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, therefore the land of the future, where, in the ages that lie before us, the burden of the World’s history shall reveal itself. It is a land of desire for all those who are weary of the historical lumber-room of Old Europe.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Throughout the history of commercial life nobody has ever quite liked the commission man. His function is too vague, his presence always seems one too many, his profit looks too easy, and even when you admit that he has a necessary function, you feel that this function is, as it were, a personification of something that in an ethical society would not need to exist. If people could deal with one another honestly, they would not need agents.”
—Raymond Chandler (1888–1959)
“No one can understand Paris and its history who does not understand that its fierceness is the balance and justification of its frivolity. It is called a city of pleasure; but it may also very specially be called a city of pain. The crown of roses is also a crown of thorns. Its people are too prone to hurt others, but quite ready also to hurt themselves. They are martyrs for religion, they are martyrs for irreligion; they are even martyrs for immorality.”
—Gilbert Keith Chesterton (1874–1936)