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;Task:
Calculate the &nbsp; FFT &nbsp; (<u>F</u>ast <u>F</u>ourier <u>T</u>ransform) &nbsp; of an input sequence.

The most general case allows for complex numbers at the input
and results in a sequence of equal length, again of complex numbers.
If you need to restrict yourself to real numbers, the output should
be the magnitude (i.e. sqrt(re²+im²)) of the complex result.

The classic version is the recursive Cooley–Tukey FFT. [http://en.wikipedia.org/wiki/Cooley–Tukey_FFT_algorithm Wikipedia] has pseudo-code for that.
Further optimizations are possible but not required.
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