# The Discrete Fourier Transform -- A Primer

DevFeed: [The Discrete Fourier Transform -- A Primer](<https://devfeed.tech/articles/the-discrete-fourier-transform-a-primer-40278.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/06/23/the-discrete-fourier-transform/>)

Published: 2012-06-23T14:13:53Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Programming](<https://devfeed.tech/topics/programming.md>)

Tags: [analysis](<https://devfeed.tech/tags/analysis.md>), [course](<https://devfeed.tech/tags/course.md>), [fourier-analysis](<https://devfeed.tech/tags/fourier-analysis.md>), [fourier-transform](<https://devfeed.tech/tags/fourier-transform.md>), [function](<https://devfeed.tech/tags/function.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [primer](<https://devfeed.tech/tags/primer.md>), [vector-spaces](<https://devfeed.tech/tags/vector-spaces.md>)

## AI overview

This primer explains the intuitive connections between continuous and discrete Fourier transforms. It covers discrete approximations of functions and transforms, the transition between discrete representations, and the role of sampling as motivation.

## Source excerpt

So here we are. We have finally made it to a place where we can transition with confidence from the classical continuous Fourier transform to the discrete version, which is the foundation for applications of Fourier analysis to programming. Indeed, we are quite close to unfurling the might of the Fast Fourier Transform algorithm, which efficiently computes the discrete Fourier transform. But because of its focus on algorithmic techniques, we will save it for a main content post and instead focus here on the intuitive connections between the discrete and continuous realms.