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:
“In nature, all is useful, all is beautiful. It is therefore beautiful, because it is alive, moving, reproductive; it is therefore useful, because it is symmetrical and fair. Beauty will not come at the call of a legislature, nor will it repeat in England or America its history in Greece. It will come, as always, unannounced, and spring up between the feet of brave and earnest men.”
—Ralph Waldo Emerson (1803–1882)
“The awareness that health is dependent upon habits that we control makes us the first generation in history that to a large extent determines its own destiny.”
—Jimmy Carter (James Earl Carter, Jr.)
“I cannot be much pleased without an appearance of truth; at least of possibility—I wish the history to be natural though the sentiments are refined; and the characters to be probable, though their behaviour is excelling.”
—Frances Burney (1752–1840)