Free Printable Revision Unit 3 B

1.

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)

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

2.

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)

$jfX\left(f\right)$

3.

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

a)

True

b)

False

4.

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

a)

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

b)

$2\pi$

c)

$\frac{1}{\pi}$

d)

$\pi$

5.

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)

$\frac{1}{jw}$

6.

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

a)

True

b)

False

7.

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)

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

8.

Fourier transform is a linear operation

a)

True

b)

False

9.

$If\ F_c\left[f\left(ax\right)\right]=k\ F_c\left(\frac{s}{a}\right)\ then\ k=$

(a)

10.

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

a)

True

b)

False

11.

Kernel of Fourier Transform is $e^{sx}$

a)

True

b)

False

Revision Unit 3 B

Total questions: 11

Worksheet time: 6mins

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