ABSTRACT

The Fourier series is named after the French mathematician Jean-Baptiste Joseph Fourier. A Fourier series is a mathematical way of representing a wavelike function as a sum of simple sine and cosine waves. It decomposes a periodic function or periodic signal into a sum of an infinite set of sinusoidal functions. When these sines and cosines are expressed as complex exponentials this gives the Fourier series in complex form. One of the most important operations in signal processing is the idea of the convolution of functions in the time domain. Signal processing uses one signal to modify another. The essence of the Fourier transform of a waveform is to decompose or separate the waveform into a sum of sinusoids of different frequencies. If these sinusoids sum together to form the original signal waveform, then the Fourier transform of the waveform has been found.