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# Fourier Transform
Fourier Transform (FT) is one of the most important transformations/[algorithms](algorithm.md) in [signal](signal.md) processing (and really in [computer science](compsci.md) and [mathematics](math.md) in general), which enables us to express and manipulate a signal (such as a sound or picture) in terms of [frequencies](frequency.md) it is composed of (rather than in terms of individual [samples](samples.md)). It is so important because frequencies (basically [sine](sine.md) waves) are actually THE important thing in signals, they allow us to detect things (voices, visual objects, chemical elements, ...), [compress](compression.md) signals, modify them in useful ways (e.g. filter out [noise](noise.md) of specific frequency band, enhance specific frequency bands, ...). There also exists a related algorithms called **[Fast Fourier Transform](fft.md)** (FFT) which is able to compute one specific version of FT very quickly and so is often used in practice.
Fourier Transform (FT) is one of the most important transformations/[algorithms](algorithm.md) in [signal](signal.md) processing (and really in [computer science](compsci.md) and [mathematics](math.md) in general), which enables us to express and manipulate a signal (such as a sound or picture) in terms of [frequencies](frequency.md) it is composed of (rather than in terms of individual [samples](samples.md)). It is so important because frequencies (basically [sine](sine.md) waves) are actually THE important thing in signals, they allow us to detect things (voices, visual objects, chemical elements, ...), [compress](compression.md) signals, modify them in useful ways (e.g. filter out [noise](noise.md) of specific frequency band, enhance specific frequency bands, ...). There also exists a related algorithm called **[Fast Fourier Transform](fft.md)** (FFT) which is able to compute one specific version of FT very quickly and so is often used in practice.
For newcomers FT is typically not easy to understand, it takes time to wrap one's head around it. There is also a very confusing terminology; there exist slightly different kinds of the Fourier Transform that are called by similar names, or sometimes all simply just "Fourier Transform" -- what programmers usually mean by FT is DFT or FFT. There also exist Fourier Transforms in higher dimensions (2D, 3D, ...) -- the base case is called one dimensional (because our input signal has one coordinate). All this will be explained below.