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Casio CLASSPAD 330 3.04 User Manual

Page 171

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20060301

2-8-11

Using the Action Menu

S FFT, IFFT

Function:

FFT

is the command for the fast Fourier Transform, and

IFFT

is the

command for the inverse fast Fourier Transform.

2

n

data values are needed to perform FFT and IFFT. On the ClassPad, FFT and IFFT are

calculated numerically.

Syntax: FFT( list ) or FFT( list,

m

)

IFFT( list ) or IFFT( list,

m

)

• Data size must be 2

n

for

n

= 1, 2, 3, ...

• The value for

m

is optional. It can be from 0 to 2, indicating the FFT parameter to use.

m

= 0 Signal Processing

m

= 1 Pure Math

m

= 2 Data Analysis

The Fourier Transform is defined as the following:

Some authors (especially physicists) prefer to write the transform in terms of angular

frequency

W

N instead of the oscillation frequency N.

However, this destroys the symmetry, resulting in the transform pair shown below.

F

(

k

)

e

2

ikx

dk

f

(

x

)

=

f

(

x

)

e

–2

ikx

dx

F

(

k

)

=

h

(

t

)

e

i

t

dt

H

(

)

=

F

[

h

(

t

)]

=

H

(

)

e

i

t

d

h

(

t

)

=

F

–1

[

H

(

)]

=

1

2

f

(

t

)

e

iyt

dt

g

(

y

)

=

F

[

f

(

t

)]

=

1

2

g

(

y

)

e

iyt

dy

f

(

t

)

=

F

–1

[

g

(

y

)]

=

1

2

To restore the symmetry of the transforms, the convention shown below is sometimes
used.