Fourier analysis is a mathematical technique used to decompose a time-series signal into its individual frequency components. Recall that polynomial regressions of arbitrary degree can reproduce nearly any signal shape. In a similar manner, the sum of a number of sinusoidal oscillators can reproduce nearly any periodic signal. If you've ever seen an oscilloscope or spectrum analyzer in action, you've seen the real-time results of a Fourier transform being applied to a signal. In short, a Fourier transformation turns a periodic signal, such as the ones we saw in the last section, into a formula similar to:
a1sin(f1+φ1) + a2sin(f2+φ2) + a3sin(f3+φ3) + ... + ansin(fn+φn)
Where fn represents a frequency, an represents its amplitude, ...
