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Sync two FFT managers so they agree for basic inputs #1
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I made the fftw version single-precision, but most of the change is to use a homebrew hamming window.
Some examples of hamming windows in the wild:
https://developer.apple.com/library/mac/documentation/Accelerate/Reference/vDSPRef/#//apple_ref/c/func/vDSP_hamm_window
http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.hamming.html
https://en.wikipedia.org/wiki/Window_function#Hamming_window
http://www.mathworks.com/help/signal/ref/hamming.html
https://www.dsprelated.com/freebooks/sasp/Matlab_Hamming_Window.html