drummyfish/less_retarded_wiki
5
1
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

Update

Browse source
This commit is contained in:
Miloslav Ciz 2024-07-27 17:25:21 +02:00
parent 2ef693bc96
commit 9005259ff3
14 changed files with 1800 additions and 1779 deletions
Download patch file Download diff file Expand all files Collapse all files

2
fourier_transform.md
View file

@ -1,6 +1,6 @@
# 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 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.
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) in specific frequency band, enhance specific frequency bands, change audio speed without changing its pitch, pitch-shift a song without changing its speed and so on). 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.