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# Fourier Transform
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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.
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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.
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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.
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