User's Manual

20060301
2-8-11
Using the Action Menu
u
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
ω ≡
2
π n
instead of the oscillation frequency
n
.
However, this destroys the symmetry, resulting in the transform pair shown below.
∫
∞
–∞
F(k)e
2πikx
dk
f(x) =
∫
∞
–∞
f(x)e
–2πikx
dx
F(k) =
∫
∞
–∞
h(t)e
–iωt
dt
H(ω) = F [h(t)] =
∫
∞
–∞
H(ω)e
iωt
dω
h(t) = F
–1
[H(ω)] =
1
2π
∫
∞
–∞
f(t)e
–iyt
dt
g(y) = F [ f(t)] =
1
2π
∫
∞
–∞
g(y)e
iyt
dy
f(t) = F
–1
[g(y)] =
1
2π
To restore the symmetry of the transforms, the convention shown below is sometimes
used.