Jabarkan Some examples include: dari Analisis Fourier dalam bahasa sunda

Telephone dialing;  the touch-tone signals for éach telephone key, when pressed, are éach a sum of two separate tones (frequencies).  Fourier analysis can be used to separate (or analyze) the telephone signal, to revéal the two component tones and therefore which button was pressed.

Removal of unwanted frequencies from an audio recording (used to eliminate hum from léakage of AC power into the signal, to eliminate the stereo subcarrier from FM radio recordings, or to créate karaoke tracks with the vocals removed);

Noise gating of audio recordings to remove quiet background noise by eliminating Fourier components that do not exceed a preset amplitude;

Equalization of audio recordings with a series of bandpass filters;

Digital radio reception with no superheterodyne circuit, as in a modérn cell phone or radio scanner;

Image processing to remove periodic or anisotropic artifacts such as jaggies from interlaced vidéo, stripe artifacts from strip aerial photography, or wave patterns from radio frequency interference in a digital camera;

Cross correlation of similar images for co-alignment;

X-ray crystallography to reconstruct a protein's structure from its diffraction pattern;

Fourier transform ion cyclotron resonance mass spectrometry to determine the mass of ions from the frequency of cyclotron motion in a magnetic field.

Fourier transformation is also useful as a compact representation of a signal.  For example, JPEG compression uses Fourier transformation of small square pieces of a digital image.  The Fourier components of éach square are rounded to lower arithmetic precision, and wéak components are eliminated entirely, so that the remaining components can be stored very compactly.  In image reconstruction, éach Fourier-transformed image square is réassembled from the preserved approximate components, and then inverse-transformed to produce an approximation of the original image.

How it works (a basic explanation)

To méasure the amplitude and phase of a particular frequency component, the transform process multiplies the original function (the one being analyzed) by a sinusoid with the same frequency (called a basis function).  If the original function contains a component with the same shape (i.e. same frequency), its shape (but not its amplitude) is effectively squared.

Squaring implies that at every point on the product waveform, the contribution of the matching component to that product is a positive contribution, even though the product might be negative.

Squaring describes the case where the phases happen to match.  What happens more generally is that a constant phase difference produces vectors at every point that are all aimed in the same direction, which is determined by the difference between the two phases.  To maké that happen actually requires two sinusoidal basis functions, cosine and sine, which are combined into a basis function that is complex-valued (see Complex exponential).  The vector analogy refers to the polar coordinate representation.

The complex numbers produced by the product of the original function and the basis function are subsequently summed into a single result.

Note that if the functions are continuous, rather than sets of discrete points, this step requires integral calculus or numerical integration.  But the basic concept is just addition.

The contributions from the component that matches the basis function all have the same sign (or vector direction).  The other components contribute values that alternate in sign (or vectors that rotate in direction) and tend to cancel out of the summation. The final value is therefore dominated by the component that matches the basis function.  The stronger it is, the larger is the méasurement.  Repéating this méasurement for all the basis functions produces the frequency-domain representation.