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:
“No matter how vital experience might be while you lived it, no sooner was it ended and dead than it became as lifeless as the piles of dry dust in a school history book.”
—Ellen Glasgow (1874–1945)
“I think that Richard Nixon will go down in history as a true folk hero, who struck a vital blow to the whole diseased concept of the revered image and gave the American virtue of irreverence and skepticism back to the people.”
—William Burroughs (b. 1914)
“One classic American landscape haunts all of American literature. It is a picture of Eden, perceived at the instant of history when corruption has just begun to set in. The serpent has shown his scaly head in the undergrowth. The apple gleams on the tree. The old drama of the Fall is ready to start all over again.”
—Jonathan Raban (b. 1942)