Casio ClassPad OS Version 3.03 H(ω) = F [h(t)] = ∫–∞∞ h(t)e–iωt dt, ∫–∞∞ g(y)eiyt dy, f(x) = ∫–∞∞ F(k)e2πikx dk F(k) = ∫–∞∞ f(x)e–2πikx dx

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Using the Action Menu

uFFT, 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)e2πikx dk F(k) = ∫–∞∞f(x)e–2πikxdx

Some authors (especially physicists) prefer to write the transform in terms of angular frequency ω ≡ 2πν instead of the oscillation frequency ν.

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

H(ω) = F [h(t)] = ∫–∞∞h(t)e–iωtdt

h(t) = F –1[H(ω)] =	1	∫ ∞ H(ω)eiωt dω
	2π
		–∞

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

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

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