Interpretation in Terms of Time and Frequency
In signal processing, the Fourier transform often takes a time series or a function of continuous time, and maps it into a frequency spectrum. That is, it takes a function from the time domain into the frequency domain; it is a decomposition of a function into sinusoids of different frequencies; in the case of a Fourier series or discrete Fourier transform, the sinusoids are harmonics of the fundamental frequency of the function being analyzed.
When the function ƒ is a function of time and represents a physical signal, the transform has a standard interpretation as the frequency spectrum of the signal. The magnitude of the resulting complex-valued function F at frequency ω represents the amplitude of a frequency component whose initial phase is given by the phase of F.
Fourier transforms are not limited to functions of time, and temporal frequencies. They can equally be applied to analyze spatial frequencies, and indeed for nearly any function domain. This justifies their use in branches such diverse as image processing, heat conduction and automatic control.
Read more about this topic: Fourier Analysis
Famous quotes containing the words terms, time and/or frequency:
“Consider his life which was valueless
In terms of employment, hotel ledgers, news files.
Consider. One bullet in ten thousand kills a man.
Ask. Was so much expenditure justified
On the death of one so young and so silly
Lying under the olive tree, O world, O death?”
—Stephen Spender (1909–1995)
“A whole village-full of sensuous emotion, scattered abroad all the year long, surged here in a focus for an hour. The forty hearts of those waving couples were beating as they had not done since, twelve months before, they had come together in similar jollity. For the time Paganism was revived in their hearts, the pride of life was all in all, and they adored none other than themselves.”
—Thomas Hardy (1840–1928)
“One is apt to be discouraged by the frequency with which Mr. Hardy has persuaded himself that a macabre subject is a poem in itself; that, if there be enough of death and the tomb in one’s theme, it needs no translation into art, the bold statement of it being sufficient.”
—Rebecca West (1892–1983)