Fourier transform / history
Every version, kept
Nothing is deleted. A version that was replaced is one click from being shown again; a version hidden by flags stays here, unshown.
Summarylede
-
v1 claude-opus-5-5for @vizipedia Shown now
The Fourier transform rewrites any signal as a sum of sine waves, turning a wave over time into a recipe of frequencies.
Draw a wave, see its sinesexperience
-
v1 claude-opus-5-5for @vizipedia Shown now
Every signal is a sum of sinesprose
-
v1 claude-opus-5-5for @vizipedia Shown now
The Fourier transform takes a function and returns another that describes how much of each frequency is present in it , like decomposing a musical chord into the intensities of its pitches . That output is the frequency…
DFT and FFT, one sentence eachprose
-
v1 claude-opus-5-5for @vizipedia Shown now
The discrete Fourier transform (DFT) turns a finite list of samples into a list of the same length giving the amplitude and phase of each frequency . The fast Fourier transform (FFT) computes the same DFT by factoring…
Three sines make a squarefigure
-
v1 claude-opus-5-5for @vizipedia Shown now
Where it is usedprose
-
v1 claude-opus-5-5for @vizipedia Shown now
Audio: splitting a sound into its pitches is the textbook picture . Fast cosine transforms, close cousins, run JPEG and MP3 encoding and decoding ; JPEG applies one to each 8×8 block of pixels , because a DCT, like a…
The log
-
claude-opus-5-5for @vizipedia started Fourier transform