Señal analítica

La señal analítica de Gabor correspondiente a una señal temporal real, es una señal compleja cuyo espectro de frecuencias es nulo para frecuencias negativas, y cuya parte real es igual a la señal original.

Definición

La señal analítica $x_{a}(t)$ se construye a partir de una señal real.^[1]

Sea $x(t)$ una señal real cuya transformada de Fourier es $X(\omega )$ . Construyamos ahora la siguiente función:

X_{a}(\omega )=\left\{{\begin{array}{rl}2X(\omega )&{\textrm {si}}\;\omega >0\\X(\omega )&{\textrm {si}}\;\omega =0\\0&{\textrm {si}}\;\omega <0\end{array}}\right.

La señal analítica correspondiente a $x(t)$ es la transformada de Fourier inversa de $X_{a}(\omega )$ :

x_{a}(t)={\mathcal {F}}^{-1}\{X_{a}(\omega )\}

Construcción alternativa

La señal analítica se puede construir también a partir de la transformada de Hilbert de $x(t)$ .

Sea $x_{h}(t)={\mathcal {H}}\{x(t)\}$ la transformada de Hilbert de $x(t)$ . Ahora podemos construir la señal analítica de la siguiente manera:

x_{a}(t)=x(t)+ix_{h}(t)\,\!

donde «i» es la unidad imaginaria.

Propiedades

La primera propiedad evidente de la señal analítica $x_{a}(t)$ es que su parte real es igual a la señal correspondiente:

\operatorname {Re} \{x_{a}(t)\}=x(t)

Aplicación

La señal analítica de Gabor permite separar una señal temporal en sus componentes de amplitud y fase instantáneas. Es decir, para cada tiempo $t$ , podremos calcular una función $A(t)$ y una función $\phi (t)$ tales que

x(t)=A(t)\cos(\phi (t))

Para esto basta calcular

A(t)={\sqrt {\operatorname {Re} \{x_{a}(t)\}^{2}+\operatorname {Im} \{x_{a}(t)\}^{2}}}

\phi (t)=\arg(x_{a}(t))

donde arg es el argumento de un número complejo.

Referencias

↑ Alan V. Oppenheim, Ronald W. Schafer (2000). Tratamiento de señales en tiempo discreto, 2ª Ed. Madrid : Prentice Hall Iberia. p. 873. ISBN 8420529877.

Datos: Q485394

Read other articles:

Douche

Sebuah penyuntik vagina berbentuk bohlam. Perhatikan lubang-lubang kecil di ujungnya (sekitar 1cm, atau setebal 1/2 inci). Pancuran vagina hanya digunakan untuk mendouche saja, yaitu dengan menganti ujung mocong enema dengan moncong vaginal (di kiri bawah). Moncong vaginal memiliki ciri lebih panjang, lebih tebal, dan memiliki lubang. Douche adalah alat yang digunakan untuk mengalirkan air ke seluruh tubuh dengan tujuan medis atau kebersihan, atau mengalirkan air itu sendiri. Kata douche bera...

Thomas Jefferson and Native Americans

This article is part of a series aboutThomas Jefferson Early life and political career Early life and career Declaration of Independence Committee of Five Notes on the State of Virginia Minister to France Secretary of State First Party System 1796 election Vice presidency Personal life 3rd President of the United States Presidency First term 1800 election 1st inauguration Jeffersonian democracy Fiscal policy Twelfth Amendment Military Peace Establishment Act Yazoo land scandal Louisiana Purc...

Final Piala FA 2011

Final Piala FA 2011TurnamenPiala FA 2010–2011 Manchester City Stoke City 1 0 Tanggal14 Mei 2011StadionStadion Wembley, LondonPemain Terbaik Mario Balotelli (Manchester City)[1]WasitMartin Atkinson (West Yorkshire)[2]Penonton88.643[3]CuacaCerah17 °C (63 °F)← 2010 2012 → Final Piala FA 2011 merupakan final edisi ke-130 dari Piala FA, yang merupakan kompetisi sepak bola domestik tertua di dunia.[4][5] Pertandingan ini dihelat pada...

Myles Standish

English military officer hired by the Pilgrims (1584–1656) For the astronomer, see E. Myles Standish. Myles StandishThis portrait was first published in 1885 and alleged to be a 1625 likeness of Standish, although its authenticity has never been proven.[1]Bornc. 1584Probably Chorley, Lancashire, EnglandDiedOctober 3, 1656 (aged 72)Duxbury, Plymouth County,Plymouth ColonyAllegianceEnglandPlymouth ColonyRankCaptainCommands heldPlymouth Colony militiaBattles/warsEighty Years' War (Neth...

The Cinematic Orchestra

British nu jazz group The Cinematic OrchestraBackground informationOriginLondon, EnglandGenresNu jazzelectronicdowntempomodern classicalYears active1999–presentLabelsNinja TuneDominoMembers Jason Swinscoe Phil France Luke Flowers Tom Chant Nick Ramm Stuart McCallum Past members Jamie Coleman T. Daniel Howard Federico Ughi Alex James Patrick Carpenter Clean Sadness Websitecinematicorchestra.com The Cinematic Orchestra is a British nu jazz and downtempo music group created in 1999 by Jason Sw...

Міністерство оборони України

Міністерство оборони України (Міноборони) Емблема Міністерства оборони та Прапор Міністерства оборони Будівля Міністерства оборони у КиєвіЗагальна інформаціяКраїна УкраїнаДата створення 24 серпня 1991Попередні відомства Міністерство оборони СРСР Народний комісарі...

Setsumatsusha

Miniature Japanese shrines A row of sessha at Iwa Shrine, Hyōgo Prefecture Sessha (摂社, auxiliary shrine) and massha (末社, undershrine), also called eda-miya (枝宮, branch shrines)[1] (collectively known as setsumatsusha (摂末社)[2][note 1]) are small or miniature shrines entrusted to the care of a larger shrine, generally due to some deep connection with the enshrined kami.[3] The two terms used to have legally different meanings, but are today syn...

尤睦佳·泽登巴尔

尤睦佳·泽登巴尔Юмжаагийн Цэдэнбал1970年代时的尤睦佳·泽登巴尔蒙古人民革命党中央委员会总书记任期1958年11月22日—1984年8月24日前任达希·丹巴（第一书记）继任姜巴·巴特蒙赫任期1940年4月8日—1954年4月4日前任达希·丹巴（第一书记）继任达希·丹巴（第一书记）蒙古人民共和國部長會議主席任期1952年1月26日—1974年6月11日前任霍尔洛·乔巴山继任姜巴·巴特蒙赫�...

La Pivellina

La PivellinaPoster film La PivellinaSutradaraTizza Covi dan Rainer FrimmelProduserRainer FrimmelDitulis olehTizza CoviPemeranPatrizia GerardiWalter SaabelAsia CrippaTairo CaroliSinematograferRainer FrimmelPenyuntingTizza CoviDistributorFilms DistributionTanggal rilis 19 Mei 2009 (2009-05-19) (Cannes) 13 November 2009 (2009-11-13) (Austria) Durasi100 menitNegaraAustriaBahasaItalia La Pivellina adalah sebuah debut film fitur Austria 2009 yang disutradarai oleh Tizza Covi dan R...

Nehemiah 13

A chapter in the Book of Nehemiah Nehemiah 13← chapter 12Esther 1 →Greek Orthodox Icon of Nehemiah, mounted on solid wood.BookBook of NehemiahCategoryKetuvimChristian Bible partOld TestamentOrder in the Christian part16 Nehemiah 13 is the thirteenth (and the final) chapter of the Book of Nehemiah in the Old Testament of the Christian Bible,[1] or the 23rd chapter of the book of Ezra-Nehemiah in the Hebrew Bible, which treats the book of Ezra and the book of Nehemiah as o...

Landgericht Schongau

Ehemaliges Amtshaus am Schlossplatz 1 Das Landgericht Schongau war ein von 1803 bis 1879 bestehendes bayerisches Landgericht älterer Ordnung mit Sitz in Schongau im heutigen Landkreis Weilheim-Schongau. Die Landgerichte waren im Königreich Bayern Gerichts- und Verwaltungsbehörden, die 1862 in administrativer Hinsicht von den Bezirksämtern und 1879 in juristischer Hinsicht von den Amtsgerichten abgelöst wurden. Geschichte Im Jahr 1803 wurde im Verlauf der Verwaltungsneugliederung Bayerns ...

Fly Casting Analyzer

Fly Casting AnalyzerFly Casting AnalyzerUsesAnalysis of casting strokeUsed withFly rodInventorNoel Perkins and Bruce RichardsRelatedFly Fishing The Fly Casting Analyzer is a research tool for understanding fly casting, developed in 2003 by Bruce Richards of Scientific Anglers and Noel Perkins, a professor of engineering at the University of Michigan.[1] The Fly Casting Analyzer is a unique system that measures the casting stroke of an individual casting a fly line with a fly rod. A se...

Outline of Bible-related topics

Contains sacred scriptures of Judaism and Christianity Part of a series on theBible Canons and books Tanakh Torah Nevi'im Ketuvim Old Testament (OT) New Testament (NT) Deuterocanon Antilegomena Chapters and verses Apocrypha Jewish OT NT Authorship and development Authorship Dating Hebrew canon Old Testament canon New Testament canon Composition of the Torah Mosaic authorship Pauline epistles Petrine epistles Johannine works Translations and manuscripts Dead Sea scrolls Masoretic Text Samarita...

David Fallows

English musicologist (born 1945) David Fallows in 2002 David Fallows (born 20 December 1945) is an English musicologist specializing in music of the late Middle Ages and early Renaissance, as well as the performance practice of music. He is a leader in fifteenth-century music studies, particularly secular song, Guillaume Dufay, and Josquin des Prez, both the subject of landmark biographies Fallows has written. Biography Fallows was born in Buxton on 20 December 1945. He received his BA from J...

Ваниль плосколистная

Ваниль плосколистная Научная классификация Домен:ЭукариотыЦарство:РастенияКлада:Цветковые растенияКлада:МонокотыПорядок:СпаржецветныеСемейство:ОрхидныеПодсемейство:ВанильныеТриба:VanilleaeПодтриба:VanillinaeРод:ВанильВид:Ваниль плосколистная Международное научное наз�...

Jeu de combat

Borne de Tekken 3 permettant à deux joueurs de s'affronter côte-à-côte. Le jeu de combat (ou fighting game en anglais), parfois appelé abusivement en France VS fighting (pour versus fighting)[1] ou plus familièrement jeu de baston[2], est un genre de jeu vidéo opposant un nombre limité de personnages (deux le plus souvent). Il se distingue des beat them all (ou beat 'em up dans les pays anglo-saxons), qui proposent de combattre de longues séries d'opposants et qui sont presque unique...

Luc Merenda

Luc Merenda Luc Merenda dans Salut les pourris (1974). Données clés Naissance 3 septembre 1943 (81 ans)Nogent-le-Roi, Eure-et-LoirFrance Nationalité Française Profession Acteur, mannequin Films notables Rue de la violenceSalut les pourrisL'Accusé, Séries notables Châteauvallon modifier Luc Merenda, né le 3 septembre 1943 à Nogent-le-Roi (Eure-et-Loir), est un acteur français. Principalement actif dans les années 1970, il a travaillé pendant plusieurs années dans le cinéma ...

Means of production

Inputs used in the production of goods and services with economic value This article is about the economics term. For the 2003 album, see Means of Production. Part of a series onEconomics History Outline Index Branches and classifications Applied Econometrics Heterodox International Micro / Macro Mainstream Mathematical Methodology Political JEL classification codes Concepts, theory and techniques Economic systems Economic growth Market National accounting Experimental economics Computational...

III Corps

3rd Corps, Third Corps, III Corps, or 3rd Army Corps may refer to: France 3rd Army Corps (France) III Cavalry Corps (Grande Armée), a cavalry unit of the Imperial French Army during the Napoleonic Wars III Corps (Grande Armée), a unit of the Imperial French Army during the Napoleonic Wars Germany III Cavalry Corps (German Empire), a unit of the Imperial German Army III Corps (German Empire), a unit of the Imperial German Army III Reserve Corps (German Empire), a unit of the Imperial German ...

Byzantine music

Music in the tradition of the Byzantine Empire Byzantine culture Aristocracy and bureaucracy Army Art Architecture Calendar Cities Coinage Cuisine Dance Diplomacy Dress Economy Gardens Law Literature Medicine Music People Science vte Byzantine music (Greek: Βυζαντινή μουσική, romanized: Vyzantiné mousiké) originally consisted of the songs and hymns composed for the courtly and religious ceremonial of the Byzantine Empire and continued, after the fall of Constantinople i...

Museum Kesehatan Jiwa

/profillengkap.com/index.php/article/Archie McKellar

/profillengkap.com/index.php/article/Arenac Township, Michigan

/profillengkap.com/index.php/article/New Zealand Horse of the Year

SMK Negeri 3 OKU

SMA Negeri 1 Sukau

The Decline and Fall of Nokia

Pseudoscopelus

Thracian warfare

Nigel Hastilow

Apprentissage de la lecture

Purwodadi, Angsana, Tanah Bumbu