﻿{"id":67,"date":"2015-12-19T05:56:48","date_gmt":"2015-12-19T05:56:48","guid":{"rendered":"http:\/\/www.ana-log.org\/signaladvance\/?page_id=67"},"modified":"2016-01-25T15:48:50","modified_gmt":"2016-01-25T15:48:50","slug":"visible-temporal-advance","status":"publish","type":"page","link":"https:\/\/www.signaladvance.com\/?page_id=67","title":{"rendered":"Wave Propagation Physics"},"content":{"rendered":"<p>[et_pb_section admin_label=&#8221;section&#8221;][et_pb_row admin_label=&#8221;Row&#8221;][et_pb_column type=&#8221;4_4&#8243;][et_pb_text admin_label=&#8221;Text&#8221; background_layout=&#8221;light&#8221; text_orientation=&#8221;left&#8221; text_font_size=&#8221;14&#8243; use_border_color=&#8221;off&#8221; border_color=&#8221;#ffffff&#8221; border_style=&#8221;solid&#8221;]<\/p>\n<h3><span style=\"color: #008080;\"><strong>Wave Propagation Physics<\/strong><\/span><\/h3>\n<p>[\/et_pb_text][et_pb_divider admin_label=&#8221;Divider&#8221; color=&#8221;#09535e&#8221; show_divider=&#8221;on&#8221; divider_style=&#8221;solid&#8221; divider_position=&#8221;top&#8221; divider_weight=&#8221;1&#8243; hide_on_mobile=&#8221;on&#8221;] [\/et_pb_divider][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;row&#8221;][et_pb_column type=&#8221;4_4&#8243;][et_pb_image admin_label=&#8221;Image&#8221; src=&#8221;http:\/\/www.ana-log.org\/signaladvance\/wp-content\/uploads\/2015\/12\/group-velocity.jpg&#8221; show_in_lightbox=&#8221;off&#8221; url_new_window=&#8221;off&#8221; animation=&#8221;left&#8221; sticky=&#8221;off&#8221; align=&#8221;left&#8221; force_fullwidth=&#8221;off&#8221; always_center_on_mobile=&#8221;on&#8221; use_border_color=&#8221;off&#8221; border_color=&#8221;#ffffff&#8221; border_style=&#8221;solid&#8221;] [\/et_pb_image][et_pb_text admin_label=&#8221;Text&#8221; background_layout=&#8221;light&#8221; text_orientation=&#8221;left&#8221; text_font_size=&#8221;14&#8243; use_border_color=&#8221;off&#8221; border_color=&#8221;#ffffff&#8221; border_style=&#8221;solid&#8221;]<\/p>\n<p id=\"u2398-2\">In order to understand this seemingly contradictory behavior it is important to point out that electromagnetic propagation is characterized by five unique waveform velocities [Brillouin L, Wave Propagation and Group Velocity (Pure and Applied Physics), New York: Academic Press, 1960]. These include:<\/p>\n<ul>\n<li id=\"u2398-7\"><span id=\"u2398-5\">Phase velocity<\/span>\u00a0&#8211; the speed at which the phase of any one spectral frequency component of the wave travels.<\/li>\n<li id=\"u2398-11\"><span id=\"u2398-9\">Group velocity<\/span>\u00a0&#8211; the speed at which the variations in the shape of the wave&#8217;s amplitude (known as the modulation or envelope of the wave) propagates (see diagram below).<\/li>\n<li id=\"u2398-15\"><span id=\"u2398-13\">Front velocity<\/span>\u00a0&#8211; the speed of an abrupt signal discontinuity (signal abruptly turned on or off). It is considered as the very beginning of the signal in time, and it never exceeds \u201cc\u201d, the speed of light (see diagram below).<\/li>\n<li id=\"u2398-19\"><span id=\"u2398-17\">Energy velocity<\/span>\u00a0&#8211; the speed of energy transfer.<\/li>\n<li id=\"u2398-23\"><span id=\"u2398-21\">Signal velocity\u00a0<\/span>&#8211; the speed of information transfer, which, under various conditions, may be equivalent to one or more of the above four velocities.<\/li>\n<\/ul>\n<p>The \u201cfront velocity will correspond to the speed at which the first, extremely small (perhaps invisible) vibrations will occur, while the signal velocity yields the arrival of the main signal, with intensities on the order of the magnitude of the input signal.\u201d [Brillouin]<\/p>\n<p id=\"u2398-29\">In most cases, the signal velocity is equivalent to both the group and energy velocities. While the front velocity cannot exceed the speed of light, in special cases (e.g. media or circuitry that amplifies the initial or anterior-most portion of a waveform and attenuates the posterior portion), \u201c\u2026 the group velocity \u2026 can be greater than the velocity of light, can be infinite and even negative!\u201d [Brillouin]. That is, the detection of a pulsatile input or extended-in-time waveform at the output of the medium can precede its complete detection of the waveform at the input.<\/p>\n<p id=\"u2398-32\">During the time interval between the arrival of the wavefront (front velocity) and the actual detection of the group waveform, electromagnetic energy begins to propagate through the medium, the magnitude of which is not detectable until the oscillations achieve sufficient amplitude. These very early, very low amplitude (typically undetected) perturbations (referred to as \u201cforerunners\u201d by Brillouin) actually contain sufficient information to reproduce a temporally advanced signal. Signal Advance Technology acts to temporally advance the wave envelope of an analog signal resulting in earlier detection.<\/p>\n<p id=\"u2398-43\">This technology has been reviewed by\u00a0<span id=\"u2398-37\"><a class=\"nonblock\" href=\"https:\/\/www.signaladvance.com\/?page_id=70\" data-href=\"page:U1928\">experts<\/a><\/span>\u00a0in various fields, find out\u00a0<span id=\"u2398-41\"><a class=\"nonblock\" href=\"https:\/\/www.signaladvance.com\/?page_id=100\" data-href=\"page:U86\">more<\/a><\/span>.<\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[et_pb_section admin_label=&#8221;section&#8221;][et_pb_row admin_label=&#8221;Row&#8221;][et_pb_column type=&#8221;4_4&#8243;][et_pb_text admin_label=&#8221;Text&#8221; background_layout=&#8221;light&#8221; text_orientation=&#8221;left&#8221; text_font_size=&#8221;14&#8243; use_border_color=&#8221;off&#8221; border_color=&#8221;#ffffff&#8221; border_style=&#8221;solid&#8221;] Wave Propagation Physics [\/et_pb_text][et_pb_divider admin_label=&#8221;Divider&#8221; color=&#8221;#09535e&#8221; show_divider=&#8221;on&#8221; divider_style=&#8221;solid&#8221; divider_position=&#8221;top&#8221; divider_weight=&#8221;1&#8243; hide_on_mobile=&#8221;on&#8221;] [\/et_pb_divider][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;row&#8221;][et_pb_column type=&#8221;4_4&#8243;][et_pb_image admin_label=&#8221;Image&#8221; src=&#8221;http:\/\/www.ana-log.org\/signaladvance\/wp-content\/uploads\/2015\/12\/group-velocity.jpg&#8221; show_in_lightbox=&#8221;off&#8221; url_new_window=&#8221;off&#8221; animation=&#8221;left&#8221; sticky=&#8221;off&#8221; align=&#8221;left&#8221; force_fullwidth=&#8221;off&#8221; always_center_on_mobile=&#8221;on&#8221; use_border_color=&#8221;off&#8221; border_color=&#8221;#ffffff&#8221; border_style=&#8221;solid&#8221;] [\/et_pb_image][et_pb_text admin_label=&#8221;Text&#8221; background_layout=&#8221;light&#8221; text_orientation=&#8221;left&#8221; text_font_size=&#8221;14&#8243; use_border_color=&#8221;off&#8221; border_color=&#8221;#ffffff&#8221; border_style=&#8221;solid&#8221;] In order to understand this seemingly contradictory behavior it is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=\/wp\/v2\/pages\/67"}],"collection":[{"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=67"}],"version-history":[{"count":6,"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=\/wp\/v2\/pages\/67\/revisions"}],"predecessor-version":[{"id":695,"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=\/wp\/v2\/pages\/67\/revisions\/695"}],"wp:attachment":[{"href":"https:\/\/www.signaladvance.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}