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:
“I believe that history might be, and ought to be, taught in a new fashion so as to make the meaning of it as a process of evolution intelligible to the young.”
—Thomas Henry Huxley (1825–95)
“You that would judge me do not judge alone
This book or that, come to this hallowed place
Where my friends’ portraits hang and look thereon;
Ireland’s history in their lineaments trace;
Think where man’s glory most begins and ends
And say my glory was I had such friends.”
—William Butler Yeats (1865–1939)
“In the history of the human mind, these glowing and ruddy fables precede the noonday thoughts of men, as Aurora the sun’s rays. The matutine intellect of the poet, keeping in advance of the glare of philosophy, always dwells in this auroral atmosphere.”
—Henry David Thoreau (1817–1862)