Inverse Fourier analysis problem - matlabMatLab - Fast Fourier TransformProgramming discrete fourier coefficients in matlabreducing amplitude of fft spectrum with constant phaseUnderstanding Fourier transform example in MatlabMATLAB: Plotting the inverse Fourier transform of a rectangular pulse.How to plot fourier series in matlabHow to fit model to data using MATLABPlotting Fourier series in MATLABFourier Curve FittingFourier series inverse problem

Are Captain Marvel's powers affected by Thanos breaking the Tesseract and claiming the stone?

Do we have to expect a queue for the shuttle from Watford Junction to Harry Potter Studio?

Is this toilet slogan correct usage of the English language?

Shouldn’t conservatives embrace universal basic income?

Can you use Vicious Mockery to win an argument or gain favours?

The Digit Triangles

What is the English pronunciation of "pain au chocolat"?

Are cause and effect the same as in our Universe in a non-relativistic, Newtonian Universe in which the speed of light is infinite?

How can I, as DM, avoid the Conga Line of Death occurring when implementing some form of flanking rule?

Has the laser at Magurele, Romania reached a tenth of the Sun's power?

Did the UK lift the requirement for registering SIM cards?

What to do when eye contact makes your coworker uncomfortable?

Microchip documentation does not label CAN buss pins on micro controller pinout diagram

Has any country ever had 2 former presidents in jail simultaneously?

When were female captains banned from Starfleet?

Pre-mixing cryogenic fuels and using only one fuel tank

C++ copy constructor called at return

What kind of floor tile is this?

What are some good ways to treat frozen vegetables such that they behave like fresh vegetables when stir frying them?

What (the heck) is a Super Worm Equinox Moon?

How can I write humor as character trait?

Quoting Keynes in a lecture

C++ check if statement can be evaluated constexpr

A variation to the phrase "hanging over my shoulders"



Inverse Fourier analysis problem - matlab


MatLab - Fast Fourier TransformProgramming discrete fourier coefficients in matlabreducing amplitude of fft spectrum with constant phaseUnderstanding Fourier transform example in MatlabMATLAB: Plotting the inverse Fourier transform of a rectangular pulse.How to plot fourier series in matlabHow to fit model to data using MATLABPlotting Fourier series in MATLABFourier Curve FittingFourier series inverse problem













0












$begingroup$


Using MATLAB, I am trying to do an analysis of a triangular pulse and recreating it from acquired coefficients of the Fourier series.



The pulse looks like this



syms t
x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;


With the code below, I acquire 16 first coefficients of the series:



NT = 15;
X=[];
ind = -NT : NT;
for p = ind
Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
X(p + NT + 1) = Xn;
end


However, while doing the inverse operation, the supposed graph of three periods is:



  • of frequency 2 times greater

  • of amplitude 2 times smaller

  • "lifted" 0.5 units up

... and looks like this



The code:



BND = [t1,t2] + offset; 
step = (BND(2) - BND(1))/1000;
tt = [BND(1)-T0 : step: BND(2) + T0];
xx1 = zeros(1,length(tt));
figure
plot(tt,xx1,'m');
hold on;
for n = ind+NT+1
xx1_n = X(n)*exp(1i*w0*n*tt);
xx1 = xx1 + xx1_n;
plot(tt,abs(xx1_n),'r');
plot(tt,abs(xx1),'m');
title(sprintf('n = %d',n-NT));
pause(0.5)
end
plot(tt,abs(xx1),'k','LineWidth',2);


What am I doing wrong?










share|cite|improve this question









$endgroup$
















    0












    $begingroup$


    Using MATLAB, I am trying to do an analysis of a triangular pulse and recreating it from acquired coefficients of the Fourier series.



    The pulse looks like this



    syms t
    x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;


    With the code below, I acquire 16 first coefficients of the series:



    NT = 15;
    X=[];
    ind = -NT : NT;
    for p = ind
    Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
    X(p + NT + 1) = Xn;
    end


    However, while doing the inverse operation, the supposed graph of three periods is:



    • of frequency 2 times greater

    • of amplitude 2 times smaller

    • "lifted" 0.5 units up

    ... and looks like this



    The code:



    BND = [t1,t2] + offset; 
    step = (BND(2) - BND(1))/1000;
    tt = [BND(1)-T0 : step: BND(2) + T0];
    xx1 = zeros(1,length(tt));
    figure
    plot(tt,xx1,'m');
    hold on;
    for n = ind+NT+1
    xx1_n = X(n)*exp(1i*w0*n*tt);
    xx1 = xx1 + xx1_n;
    plot(tt,abs(xx1_n),'r');
    plot(tt,abs(xx1),'m');
    title(sprintf('n = %d',n-NT));
    pause(0.5)
    end
    plot(tt,abs(xx1),'k','LineWidth',2);


    What am I doing wrong?










    share|cite|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      Using MATLAB, I am trying to do an analysis of a triangular pulse and recreating it from acquired coefficients of the Fourier series.



      The pulse looks like this



      syms t
      x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;


      With the code below, I acquire 16 first coefficients of the series:



      NT = 15;
      X=[];
      ind = -NT : NT;
      for p = ind
      Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
      X(p + NT + 1) = Xn;
      end


      However, while doing the inverse operation, the supposed graph of three periods is:



      • of frequency 2 times greater

      • of amplitude 2 times smaller

      • "lifted" 0.5 units up

      ... and looks like this



      The code:



      BND = [t1,t2] + offset; 
      step = (BND(2) - BND(1))/1000;
      tt = [BND(1)-T0 : step: BND(2) + T0];
      xx1 = zeros(1,length(tt));
      figure
      plot(tt,xx1,'m');
      hold on;
      for n = ind+NT+1
      xx1_n = X(n)*exp(1i*w0*n*tt);
      xx1 = xx1 + xx1_n;
      plot(tt,abs(xx1_n),'r');
      plot(tt,abs(xx1),'m');
      title(sprintf('n = %d',n-NT));
      pause(0.5)
      end
      plot(tt,abs(xx1),'k','LineWidth',2);


      What am I doing wrong?










      share|cite|improve this question









      $endgroup$




      Using MATLAB, I am trying to do an analysis of a triangular pulse and recreating it from acquired coefficients of the Fourier series.



      The pulse looks like this



      syms t
      x = triangularPulse(-0.5,0.0,0.5,t-0.2)-0.5;


      With the code below, I acquire 16 first coefficients of the series:



      NT = 15;
      X=[];
      ind = -NT : NT;
      for p = ind
      Xn = (1/T0)*int(x*exp(-1i*w0*p*t),t,BND);
      X(p + NT + 1) = Xn;
      end


      However, while doing the inverse operation, the supposed graph of three periods is:



      • of frequency 2 times greater

      • of amplitude 2 times smaller

      • "lifted" 0.5 units up

      ... and looks like this



      The code:



      BND = [t1,t2] + offset; 
      step = (BND(2) - BND(1))/1000;
      tt = [BND(1)-T0 : step: BND(2) + T0];
      xx1 = zeros(1,length(tt));
      figure
      plot(tt,xx1,'m');
      hold on;
      for n = ind+NT+1
      xx1_n = X(n)*exp(1i*w0*n*tt);
      xx1 = xx1 + xx1_n;
      plot(tt,abs(xx1_n),'r');
      plot(tt,abs(xx1),'m');
      title(sprintf('n = %d',n-NT));
      pause(0.5)
      end
      plot(tt,abs(xx1),'k','LineWidth',2);


      What am I doing wrong?







      fourier-analysis fourier-series matlab






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 14 at 16:06









      Filip FreyFilip Frey

      13




      13




















          0






          active

          oldest

          votes











          Your Answer





          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader:
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          ,
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













          draft saved

          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3148190%2finverse-fourier-analysis-problem-matlab%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes















          draft saved

          draft discarded
















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid


          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.

          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3148190%2finverse-fourier-analysis-problem-matlab%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          Solar Wings Breeze Design and development Specifications (Breeze) References Navigation menu1368-485X"Hang glider: Breeze (Solar Wings)"e

          Kathakali Contents Etymology and nomenclature History Repertoire Songs and musical instruments Traditional plays Styles: Sampradayam Training centers and awards Relationship to other dance forms See also Notes References External links Navigation menueThe Illustrated Encyclopedia of Hinduism: A-MSouth Asian Folklore: An EncyclopediaRoutledge International Encyclopedia of Women: Global Women's Issues and KnowledgeKathakali Dance-drama: Where Gods and Demons Come to PlayKathakali Dance-drama: Where Gods and Demons Come to PlayKathakali Dance-drama: Where Gods and Demons Come to Play10.1353/atj.2005.0004The Illustrated Encyclopedia of Hinduism: A-MEncyclopedia of HinduismKathakali Dance-drama: Where Gods and Demons Come to PlaySonic Liturgy: Ritual and Music in Hindu Tradition"The Mirror of Gesture"Kathakali Dance-drama: Where Gods and Demons Come to Play"Kathakali"Indian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceMedieval Indian Literature: An AnthologyThe Oxford Companion to Indian TheatreSouth Asian Folklore: An Encyclopedia : Afghanistan, Bangladesh, India, Nepal, Pakistan, Sri LankaThe Rise of Performance Studies: Rethinking Richard Schechner's Broad SpectrumIndian Theatre: Traditions of PerformanceModern Asian Theatre and Performance 1900-2000Critical Theory and PerformanceBetween Theater and AnthropologyKathakali603847011Indian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceBetween Theater and AnthropologyBetween Theater and AnthropologyNambeesan Smaraka AwardsArchivedThe Cambridge Guide to TheatreRoutledge International Encyclopedia of Women: Global Women's Issues and KnowledgeThe Garland Encyclopedia of World Music: South Asia : the Indian subcontinentThe Ethos of Noh: Actors and Their Art10.2307/1145740By Means of Performance: Intercultural Studies of Theatre and Ritual10.1017/s204912550000100xReconceiving the Renaissance: A Critical ReaderPerformance TheoryListening to Theatre: The Aural Dimension of Beijing Opera10.2307/1146013Kathakali: The Art of the Non-WorldlyOn KathakaliKathakali, the dance theatreThe Kathakali Complex: Performance & StructureKathakali Dance-Drama: Where Gods and Demons Come to Play10.1093/obo/9780195399318-0071Drama and Ritual of Early Hinduism"In the Shadow of Hollywood Orientalism: Authentic East Indian Dancing"10.1080/08949460490274013Sanskrit Play Production in Ancient IndiaIndian Music: History and StructureBharata, the Nāṭyaśāstra233639306Table of Contents2238067286469807Dance In Indian Painting10.2307/32047833204783Kathakali Dance-Theatre: A Visual Narrative of Sacred Indian MimeIndian Classical Dance: The Renaissance and BeyondKathakali: an indigenous art-form of Keralaeee

          Method to test if a number is a perfect power? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Detecting perfect squares faster than by extracting square rooteffective way to get the integer sequence A181392 from oeisA rarely mentioned fact about perfect powersHow many numbers such $n$ are there that $n<100,lfloorsqrtn rfloor mid n$Check perfect squareness by modulo division against multiple basesFor what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.Do there exist any positive integers $n$ such that $lfloore^nrfloor$ is a perfect power? What is the probability that one exists?finding perfect power factors of an integerProve that the sequence contains a perfect square for any natural number $m $ in the domain of $f$ .Counting Perfect Powers