Free Printable SS - Revision 4

1.

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)

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

2.

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)

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

3.

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)

$jfX\left(f\right)$

4.

The Fourier Transform of a Gaussian Pulse is also a Gaussian pulse

a)

True

b)

False

5.

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

a)

True

b)

False

6.

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)

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

7.

Fourier transform is a linear operation

a)

True

b)

False

8.

Finite Fourier cosine Transform of $f\left(x\right)=1\ in\ \left(0,\pi\right)$ is zero

a)

True

b)

False

9.

$If\ F\left[f\left(x\right)\right]\ =\ F\left(s\right),\ then\ F\left[f\left(ax\right)\right]=?$

a)

$e^{ias}F\left(s\right)$

b)

$\frac{1}{a}\ F\left(\frac{s}{a}\right)$

c)

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

d)

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

10.

$If\ F\left[f\left(x\right)\right]\ =\ F\left(s\right),\ then\ F\left[f\left(x\ -\ a\right)\right]=?$

a)

$e^{ias}F\left(s\right)$

b)

$\frac{1}{a}\ F\left(\frac{s}{a}\right)$

c)

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

d)

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

11.

$If\ F\left[f\left(x\right)\right]\ =\ F\left(s\right),\ then\ F\left[e^{iax}f\left(x\right)\right]=?$

a)

$e^{ias}F\left(s\right)$

b)

$\frac{1}{a}\ F\left(\frac{s}{a}\right)$

c)

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

d)

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

12.

$If\ F\left[f\left(x\right)\right]\ =\ F\left(s\right),\ then\ F\left[x^nf\left(x\right)\right]=?$

a)

$e^{ias}F\left(s\right)$

b)

$\frac{1}{a}\ F\left(\frac{s}{a}\right)$

c)

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

d)

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

13.

$If\ F\left[f\left(x\right)\right]\ =\ F\left(s\right),\ then$

a)

$F\left[f\left(-x\right)\right]=\overline{F\left(s\right)}$

b)

$F\left[f\left(x\right)\right]=\overline{F\left(s\right)}$

c)

$F\left[\overline{f\left(-x\right)}\right]\ =\overline{F\left(s\right)}$

d)

$F\left[\overline{f\left(x\right)}\right]\ =\ \overline{F\left(s\right)}$

14.

Find the fourier transform of the function f(t) = e^-a|t|, a>0.

a)

A

b)

B

c)

C

d)

D

15.

a)

A

b)

B

c)

C

d)

D

16.

a)

A

b)

B

c)

C

d)

D

17.

a)

A

b)

D

c)

C

d)

B

18.

Compute the ZT of a DT signal x(n)= (1,2,3,4,0,1)

a)

1 + 2z + 3z² + 4z³ + z⁴

b)

1 + 2z + 3z² + 4z³ + z⁵

c)

1 + 2z^-1 + 3z^-2 + 4z^-3 + z^-5

d)

1z² + 2z + 3 +z^-1 + z^-3

19.

Z-transform of an impulse function is……

a)

z

b)

z²

c)

1

d)

z³

20.

The two signal x(n) = aⁿ u(n) and x(n) = -aⁿ u(-n-1) have ROC z>a and z<a respectively.

a)

True

b)

False

21.

The Dirichlet condition for (DTFT) is……

a)

DT Signal should be absolutely differentiable

b)

DT Signal should be absolutely multipliable

c)

DT Signal should be absolutely integrable

d)

DT Signal should be absolutely summable

22.

Fourier Transform is used to analyse any elementary signals at different frequencies due to?

a)

Convert from time domain to frequency domain

b)

Convert from frequency domain to time domain

c)

Both a & b

d)

None of the above

23.

If x(n) is a DT signal then the equation x (n – n₀ ) indicates the basic ………..property.

a)

Linearity

b)

Time Reversal

c)

Frequency Shifting

d)

Time Shifting

24.

If [x(n)↔X(z)] and [y(n)↔Y(z)]. The linearity property of Z-Transform states

a)

ax(n)+by(n) ↔ aX(z).bY(z)

b)

ax(n).by(n) ↔ aX(z)+bY(z)

c)

ax(n)+by(n) ↔ aX(z)+bY(z)

d)

ax(n).by(n) ↔ aX(z).bY(z)

25.

If FT{x₁(n)}=X₁(w) and FT{x₂(n)}=X₂(w) then FT{x₁(n)*x₂(n)}=?

a)

X₁(w).X₂(w)

b)

X₁(w)+X₂(w)

c)

X₁(w)*X₂(w)

d)

None of the mentioned

26.

What is the convolution x(n) of the signals x₁(n)={-1,0,1} and x₂(n)={1,0,1,0,1,2} ?

a)

{1,1,0,0,0,0,1,2}

b)

{-1,0,0,0,0,-2,1,2}

c)

{-1,1,0,0,0,0,1,-2}

d)

{1,-1,0,0,0,0,-1,2}

27.

Determine the Nyquist rate and Nyquist interval for Cos(4πt).

a)

4 Hz, 0.25 sec

b)

0.5 Hz, 0.5 sec

c)

0.5 Hz, 2 sec

d)

2 Hz, 0.5 sec

28.

The Nyquist theorem for sampling (choose from arguments given below)

1) Converts time domain to frequency domain

2) Helps in quantization

3) Limits the bandwidth requirement

4) Provide the spectrum of the signal

a)

only 3 is correct

b)

1 and 2 are correct

c)

1 and 3 are correct

d)

All the four are correct

29.

Unit Step function is defined by

a)

u(n) = 1, n ≥ 0

= 0, n < 0

b)

u(n) = 1, n = 0

= 0, n ≠ 1

c)

u(n) = 1, n ≤ 0

= 0, n ≠ 1

d)

u(n) = 1, n ≤ 0

= 0, n ≥ 1

30.

Region of Convergence is defined as

a)

Value of z for which the z transform converges

b)

Value of frequency for which the z transform exists

c)

range of frequency for which the signal gets transmitted

d)

range in which the signal is free of noise

SS - Revision 4

Total questions: 30

Worksheet time: 15mins

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