User Manual
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
Wy
2
P
N
instead of the oscillation frequency
N
.
However, this destroys the symmetry, resulting in the transform pair shown below.
–
F(k)e
2ikx
dk
f(x)=
–
f(x)e
–2ikx
dx
F(k)=
–
h(t)e
–it
dt
H()= F [h(t)]=
–
H()e
it
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.