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:
“As I am, so shall I associate, and so shall I act; Caesar’s history will paint out Caesar.”
—Ralph Waldo Emerson (1803–1882)
“What would we not give for some great poem to read now, which would be in harmony with the scenery,—for if men read aright, methinks they would never read anything but poems. No history nor philosophy can supply their place.”
—Henry David Thoreau (1817–1862)
“Books of natural history aim commonly to be hasty schedules, or inventories of God’s property, by some clerk. They do not in the least teach the divine view of nature, but the popular view, or rather the popular method of studying nature, and make haste to conduct the persevering pupil only into that dilemma where the professors always dwell.”
—Henry David Thoreau (1817–1862)