This class implements the Fast Fourier Transform roughly as described on page 367
of "Theory and Application of Digital Signal Processing" by Rabiner and Gold.
Each instance caches tables used for transforming a given size (n = 2^nu samples) of data.

It would have been cleaner using complex numbers, but often the data is all real.

	initialization
	n nu: realData: realData:imagData:

	plugin-testing
	pluginPrepareData pluginTest pluginTransformData:

	testing
	imagData plot:in: realData samplesPerCycleForIndex: test

	transforming
	permuteData scaleData transformForward:

	bulk processing	top
	initializeHammingWindow: Initialize the windowing function to the generalized Hamming window. See F. Richard Moore, Elements of Computer Music, p. 100. An alpha of 0.54 gives the Hamming window, 0.5 gives the hanning window.
	initializeTriangularWindow Initialize the windowing function to the triangular, or Parzen, window. See F. Richard Moore, Elements of Computer Music, p. 100.
	setSize: Initialize variables and tables for performing an FFT on the given number of samples. The number of samples must be an integral power of two (e.g. 1024). Prepare data for use with the fast primitive.
	transformDataFrom:startingAt: Forward transform a block of real data taken from from the given indexable collection starting at the given index. Answer a block of values representing the normalized magnitudes of the frequency components.

	initialization	top
	n
	nu: Initialize variables and tables for transforming 2^nu points
	realData:
	realData:imagData:

	plugin-testing	top
	pluginPrepareData The FFT plugin requires data to be represented in WordArrays or FloatArrays
	pluginTest Display restoreAfter: [(FFT new nu: 12) pluginTest].
	pluginTransformData: Plugin testing -- if the primitive is not implemented or cannot be found run the simulation. See also: FFTPlugin

	testing	top
	imagData
	plot:in: Throw-away code just to check out a couple of examples
	realData
	samplesPerCycleForIndex: Answer the number of samples per cycle corresponding to a power peak at the given index. Answer zero if i = 1, since an index of 1 corresponds to the D.C. component.
	test Display restoreAfter: [(FFT new nu: 8) test]. -- Test on an array of 256 samples

	transforming	top
	permuteData
	scaleData Scale all elements by 1/n when doing inverse
	transformForward:

	instance creation	top
	new: Answer a new FFT instance for transforming data packets of the given size.