Uploaded February 2021 | Updated September 2026, 1 day ago

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In most of the cases where a Fourier Transform is actually employed, it is not an integral. In this video, I give a rapid fire introduction to functional analysis, the Schwartz space, tempered distributions, and their Fourier Transforms. We show that the Fourier Transform of a periodic function can be viewed as a Tempered Distribution, and through Dirac or Delta Combs we can show that a Fourier Transform of a periodic function is a collection of impulses and from that we can derive a Fourier Series of a Periodic Function.

Music:
Come 2gether by Ooyy
Dark Utopia by FormantX
Detergent by Dylan Sitts
Video Call from Los Angeles by Trevor Kowalski
Into the Blue by the Luwaks
A Drop in the Ocean by Jacob Ahlbom
Under the Weather by Damma Beatz
Guardians + Tek by Craig Hardgrove

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