FFT
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Function Description
Returns the fast Fourier transform (‘FFT’) (if CarryOutForwardTransform
is true) or the inverse FFT (if CarryOutForwardTransform is false) of an
array of complex numbers (i.e. input array has term, the real part
followed by the imaginary part), where must
be an integral power of two.
If the input to the FFT is (each
is a
complex number) where then
the output (of the forward transform) is another array of complex numbers as
follows:
where . When
inverting, a constant multiplier is applied to all terms to ensure that the
result of applying the transform to the output of the forward transform and
then applying the transform returns the original series.
The FFT calculates the using
rather
than the that
might appear to be needed given the above formula. This involves a very large
speed up for large data analyses, e.g. analysing large pictures or other datasets.
Some writers use , e.g.
Press et
al. (2007), and some writers multiply the expression with constants, e.g. . The
use of means
that the end result is compatible with output from the Microsoft Excel Data
Analysis Toolpack.
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