In this video, we introduce the Fourier Series and use it to represent periodic functions in terms of sine and cosine waves. In order to move to arbitrary functions, we extend the period to infinity and introduce the Fourier Transform.

This course in German Language: https://www.fau.tv/course/id/1022

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Reference
Maier, A., Steidl, S., Christlein, V., Hornegger, J. Medical Imaging Systems - An Introductory Guide, Springer, Cham, 2018, ISBN 978-3-319-96520-8, Open Access at Springer Link

Video References
3Blue1Brown - What is a Fourier Transform? A Visual Introduction https://youtu.be/spUNpyF58BY
Continuous Fourier Transform of Rect and Sinc Functions https://commons.wikimedia.org/wiki/File:Continuous_Fourier_transform_of_rect_and_sinc_functions.gif

Music Reference
XTaKeRuX - White Crow https://freemusicarchive.org/music/XTaKeRuX/Empty_Grave/White_Crow
The Zombie Dandies - Fascination https://freemusicarchive.org/music/The_Zombie_Dandies/Lo-Fi_Heroes/The_Zombie_Dandies_-_Lo-Fi_Heroes_-_06_Fascination
Ondrosik - Interlude https://freemusicarchive.org/music/Ondrosik/Nostalgic__Procrastination/Ondrosik-09-Interlude
Meydän - L'etoile danse Pt 1 https://freemusicarchive.org/music/Meydan/Havor/6-_LEtoile_danse_Pt_1_1738
Zoliborz - The secret of life https://freemusicarchive.org/music/Zoliborz/Poincare_Conjecture/Zoliborz_-_Poincare_Conjecture_-_03_The_Secret_of_Life
John Bartmann - Serial Killer https://freemusicarchive.org/music/John_Bartmann
Meydän - The beauty of maths https://freemusicarchive.org/music/Meydan/The_Beauty_of_Maths/Meydn_-_The_Beauty_of_Maths_1361
Damiano Baldoni - Red Rose https://freemusicarchive.org/music/Damiano_Baldoni/Crystal_Lake/Red_Rose
Damiano Baldoni - A Ghra https://freemusicarchive.org/music/Damiano_Baldoni/Lost_Dinasty/A_GhrO