History
The precursor of the transforms were the Fourier series to express functions in finite intervals. Later the Fourier transform was developed to remove the requirement of finite intervals.
Using the Fourier series, just about any practical function of time (the voltage across the terminals of an electronic device for example) can be represented as a sum of sines and cosines, each suitably scaled (multiplied by a constant factor), shifted (advanced or retarded in time) and "squeezed" or "stretched" (increasing or decreasing the frequency). The sines and cosines in the Fourier series are an example of an orthonormal basis.
Read more about this topic: Integral Transform
Famous quotes containing the word history:
“It takes a great deal of history to produce a little literature.”
—Henry James (1843–1916)
“There has never been in history another such culture as the Western civilization M a culture which has practiced the belief that the physical and social environment of man is subject to rational manipulation and that history is subject to the will and action of man; whereas central to the traditional cultures of the rivals of Western civilization, those of Africa and Asia, is a belief that it is environment that dominates man.”
—Ishmael Reed (b. 1938)
“The reverence for the Scriptures is an element of civilization, for thus has the history of the world been preserved, and is preserved.”
—Ralph Waldo Emerson (1803–1882)