Re:An Interactive Introduction to Fourier Transforms
by ajross on Tuesday September 10, 2019 @07:14PM
(#20934880)
One bit of pedantry to complain about: this (really clever) essay is really only describing Fourier Decomposition, the idea that any function can be described in a vector space of sinusoidal basis functions. The Fourier Transform is an algorithm that exploits some (also really clever, and obviously of critical practical impact) factoring representations to compute that sum of functions in N*log(N) time in the number of data points instead of the naive N^2 summation of products.
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Re:An Interactive Introduction to Fourier Transforms
by jauntbox on Tuesday September 10, 2019 @07:33PM
(#20935022)
You're describing the "Fast" Fourier Transform, which is a specific algorithm for efficiently calculating the Discrete Fourier Transform of a signal.
The plain ol' Fourier Transform is also a bit different than what's described in this blog post. Fourier Transforms can be thought of as an extension of the Fourier Series described there. The Fourier Series shown there all have not only finitely many terms, but also a finite frequency spacing between successive terms (eg. 1Hz, 2Hz, 3Hz, ...). Fourier Transforms build up signals from _all_ frequencies, so are expressed as an integral over frequency components instead of a sum, even if it's an infinite sum.