{"id":1320,"date":"2011-08-19T11:44:24","date_gmt":"2011-08-19T10:44:24","guid":{"rendered":"http:\/\/blogjam.name\/sid\/?page_id=1320"},"modified":"2011-10-06T11:18:09","modified_gmt":"2011-10-06T10:18:09","slug":"fourier-analysis","status":"publish","type":"page","link":"http:\/\/blogjam.name\/sid\/?page_id=1320","title":{"rendered":":Fourier analysis\/synthesis:"},"content":{"rendered":"<p>Pronunciation <strong>GB<\/strong>\u02d0 <span style=\"color: navy;\"><strong>\u02c8f\u028ari\u0259<\/strong><\/span>, <strong>GA<\/strong>: <span style=\"color: navy;\"><strong>\u02c8f\u028ari\u0259r<\/strong><\/span><\/p>\n<p><strong>Fourier analysis<\/strong> is a mathematical technique used to transform a signal in the time domain to a <a href=\"http:\/\/blogjam.name\/sid\/?page_id=824\">frequency<\/a> domain representation.  In terms of speech research this essentially means the production of an <a href=\"http:\/\/blogjam.name\/sid\/?page_id=344\">amplitude-frequency spectrum<\/a>  by processing a sampled version of the <a href=\"http:\/\/blogjam.name\/sid\/?page_id=856\">speech pressure waveform<\/a> of a sound.  The equation used is known as a <strong>Discrete Fourier Transform (DFT)<\/strong>. This is given below:<br \/>\n<center><img src=\"dftsnip.jpg\" alt=\"\" \/><\/center><br \/>\n<em>where X=a value in the frequency domain, x=a value in the time domain, N=the total number of time domain sample points.<\/em><\/p>\n<p>A related technique, known as <strong>Fourier Synthesis<\/strong>, produces a sampled time domain representation from a frequency domain representation, using the Inverse DFT:<br \/>\n<center><img src=\"idftsnip.jpg\" alt=\"\" \/><\/center><\/p>\n<p>In practice one of a number of available computationally efficient algorithms is used to perform the transformations.  These are known as <strong>Fast Fourier Transforms (FFT)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pronunciation GB\u02d0 \u02c8f\u028ari\u0259, GA: \u02c8f\u028ari\u0259r Fourier analysis is a mathematical technique used to transform a signal in the time domain to a frequency domain representation. In terms of speech research this essentially means the production of an amplitude-frequency spectrum by &hellip; <a href=\"http:\/\/blogjam.name\/sid\/?page_id=1320\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":174,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=\/wp\/v2\/pages\/1320"}],"collection":[{"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1320"}],"version-history":[{"count":4,"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=\/wp\/v2\/pages\/1320\/revisions"}],"predecessor-version":[{"id":2605,"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=\/wp\/v2\/pages\/1320\/revisions\/2605"}],"up":[{"embeddable":true,"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=\/wp\/v2\/pages\/174"}],"wp:attachment":[{"href":"http:\/\/blogjam.name\/sid\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}