{"id":1369,"date":"2008-11-14T21:23:18","date_gmt":"2008-11-14T13:23:18","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=1369"},"modified":"2019-07-08T10:15:09","modified_gmt":"2019-07-08T02:15:09","slug":"friday-math-movie-sine-wave-to-square-wave-using-fourier-series","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-sine-wave-to-square-wave-using-fourier-series-1369","title":{"rendered":"Friday Math Movie - Sine Wave to Square Wave using Fourier Series"},"content":{"rendered":"<p>We learned about <a href=\"\/trigonometric-graphs\/1-graphs-sine-cosine-amplitude.php\">sine waves in elementary trigonometry<\/a>:<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/trigonometric-graphs\/img\/sinx.gif\" alt=\"Graph of a sine curve\"  width=\"328\" height=\"207\" \/><\/p>\n<p>The idea behind the <strong>Fourier Series<\/strong> is to add sine curves with different amplitudes and frequencies and the resulting curve can be either a square wave, a sawtooth wave or many other interesting periodic shapes. You can see more on this concept in this <a href=\"https:\/\/www.intmath.com\/fourier-series\/1-overview.php\">Introduction to Fourier Series<\/a>.<\/p>\n<p>This week's movie begins with a pure sine wave tone and then the other sine curves are added to it to produce something very close to a square wave (with the odd wiggle here and there) as the number of added curves becomes very large.<\/p>\n<p><b>Warning:<\/b> The final square wave tone may be pretty loud.<\/p>\n<div class=\"videoBG\">\n<iframe title=\"YouTube video player\" width=\"480\" height=\"303\" src=\"https:\/\/www.youtube.com\/embed\/y6crWlxKB_E\" frameborder=\"0\" allowfullscreen><\/iframe>\n<\/div>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-sine-wave-to-square-wave-using-fourier-series-1369#comments\" id=\"comms\">3 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p><a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-sine-wave-to-square-wave-using-fourier-series-1369\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2008\/11\/fourier.gif\" alt=\"Fourier series Youtube movie\" title=\"Fourier series Youtube movie\" width=\"128\" height=\"85\" class=\"imgRt\" \/><\/a>This movie cleverly demonstrates what Fourier Series really gives us.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[105],"tags":[134],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/1369"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=1369"}],"version-history":[{"count":1,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/1369\/revisions"}],"predecessor-version":[{"id":12055,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/1369\/revisions\/12055"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=1369"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=1369"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=1369"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}