{"id":2315,"date":"2025-12-20T08:48:04","date_gmt":"2025-12-20T07:48:04","guid":{"rendered":"https:\/\/localdab.org\/?page_id=2315"},"modified":"2025-12-25T20:07:04","modified_gmt":"2025-12-25T19:07:04","slug":"complex-signal","status":"publish","type":"page","link":"https:\/\/localdab.org\/index.php\/glossary\/a-d\/complex-signal\/","title":{"rendered":"Complex signal"},"content":{"rendered":"\n<p class=\"has-small-font-size\">In English, the word <strong>complex<\/strong> is synonymous with difficult, but here it has a very simple and precise meaning.<\/p>\n\n\n\n<p class=\"has-small-font-size\">When one speaks of a complex signal, simply means.<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong><em>&#8220;The signal is described not by one but by two signals.&#8221;<\/em><\/strong><\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size\">Why is one signal sometimes not enough?<\/p>\n\n\n\n<p class=\"has-small-font-size\">For a classic signal representation, <strong>one quantity that varies over time<\/strong> (e.g. voltage or current) is usually sufficient.<\/p>\n\n\n\n<p class=\"has-small-font-size\">However, this has a significant disadvantage:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-small-font-size\">The <strong>phase of the signal<\/strong> is then <strong>not clearly known<\/strong><\/li>\n\n\n\n<li class=\"has-small-font-size\">There is <strong>no fixed phase reference<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-small-font-size\">As soon as <strong>phase information<\/strong> becomes important, a single signal is <strong>insufficient<\/strong>.<\/p>\n\n\n\n<p class=\"has-small-font-size\">In that case, it is necessary to describe the signal with <strong>two mutually perpendicular components<\/strong>.<\/p>\n\n\n\n<p class=\"has-small-font-size\">These two signals represent a single complex signal. They are nothing more than the projection onto the X-axis (0\u00b0) and the projection onto the Y-axis (90\u00b0) of a single rotating arrow (vector) that represents the signal.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>The word complex originates from mathematics, where numbers consisting of a <strong>real part (X-axis) <\/strong>and an<strong> imaginary part (Y-axis)<\/strong> are also called complex numbers.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"has-small-font-size\">The numbers on the X-axis (0\u00b0) are referred to as the real part or <strong>real<\/strong> signal. This is represented as the I signal (in phase).<\/p>\n\n\n\n<p class=\"has-small-font-size\">The numbers on the Y-axis (90\u00b0) are referred to as the quadrature or imaginary signal. This is represented as the Q signal (<strong>quadrature<\/strong> or 90\u00b0 shifted).<\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size\">Digital complex signals<\/p>\n\n\n\n<p class=\"has-small-font-size\">When referring to a digital IQ signal, it means that each point in time is represented by <strong>two samples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-small-font-size\">one <strong>I-sample<\/strong><\/li>\n\n\n\n<li class=\"has-small-font-size\">one <strong>Q-sample<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-small-font-size\">Together, these two samples contain all the information about:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-small-font-size\">The <strong>amplitude<\/strong><\/li>\n\n\n\n<li>The <strong>instantaneous phase<\/strong> of the signal<\/li>\n<\/ul>\n\n\n\n<p class=\"has-small-font-size\">This makes it possible to correctly process signals where phase information is important (such as with<strong> DAB\/DAB+<\/strong>) digitally.<\/p>\n\n\n\n<p><strong><em>&#8220;I and Q are not two signals, but two descriptions of the same signal.&#8221;<\/em><\/strong><\/p>\n\n\n\n<p class=\"has-small-font-size\"><a href=\"https:\/\/localdab.org\/index.php\/glossary\/\" data-type=\"page\" data-id=\"15\">Back<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In English, the word complex is synonymous with difficult, but here it has a very simple and precise meaning. When one speaks of a complex signal, simply means. &#8220;The signal is described not by one but by two signals.&#8221; Why is one signal sometimes not enough? For a classic signal representation, one quantity that varies [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":1257,"menu_order":33,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2315","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/2315","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/comments?post=2315"}],"version-history":[{"count":2,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/2315\/revisions"}],"predecessor-version":[{"id":2320,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/2315\/revisions\/2320"}],"up":[{"embeddable":true,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/1257"}],"wp:attachment":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/media?parent=2315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}