{"id":1405,"date":"2022-11-05T11:08:05","date_gmt":"2022-11-05T10:08:05","guid":{"rendered":"https:\/\/localdab.org\/?page_id=1405"},"modified":"2025-12-28T07:58:33","modified_gmt":"2025-12-28T06:58:33","slug":"symbols-glossary","status":"publish","type":"page","link":"https:\/\/localdab.org\/index.php\/glossary\/q-t\/symbols-glossary\/","title":{"rendered":"Symbols"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-large-font-size\">What are symbols in digital communications?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">We do not want to confuse the reader but let us start by defining that a digital signal is nothing else than a <strong>special<\/strong> analog signal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The reason is that an electric signal is a signal and whether analog or digital. The physics of both signals are the same.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Comparison<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consider the amplitude characteristics of an analog signal. The analog signal&#8217;s amplitude can take <strong>unending instantaneous values<\/strong> between the minimum (negative amplitude) and maximum (positive amplitude).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The digital signal is just an analog signal with only <strong>2 instantaneous values<\/strong>.<br>When an analog signal can only have two instantaneous values, as is amplitude, we call it a digital signal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Modulation<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Modulation techniques make use of this because transmitting always uses analog signals. The (digital) modulation on the carrier happens by switching (keying) between two amplitudes, frequencies, or phases.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, there is a solution to increase the bitrate in digital transmissions by choosing more than 2 instantaneous values of a signal.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When using\u00a0\u00a0 4 instantaneous values, we would be able to transmit <strong>2 bits<\/strong> at once<\/li>\n\n\n\n<li>When using\u00a0\u00a0 8 instantaneous values, we would be able to transmit <strong>3 bits<\/strong> at once<\/li>\n\n\n\n<li>When using 16 instantaneous values, we would be able to transmit <strong>4 bits<\/strong> at once<\/li>\n\n\n\n<li>Etc.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline;\">Table<\/span> &#8211; number of analog states and the number of bits per symbol.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-f56f613f wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-f56f613f wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-f56f613f wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-cyan-bluish-gray-background-color has-background wp-block-paragraph\">0  -&gt; 00<br>1  -&gt; 01<br>2  -&gt; 10<br>3  -&gt; 11<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"has-pale-cyan-blue-background-color has-background wp-block-paragraph\">0  -&gt; 000<br>1  -&gt; 001<br>2  -&gt; 010<br>3  -&gt; 011<br>4  -&gt; 100<br>5  -&gt; 101<br>6  -&gt; 110<br>7  -&gt; 111<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"has-luminous-vivid-orange-background-color has-background wp-block-paragraph\">  0  -&gt; 0000<br>  1  -&gt; 0001<br>  2  -&gt; 0010<br>  3  -&gt; 0011<br>  4  -&gt; 0100<br>  5  -&gt; 0101<br>  6  -&gt; 0110<br>  7  -&gt; 0111<br>  8  -&gt; 1000<br>  9  -&gt; 1001<br>10  -&gt; 1010<br>11  -&gt; 1011<br>12  -&gt; 1100<br>13  -&gt; 1101<br>14  -&gt; 1110<br>15  -&gt; 1111<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">We call <strong>symbols<\/strong> (similar to the unit Bauds) the number of bits we can send at once. The above example shows <strong>symbols<\/strong> of 2, 3, and 4 bits.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It is important because these techniques of sending multiple bits in one signal apply to all digital modulations.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The disadvantage of increasing the <strong>number of bits<\/strong> per symbol is that the number of values increases. When talking about amplitudes, the <strong><em><a href=\"https:\/\/localdab.org\/index.php\/glossary\/a-d\/continuous-discrete-data\/\" data-type=\"page\" data-id=\"1638\" target=\"_blank\" rel=\"noreferrer noopener\">discrete <\/a><\/em><\/strong>amplitude values will be closer and more difficult to detect correctly. Their detection tolerance becomes smaller.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Remember that noise added to a signal will make the parameters wobble in their tolerance area.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The rule to detect the values precisely is that the more bits a symbol contains, the higher the signal-to-noise ratio should be. There will be an SNR threshold to detect a signal based on symbols correctly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The parameters of the electric signal can be <strong>amplitude<\/strong>, <strong>frequency<\/strong>, and <strong>phase<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>DAB\/DAB<sup>+<\/sup><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In DAB(+) the <strong>symbols<\/strong> contain <strong>2 bits<\/strong>. The <strong>1536 carriers<\/strong> in DAB Mode-I can carry <strong>3072 bits<\/strong> in one modulation cycle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The modulation used is DQ<strong>P<\/strong>SK. The parameter of the carrier that changes is the <strong>Phase<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Q means quadrature or 4 phases and. The 4 values indicate that the symbol contains 2 bits. &#8220;SK&#8221; means Shift Keying between the 4&nbsp; values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/localdab.org\/index.php\/glossary\/\">Back<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>What are symbols in digital communications? We do not want to confuse the reader but let us start by defining that a digital signal is nothing else than a special analog signal. The reason is that an electric signal is a signal and whether analog or digital. The physics of both signals are the same. [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":1266,"menu_order":60,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1405","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/1405","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=1405"}],"version-history":[{"count":10,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/1405\/revisions"}],"predecessor-version":[{"id":2321,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/1405\/revisions\/2321"}],"up":[{"embeddable":true,"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/pages\/1266"}],"wp:attachment":[{"href":"https:\/\/localdab.org\/index.php\/wp-json\/wp\/v2\/media?parent=1405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}