MediaWiki API result
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"*": "Subscribe to the mediawiki-api-announce mailing list at <https://lists.wikimedia.org/mailman/listinfo/mediawiki-api-announce> for notice of API deprecations and breaking changes."
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"title": "Rechnen mit komplexen Zahlen (Lernvideo)",
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"*": " '''!!! The learning video is in German language (images and sound). There is an English summary at the end of this file !!! '''\n\n\n=== Inhalt ===\n* Reelle Zahlenmengen und Zahlenstrahl: Ganze Zahlen, nat\u00fcrliche ... , reelle ... , rationale ... , irrationale ... (Dauer 3:14) \n* Darstellung komplexer Zahlen und Komplexe Ebene: Realteil, Imagin\u00e4rteil, Betrag, Phase, Satz von Euler (Dauer 2:00)\n*Rechenregeln f\u00fcr komplexe Zahlen: Summe, Differenz, Produkt, Quotient, Konjugiert-komplexe, Quadrat, Quadratwurzel (Dauer 6:36)\n* Gesamtdauer 11:50\n\n\n<lntmedia preload=\"none\">\n file:Rechnen mit komplexen Zahlen.mp4\n file:Rechnen mit komplexen Zahlen.ogv\n</lntmedia>\n\n=== Erkannte Fehler ===\n* Bei (10:30) muss es hei\u00dfen: $d = z - z^\\star = 2 {\\rm j} \\cdot y$ , wenn $z = x + {\\rm j} \\cdot y$ ist. Im Video wurde die imagin\u00e4re Einheit ${\\rm j}$ vergessen.\n\n\nDieses Lernvideo wurde 2006 am [http://www.lnt.ei.tum.de/startseite \"Lehrstuhl f\u00fcr Nachrichtentechnik\"] der [https://www.tum.de/ \"Technischen Universit\u00e4t M\u00fcnchen\"] konzipiert und realisiert.<br>\nBuch und Regie: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_\u00dcbertragungstechnik#Prof._Dr.-Ing._Norbert_Hanik_(at_LNT_from_1989-1995,_at_L\u00dcT since_2004)|»Norbert Hanik«]] und [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28at_LNT_since_1974.29|»G\u00fcnter S\u00f6der«]], Sprecher: [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_\u00dcbertragungstechnik#Prof._Dr.-Ing._Norbert_Hanik_(at_LNT_from_1989-1995,_at_L\u00dcT since_2004)|»Norbert Hanik«]], Realisierung: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Franz_Kohl_.28Diplomarbeit_LB_2004.2C_danach_freie_Mitarbeit_bis_2006.29|»Franz Kohl«]] und [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Manfred_J.C3.BCrgens_.28at_LNT_from_1981-2010.29|»Manfred J\u00fcrgens«]].\n\nIm Zuge der LNTwww-Neugestaltung (Version 3) wurden diese Lernvideos 2016/2017 von \n[[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28at_L.C3.9CT_since_2014.29|»Tasn\u00e1d Kernetzky«]] und einigen Studenten in moderne Formate konvertiert, um von m\u00f6glichst vielen Browsern (wie Firefox, Chrome, Safari) als auch von Smartphones wiedergegeben werden zu k\u00f6nnen.\n\n\n<hr style=\"border-color: #000000; border-width: 15px;\">\n'''English summary:'''\n\n\n\n=Arithmetic operations involving complex numbers=\n\n=== Contents ===\n* Real number sets and number line: Integers, natural ... , real ... , rational ... , irrational ... (Duration 3:14) \n*Representation of complex numbers and complex plane: Real part, imaginary part, magnitude, phase, theorem of Euler (Duration 2:00)\n*Rules of calculation for complex numbers: Sum, difference, product, quotient, conjugate-complex, square, square root (Duration 6:36)\n*Total duration 11:50\n\n\n<lntmedia preload=\"none\">\n file:Rechnen mit komplexen Zahlen.mp4\n file:Rechnen mit komplexen Zahlen.ogv\n</lntmedia>\n\n=== Detected errors ===\n* At (10:30) it should read: $d = z - z^\\star = 2 {\\rm j} \\cdot y$ , if $z = x + {\\rm j} \\cdot y$. In the video the imaginary unit ${\\rm j}$ was forgotten.\n\n\nThis educational video was conceived and realized in 2006 at the [http://www.lnt.ei.tum.de/startseite \"Chair of Communications Engineering\"] of the [https://www.tum.de/ \"Technical University of Munich\"]. \n\n\n__NOTOC__\n__NOEDITSECTION__"
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"9": {
"pageid": 9,
"ns": 0,
"title": "Signal Representation",
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"*": "===Brief summary===\n\n{{BlueBox|TEXT=The book focuses on the mathematical description of typical signals in Communications Engineering, which can be done alternatively in the time or frequency domain:\n# Components of communication systems and classification of different signals.\n# The Fourier series for the description of periodic signals with the special case »harmonic oscillation« and the limiting case »direct current signal«.\n# The laws of the Fourier transform for describing aperiodic $($impulsive$)$ signals and their spectra; first and second Fourier integral. \n# Peculiarities of band-pass signals and their description by the analytical signal and the equivalent low-pass signal. \n# Discrete Fourier transform for the description of discrete-time signals; application for spectral analysis; FFT as an efficient computer implementation.\n\n\nThe spectral transforms $($Laplace transform, z-transform, Hilbert transform$)$ applicable exclusively to causal signals and systems are not treated in this book. Here we refer to the book [[Lineare_zeitinvariante_Systeme|»Linear and Time Invariant Systems«]].\n\n⇒ First a »'''content overview'''« on the basis of the »'''five main chapters'''« with a total of »'''19 individual chapters'''« and »'''127 sections'''«.}}\n\n\n===Contents===\n{{Collapsible-Kopf}}\n{{Collapse1| header=Basic Terms of Communications Engineering\n| submenu= \n*[[/Principles of Communication/]]\n*[[/Signal Classification/]]\n*[[/Calculating with Complex Numbers/]]\n}}\n{{Collapse2 | header=Periodic Signals\n|submenu=\n*[[/General Description/]]\n*[[/Direct Current Signal - Limit Case of a Periodic Signal/]]\n*[[/Harmonic Oscillation/]]\n*[[/Fourier Series/]]\n}}\n{{Collapse3 | header=Aperiodic Signals - Pulses\n|submenu=\n*[[/The Fourier Transform and its Inverse/]]\n*[[/Special Cases of Pulses/]]\n*[[/The Fourier Transform Theorems/]]\n*[[/The Convolution Theorem and Operation/]]\n}}\n{{Collapse4 | header=Band-Pass Signals\n|submenu=\n*[[/Differences and Similarities of Low-Pass and Band-Pass Signals/]]\n*[[/Analytical Signal and its Spectral Function/]]\n*[[/Equivalent Low-Pass Signal and its Spectral Function/]]\n}}\n{{Collapse5 | header=Time-Discrete and Frequency-Discrete Signal Representation\n|submenu=\n*[[/Discrete-Time Signal Representation/]]\n*[[/Discrete Fourier Transform (DFT)/]]\n*[[/Possible Errors when using DFT/]]\n*[[/Spectrum Analysis/]]\n*[[/Fast Fourier Transform (FFT)/]]\n}}\n{{Collapsible-Fu\u00df}}\n\n===Exercises and multimedia===\n\n{{BlaueBox|TEXT=\nIn addition to these theory pages, we also offer exercises and multimedia modules on this topic, which could help to clarify the teaching material:\n\n$(1)$ [https://en.lntwww.de/Category:Signal_Representation:_Exercises $\\text{Exercises}$]\n\n$(2)$ [[LNTwww:Learning_Videos_Related_to_Signal_Representation|$\\text{Learning videos}$]]\n\n$(3)$ [[LNTwww:Applets_Related_to_Signal_Representation|$\\text{Applets}$]] }} \n\n\n===Further links===\n\n{{BlaueBox|TEXT=\n$(4)$ [[LNTwww:Bibliography_to_Signal_Representation|$\\text{Bibliography}$]]\n\n$(5)$ [[LNTwww:Imprint_for_the_book_\"Signal_Representation\"|$\\text{Impressum}$]]}}\n<br><br>\n\n\n\n\n\n\n\n\n\n__NOTOC__\n__NOEDITSECTION__"
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