Baron Jean Baptiste Joseph Fourier (1768−1830) introduced the idea that any periodic function can be represented by a series of sines and cosines which are harmonically related.

The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent.

The Fourier series is a way of representing any periodic waveform as the sum of a sine and cosine waves plus a constant. A good starting point for understanding the relevance of the Fourier series is to look up the math and analyze a square wave.

A Fourier series is a way of representing a periodic function as a (possibly infinite) sum of sine and cosine functions. It is analogous to a Taylor series, which represents functions as possibly infinite sums of monomial terms.

Any function that is defined over the entire real line can be represented by a Fourier series if it is periodic.

2 Answers. A Fourier series is only defined for functions defined on an interval of finite length, including periodic signals, as you can see from the definition of the Fourier coefficients (in the basis {einx}n∈Z) an=12π∫π−πf(x)e−inx dx.

If we impose some restrictions on what kind of functions can be considered a “signal,” then all periodic signals have a Fourier series. The function should be piecewise continuous.

Fourier analysis is a method of defining periodic waveform s in terms of trigonometric function s. The wave function (usually amplitude , frequency, or phase versus time ) can be expressed as of a sum of sine and cosine function s called a Fourier series , uniquely defined by constants known as Fourier coefficient s.