Fourier analysis

Fourier analysis is based on the Fourier series named after the mathematician Joseph Fourier. The Fourier series is a mathematical method used to represent functions as an infinite series of sine and cosine terms. The functions in question can be real or complex valued:

The most efficient algorithm for Fourier analysis is the Fast Fourier Transform (FFT). This algorithm is implemented in SciPy and NumPy. When applied to the time series data, the Fourier analysis transforms maps onto the frequency domain, producing a frequency spectrum. The frequency spectrum displays harmonics as distinct spikes at certain frequencies. Music, for example, is composed from different frequencies with the note A at 440 Hz. The note A can be produced by a pitch fork. We can produce this and other notes with musical instruments such as a piano. White noise is a signal consisting of many frequencies, which are represented equally. White light is a mix of all the visible frequencies of light, also...