Free Printable Revision Unit 3 A

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 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)

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

4.

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)

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

5.

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)

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

6.

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

a)

sinsx

b)

i sinsx

c)

cossx

d)

cosx

7.

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

a)

sinsx

b)

i sinsx

c)

cossx

d)

cosx

8.

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

a)

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

b)

$\sqrt{\frac{2}{\pi}}\int_0^{\infty}\ F_c\left[s\right]\ \cos 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)

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

9.

The Fourier Sine Transform of

e-^{ax}

a)

$F_s\left[e-^{ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{a}{a^2+s^2}$

b)

$F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$

c)

$F_c\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$

d)

none of the above

10.

The Fourier cosine Transform of

e-^{ax}

a)

$F_s\left[e-^{ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{a}{a^2+s^2}$

b)

$F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{s}{a^2+s^2}$

c)

$F_c\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\ \frac{a}{a^2+s^2}$

d)

none of the above

Revision Unit 3 A

Total questions: 10

Worksheet time: 5mins

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