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:
“America is the only nation in history which, miraculously, has gone directly from barbarism to degeneration without the usual interval of civilization.”
—Attributed to Georges Clemenceau (1841–1929)
“The principle that human nature, in its psychological aspects, is nothing more than a product of history and given social relations removes all barriers to coercion and manipulation by the powerful.”
—Noam Chomsky (b. 1928)
“When we of the so-called better classes are scared as men were never scared in history at material ugliness and hardship; when we put off marriage until our house can be artistic, and quake at the thought of having a child without a bank-account and doomed to manual labor, it is time for thinking men to protest against so unmanly and irreligious a state of opinion.”
—William James (1842–1910)