\ }\ =\ \cos sx\ \ and\ e^{-isx\ }\ =\ \ \sin sx\ \$

d)

None of the above

4.

The Real part of $e^{isx\ }$ is

a)

sinsx

b)

i sinsx

c)

cossx

d)

cosx

5.

The Imaginary part of $e^{isx\ }$ is

a)

sinsx

b)

i sinsx

c)

cossx

d)

cosx

6.

The Fourier sine Transform of f(x) is $F_s[f(x)]=$

a)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ dx\ =\ F_s\left[s\right]$

b)

$\frac{1}{\sqrt{2\pi}}\int_0^{\infty}f\left(x\right)\ \sin sx\ dx\ =\ F_s\left[s\right]$

c)

$\sqrt{\frac{2}{\pi}}\int_0^{\infty}f\left(x\right)\ \sin sx\ dx\ =\ F_s\left[s\right]$

d)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ \ \cos sx\ dx\ =\ F_s\left[s\right]$

7.

The inverse Fourier sine Transform of $F^{-1}\left\{F_s[f(x)]\right\}\ =\ f\left(x\right)$

a)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ ds=\ F_s\left[s\right]$

b)

$\frac{1}{\sqrt{2\pi}}\int_0^{\infty}\ F_s\left[s\right]\sin sx\ ds=f\left(x\right)\$

c)

$\sqrt{\frac{2}{\pi}}\int_0^{\infty}F_s\left[s\right]\sin sx\ ds\ =\ f\left(x\right)\$

d)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\ F_s\left[s\right]\ \ \cos sx\ dx\ =f\left(x\right)$

8.

The Fourier cosine Transform of f(x) is $F_c[f(x)]=$

a)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ \cos sx\ dx\ =\ F_c\left[s\right]$

b)

$\frac{1}{\sqrt{2\pi}}\int_0^{\infty}f\left(x\right)\ \cos sx\ dx\ =\ F_c\left[s\right]$

c)

$\sqrt{\frac{2}{\pi}}\int_0^{\infty}f\left(x\right)\ \cos sx\ dx\ =\ F_c\left[s\right]$

d)

$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f\left(x\right)\ \ \cos sx\ dx\ =\ F_s\left[s\right]$

9.

Infinite Fourier Transform pair is also called

a)

complex form

b)

Complex pair

c)

complex transform pair

d)

none of the above

10.

$f(x)=\ x^2\ in\ the\ interval\ \left|x\right|\ \le1\$ means what and find the value of f(0) ?

a)

$f(x)=\ x^2\ in\ the\ interval\ \ x\ \le1\ \ and\ f\left(0\right)\ =1$

b)

$f(x)=\ x^2\ in\ the\ interval\ -1\le x\ \le1\ \ and\ f\left(0\right)\ =\ 1$

c)

$f(x)=\ x^2\ in\ the\ interval\ \ \ 0\le x\ \le1\ \ and\ f\left(0\right)\ =\ 0$

d)

$f(x)=\ x^2\ in\ the\ interval\ -1\le x\ \le1\ \ and\ f\left(0\right)\ =\ 0$

11.

$f(x)=a^2-\ x^2\ in\ the\ interval\ \left|x\right|\ \le a\ ,\ where\ a>0\$ means what and find the value of f(0) ?

a)

$f(x)=\ a^2-x^2\ in\ the\ interval\ \ x\ \le a\ \ and\ f\left(0\right)\ =1$

b)

$f(x)=\ a^2-x^2\ in\ the\ interval\ -a\le x\ \le a\ \ and\ f\left(0\right)\ =\ a^2$

c)

$f(x)=a^2-\ x^2\ in\ the\ interval\ \ \ 0\le x\ \le1\ \ and\ f\left(0\right)\ =\ a^2$

d)

$f(x)=\ a^2-x^2\ in\ the\ interval\ -a\le x\ \le a\ \ and\ f\left(0\right)\ =\ 0$

12.

Given that W=e^-i(2π/N) , where N=3. Then F=W^N can be computed as F=

a)

0

b)

1

c)

-1

d)

e

13.

Given that W=e^-i(2π/N) , where N=3. Then F=W^(N/2) can be computed as F=

a)

0

b)

1

c)

-1

d)

e

14.

Which of the following relations are true if x(n) is real?

a)

X(ω)=X(-ω)

b)

X(ω)=-X(-ω)

c)

X*(ω)=X(ω)

d)

X*(ω)=X(-ω)

15.

The time system which operates with a continuous time signal and produces a continuous time output signal is

a)

CTF system

b)

DTF System

c)

Time invariant System

d)

Time variant System

16.

DFT is applied to

a)

Infinite sequences

b)

Finite discrete sequences

c)

Continuous infinite signals

d)

Continuous finite sequences

17.

The circular convolution of two sequences in time domain is equivalent to

a)

Multiplication of DFTs of two sequences

b)

Summation of DFTs of two sequences

c)

Difference of DFTs of two sequences

d)

Square of multiplication of DFTs of two sequences

18.

The basic properties of DFT includes

1)Linearity

2) Periodicity

3) Circular symmetry

4) Summation

a)

1, 2 and 3 are correct

b)

1, 2 and 4 are correct

c)

1 and 3 are correct

d)

All the four are correct

19.

The DFT is preferred for

1) Its ability to determine the frequency component of the signal

2) Removal of noise

3) Filter design

4) Quantization of signal

a)

1, 2 and 3 are correct

b)

1 and 2 are correct

c)

1 and 3 are correct

d)

All the four are correct

20.

DTFT is the representation of

a)

Periodic Discrete time signals

b)

Aperiodic Discrete time signals

c)

Aperiodic continuous signals

d)

Periodic continuous signals

21EC5252_DSP_Unit 1_FFT

Total questions: 20

Worksheet time: 10mins

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