https://www.lntwww.de/index.php?action=history&feed=atom&title=Applets%3ADiscrete_Fouriertransform_and_Inverse Applets:Discrete Fouriertransform and Inverse - Versionsgeschichte 2026-05-04T02:33:28Z Versionsgeschichte dieser Seite in LNTwww MediaWiki 1.34.1 https://www.lntwww.de/index.php?title=Applets:Discrete_Fouriertransform_and_Inverse&diff=34484&oldid=prev Höfler: Textersetzung - „Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29“ durch „Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_von_1974-2024.29“ 2025-02-24T09:42:50Z <p>Textersetzung - „Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29“ durch „Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_von_1974-2024.29“</p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 24. Februar 2025, 09:42 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l452" >Zeile 452:</td> <td colspan="2" class="diff-lineno">Zeile 452:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Über die Autoren==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Über die Autoren==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dieses interaktive Berechnungstool  wurde am&amp;nbsp; [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&amp;nbsp; der&amp;nbsp; [https://www.tum.de/ Technischen Universität München]&amp;nbsp; konzipiert und realisiert.  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dieses interaktive Berechnungstool  wurde am&amp;nbsp; [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&amp;nbsp; der&amp;nbsp; [https://www.tum.de/ Technischen Universität München]&amp;nbsp; konzipiert und realisiert.  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die erste Version wurde 2003 von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&amp;nbsp; im Rahmen ihrer Diplomarbeit mit &amp;bdquo;FlashMX&amp;ndash;Actionscript&amp;rdquo; erstellt (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.<del class="diffchange diffchange-inline">28am_LNT_seit_1974</del>.29|Günter Söder]]).  </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die erste Version wurde 2003 von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&amp;nbsp; im Rahmen ihrer Diplomarbeit mit &amp;bdquo;FlashMX&amp;ndash;Actionscript&amp;rdquo; erstellt (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.<ins class="diffchange diffchange-inline">28am_LNT_von_1974-2024</ins>.29|Günter Söder]]).  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 2019 wurde das Programm  von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]]&amp;nbsp; im Rahmen einer Werkstudententätigkeit auf  &amp;bdquo;HTML5&amp;rdquo; umgesetzt und neu gestaltet (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_LÜT-Angehörige#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28bei_L.C3.9CT_von_2014-2022.29|Tasnád Kernetzky]]).</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 2019 wurde das Programm  von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]]&amp;nbsp; im Rahmen einer Werkstudententätigkeit auf  &amp;bdquo;HTML5&amp;rdquo; umgesetzt und neu gestaltet (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_LÜT-Angehörige#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28bei_L.C3.9CT_von_2014-2022.29|Tasnád Kernetzky]]).</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <!-- diff cache key mediawiki:diff::1.12:old-34358:rev-34484 --> </table> Höfler https://www.lntwww.de/index.php?title=Applets:Discrete_Fouriertransform_and_Inverse&diff=34358&oldid=prev Höfler am 26. Oktober 2023 um 09:47 Uhr 2023-10-26T09:47:18Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 26. Oktober 2023, 09:47 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l453" >Zeile 453:</td> <td colspan="2" class="diff-lineno">Zeile 453:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dieses interaktive Berechnungstool  wurde am&amp;nbsp; [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&amp;nbsp; der&amp;nbsp; [https://www.tum.de/ Technischen Universität München]&amp;nbsp; konzipiert und realisiert.  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dieses interaktive Berechnungstool  wurde am&amp;nbsp; [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&amp;nbsp; der&amp;nbsp; [https://www.tum.de/ Technischen Universität München]&amp;nbsp; konzipiert und realisiert.  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die erste Version wurde 2003 von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&amp;nbsp; im Rahmen ihrer Diplomarbeit mit &amp;bdquo;FlashMX&amp;ndash;Actionscript&amp;rdquo; erstellt (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die erste Version wurde 2003 von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&amp;nbsp; im Rahmen ihrer Diplomarbeit mit &amp;bdquo;FlashMX&amp;ndash;Actionscript&amp;rdquo; erstellt (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 2019 wurde das Programm  von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]]&amp;nbsp; im Rahmen einer Werkstudententätigkeit auf  &amp;bdquo;HTML5&amp;rdquo; umgesetzt und neu gestaltet (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/<del class="diffchange diffchange-inline">Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik</del>#<del class="diffchange diffchange-inline">Tasn.C3</del>.<del class="diffchange diffchange-inline">A1d_Kernetzky</del>.<del class="diffchange diffchange-inline">2C_M</del>.<del class="diffchange diffchange-inline">Sc</del>.<del class="diffchange diffchange-inline">_</del>.28bei_L.C3.<del class="diffchange diffchange-inline">9CT_seit_2014</del>.29|Tasnád Kernetzky]]).</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 2019 wurde das Programm  von&amp;nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]]&amp;nbsp; im Rahmen einer Werkstudententätigkeit auf  &amp;bdquo;HTML5&amp;rdquo; umgesetzt und neu gestaltet (Betreuer:&amp;nbsp; [[Biografien_und_Bibliografien/<ins class="diffchange diffchange-inline">An_LNTwww_beteiligte_LÜT-Angehörige</ins>#<ins class="diffchange diffchange-inline">Dr</ins>.<ins class="diffchange diffchange-inline">-Ing</ins>.<ins class="diffchange diffchange-inline">_Tasn</ins>.<ins class="diffchange diffchange-inline">C3</ins>.<ins class="diffchange diffchange-inline">A1d_Kernetzky_</ins>.28bei_L.C3.<ins class="diffchange diffchange-inline">9CT_von_2014-2022</ins>.29|Tasnád Kernetzky]]).</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <!-- diff cache key mediawiki:diff::1.12:old-30815:rev-34358 --> </table> Höfler https://www.lntwww.de/index.php?title=Applets:Discrete_Fouriertransform_and_Inverse&diff=30815&oldid=prev Guenter am 10. Juni 2020 um 10:27 Uhr 2020-06-10T10:27:53Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 10. Juni 2020, 10:27 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l294" >Zeile 294:</td> <td colspan="2" class="diff-lineno">Zeile 294:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Ausgabe eines &amp;bdquo;Reset&amp;ndash;Textes&amp;rdquo; mit weiteren Erläuterungen zum Applet.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Ausgabe eines &amp;bdquo;Reset&amp;ndash;Textes&amp;rdquo; mit weiteren Erläuterungen zum Applet.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{BlaueBox|TEXT=</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''(1)'''&amp;nbsp; New setting:&amp;nbsp; DFT of signal&amp;nbsp; $\rm (b)$ &amp;nbsp; &amp;rArr; &amp;nbsp; Constant signal.&amp;nbsp; Interpret the result in the frequency domain.&amp;nbsp; What is the analogon of the conventional Fourier Transform?}}</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:*&amp;nbsp;All coefficients in the time domain are&amp;nbsp; $d(\nu)=1$.&amp;nbsp; Thus all&amp;nbsp; $D(\mu)=0$&amp;nbsp; with the exeption of&amp;nbsp; $\textrm{Re}[D(0)]=1$.</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:*&amp;nbsp;This corresponds to the conventional (time-continuous) Fourier Transform: &amp;nbsp; $x(t)=A\hspace{0.15cm}\circ\!\!\!-\!\!\!-\!\!\!-\!\!\bullet\hspace{0.15cm} X(f)=A\cdot \delta (f=0)$&amp;nbsp; with&amp;nbsp; $A=1$.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{BlaueBox|TEXT=</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{BlaueBox|TEXT=</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&amp;nbsp; Neue Einstellung:&amp;nbsp; $\text{DFT von Signal (b): Gleichsignal}$. &amp;nbsp;Interpretieren Sie das Ergebnis im Frequenzbereich. Wie lautet das Analogon der herkömmlichen&amp;nbsp; $\text{FT}$&amp;nbsp;?}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&amp;nbsp; Neue Einstellung:&amp;nbsp; $\text{DFT von Signal (b): Gleichsignal}$. &amp;nbsp;Interpretieren Sie das Ergebnis im Frequenzbereich. Wie lautet das Analogon der herkömmlichen&amp;nbsp; $\text{FT}$&amp;nbsp;?}}</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::*&amp;nbsp;<del class="diffchange diffchange-inline">Im Zeitbereich sind alle&amp;nbsp; </del>$d(\nu) =1$. <del class="diffchange diffchange-inline">Im Frequenzbereich sind alle&amp;nbsp; </del>$D(\mu) =0$<del class="diffchange diffchange-inline">&amp;nbsp; mit Ausnahme von&amp;nbsp; </del>${<del class="diffchange diffchange-inline">\rm </del>Re}<del class="diffchange diffchange-inline">\big </del>[D(0)] =1$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::*&amp;nbsp;<ins class="diffchange diffchange-inline">All coefficients in the time domain are </ins>$d(\nu)=1$. <ins class="diffchange diffchange-inline">Thus all </ins>$D(\mu)=0$ <ins class="diffchange diffchange-inline">with the exeption of </ins>$<ins class="diffchange diffchange-inline">\textrm</ins>{Re}[D(0)]=1$.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::*&amp;nbsp;<del class="diffchange diffchange-inline">Dies entspricht bei der herkömmlichen </del>(<del class="diffchange diffchange-inline">zeitkontinuierlichen</del>) <del class="diffchange diffchange-inline">Fouriertransformation</del>:<del class="diffchange diffchange-inline">&amp;nbsp; &amp;nbsp;</del>$x(t) = A\hspace{0.15cm}\circ\!\!\!-\!\!\!-\!\!\!-\!\!\bullet\hspace{0.15cm}X(f) = A \cdot \delta(f=0)$<del class="diffchange diffchange-inline">&amp;nbsp; </del>mit<del class="diffchange diffchange-inline">&amp;nbsp; </del>$A=1$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::*&amp;nbsp;<ins class="diffchange diffchange-inline">This corresponds to the conventional </ins>(<ins class="diffchange diffchange-inline">time-continuous</ins>) <ins class="diffchange diffchange-inline">Fourier transformation</ins>: $x(t)=A\hspace{0.15cm}\circ\!\!\!-\!\!\!-\!\!\!-\!\!\bullet\hspace{0.15cm} X(f)=A\cdot \delta (f=0)$ mit $A=1$.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{BlaueBox|TEXT=</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{BlaueBox|TEXT=</div></td></tr> <!-- diff cache key mediawiki:diff::1.12:old-30725:rev-30815 --> </table> Guenter https://www.lntwww.de/index.php?title=Applets:Discrete_Fouriertransform_and_Inverse&diff=30725&oldid=prev Guenter am 28. Mai 2020 um 11:45 Uhr 2020-05-28T11:45:45Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 28. Mai 2020, 11:45 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Zeile 3:</td> <td colspan="2" class="diff-lineno">Zeile 3:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Programmbeschreibung==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Programmbeschreibung==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br&gt;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Das Applet verdeutlicht die Eigenschaften zweidimensionaler Gaußscher Zufallsgrößen</del>&amp;nbsp; $XY\hspace{-0.1cm}$, <del class="diffchange diffchange-inline">gekennzeichnet durch die Standardabweichungen </del>(<del class="diffchange diffchange-inline">Streuungen</del>)&amp;nbsp; $\sigma_X$&amp;nbsp; <del class="diffchange diffchange-inline">und</del>&amp;nbsp; $\sigma_Y$&amp;nbsp; <del class="diffchange diffchange-inline">ihrer beiden Komponenten sowie den Korrelationskoeffizienten</del>&amp;nbsp; $\rho_{XY}$&amp;nbsp;<del class="diffchange diffchange-inline">zwischen diesen</del>. <del class="diffchange diffchange-inline">Die Komponenten werden als mittelwertfrei vorausgesetzt</del>:&amp;nbsp; $m_X = m_Y = 0$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;br&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The applet illustrates the properties of two-dimensional Gaussian random variables</ins>&amp;nbsp; $XY\hspace{-0.1cm}$, <ins class="diffchange diffchange-inline">characterized by the standard deviations </ins>(<ins class="diffchange diffchange-inline">scatter</ins>)&amp;nbsp; $\sigma_X$&amp;nbsp; <ins class="diffchange diffchange-inline">and</ins>&amp;nbsp; $\sigma_Y$&amp;nbsp; <ins class="diffchange diffchange-inline">of their two components as well as the correlation coefficient</ins>&amp;nbsp; $\rho_{XY}$&amp;nbsp;<ins class="diffchange diffchange-inline">between them</ins>. <ins class="diffchange diffchange-inline">The components are assumed to be mean free</ins>:&amp;nbsp; $m_X = m_Y = 0$<ins class="diffchange diffchange-inline">.</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The applet shows</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* the two-dimensional probability density function &amp;nbsp; &amp;rArr; &amp;nbsp; $\rm 2D\hspace{-0.1cm}-\hspace{-0.1cm}WDF$&amp;nbsp; $f_{XY}(x, \hspace{0.1cm}y)$&amp;nbsp; in three-dimensional representation as well as in the form of contour lines</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* the associated boundary probability density function&amp;nbsp; &amp;rArr; &amp;nbsp; $\rm 1D\hspace{-0.1cm}-\hspace{-0.1cm}WDF$&amp;nbsp; $f_{X}(x)$&amp;nbsp; of the random variable&amp;nbsp; $X$&amp;nbsp; as a blue curve; also&amp;nbsp; $f_{Y}(y)$&amp;nbsp; for the second random variable, </ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* the two-dimensional distribution function &amp;nbsp; &amp;rArr; &amp;nbsp; $\rm 2D\hspace{-0.1cm}-\hspace{-0.1cm}VTF$&amp;nbsp; $F_{XY}(x, \hspace{0.1cm}y)$&amp;nbsp; as a 3D plot</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* the distribution function&amp;nbsp; &amp;rArr; &amp;nbsp; $\rm 1D\hspace{-0.1cm}-\hspace{-0.1cm}VTF$&amp;nbsp; $F_{X}(x)$&amp;nbsp; the random variable&amp;nbsp; $X$; also&amp;nbsp; $F_{Y}(y)$&amp;nbsp; as a red curve</ins>.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Das Applet zeigt</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* die zweidimensionale Wahrscheinlichkeitsdichtefunktion &amp;nbsp; &amp;rArr; &amp;nbsp; $\rm 2D\hspace{-0.1cm}-\hspace{-0.1cm}WDF$&amp;nbsp; $f_{XY}(x, \hspace{0.1cm}y)$&amp;nbsp; in dreidimensionaler Darstellung sowie in Form von Höhenlinien,</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* die zugehörige Randwahrscheinlichkeitsdichtefunktion&amp;nbsp; &amp;rArr; &amp;nbsp;  $\rm 1D\hspace{-0.1cm}-\hspace{-0.1cm}WDF$&amp;nbsp; $f_{X}(x)$&amp;nbsp;  der Zufallsgröße&amp;nbsp; $X$&amp;nbsp; als blaue Kurve;  ebenso&amp;nbsp; $f_{Y}(y)$&amp;nbsp; für die zweite Zufallsgröße, </del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* die zweidimensionale Verteilungsfunktion  &amp;nbsp; &amp;rArr; &amp;nbsp; $\rm 2D\hspace{-0.1cm}-\hspace{-0.1cm}VTF$&amp;nbsp; $F_{XY}(x, \hspace{0.1cm}y)$&amp;nbsp; als 3D-Plot,</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* die Verteilungsfunktion&amp;nbsp; &amp;rArr; &amp;nbsp; $\rm 1D\hspace{-0.1cm}-\hspace{-0.1cm}VTF$&amp;nbsp; $F_{X}(x)$&amp;nbsp; der Zufallsgröße&amp;nbsp; $X$;  ebenso&amp;nbsp; $F_{Y}(y)$&amp;nbsp; als rote Kurve.</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <!-- diff cache key mediawiki:diff::1.12:old-30724:rev-30725 --> </table> Guenter https://www.lntwww.de/index.php?title=Applets:Discrete_Fouriertransform_and_Inverse&diff=30724&oldid=prev Guenter: Die Seite wurde neu angelegt: „{{LntAppletLink|dft}} ==Programmbeschreibung== <br> Das Applet verdeutlicht die Eigenschaften zweidimensionaler Gaußscher Zufallsgrößen&nbsp; $XY\hspace{-…“ 2020-05-28T11:35:48Z <p>Die Seite wurde neu angelegt: „{{LntAppletLink|dft}} ==Programmbeschreibung== &lt;br&gt; Das Applet verdeutlicht die Eigenschaften zweidimensionaler Gaußscher Zufallsgrößen  $XY\hspace{-…“</p> <a href="//www.lntwww.de/index.php?title=Applets:Discrete_Fouriertransform_and_Inverse&amp;diff=30724">Änderungen zeigen</a> Guenter