{"id":209468,"date":"2025-03-21T17:38:16","date_gmt":"2025-03-21T22:38:16","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/03\/digital-music-couldnt-exist-without-the-fourier-transform"},"modified":"2025-03-21T17:38:16","modified_gmt":"2025-03-21T22:38:16","slug":"digital-music-couldnt-exist-without-the-fourier-transform","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/03\/digital-music-couldnt-exist-without-the-fourier-transform","title":{"rendered":"Digital Music Couldn\u2019t Exist Without the Fourier Transform"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/digital-music-couldnt-exist-without-the-fourier-transform.jpg\"><\/a><\/p>\n<p>This is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny little JPG files, and even powering your noise-canceling headphones. Here\u2019s how it works.<\/p>\n<p>The equation owes its power to the way that it lets mathematicians quickly understand the frequency content of any kind of signal. It\u2019s quite a feat. But don\u2019t just take my word for it\u2014in 1867, the physicist Lord Kelvin expressed his undying love for this fine piece of mathematics, too. He wrote, \u201cFourier\u2019s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.\u201d And so it remains.<\/p>\n<p><b>Math Will Tear Us Apart<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny little JPG files, and even powering your noise-canceling headphones. Here\u2019s how it works. The equation owes its power to the way that it lets mathematicians quickly understand [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41,2229,42,219],"tags":[],"class_list":["post-209468","post","type-post","status-publish","format-standard","hentry","category-information-science","category-mathematics","category-media-arts","category-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/209468","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=209468"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/209468\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=209468"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=209468"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=209468"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}