Casio 3.04 S FFT, IFFT, g(y)
= F [ f(t)]
, f(t)
= F –1[g(y)]

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.

2n 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 2n 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:



f(x)
= –F(k)e2ikx dk



F(k)
= –f(x)e–2ikxdx

Some authors (especially physicists) prefer to write the transform in terms of angular frequency ΩΩψ 2ΠΝ instead of the oscillation frequency Ν.

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



H()
= F [h(t)]
= –h(t)e–itdt

h(t)
= F –1[H()]
= 21 –H()eit d

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

g(y) = F [ f(t)] =	1			 f(t)e–iytdt
2				–
f(t) = F –1[g(y)] =		1			 g(y)eiyt dy
	2
					–

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