In the Maple 6 worksheet, The Mathematics of Synthesizers, we saw how we can create arbitrary waveforms using Fourier Series of sine waves in Maple. This worksheet shows how Maple can be used to perform the reverse analysis. That is, import a signal and then extract the component sine waves. The tool for doing this is called the Fast Fourier Transform (FFT). This is an intensely numeric process and illustrates Maple's handling of numerics at the hardware level through the use of the evalhf() function and hfarrays. The hfarray is a special array type that allows you to handle numeric data at the hardware level, thus dramatically speeding up purely numeric operations.