Using the MATLAB script disspct.m, determine and plot the magnitude and phase spectra of the periodic signal x(t) with a period of T0=4.6 and described in the interval [-2.3,2.3] by the relation x(t)=Λ(t). Plot the spectra for -24 ≤n ≤24. Now, analyticall (2024)

`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`

${elem}

`); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`

  • ${book_segment.title}
  • `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`

    ${elem.title} ${ordinal(elem.edition)} ${elem.author}

    `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "6QszHhiLMHyrUb7ih2xh1ymdcquFyYYuhVqcwi8em8jpR7NnwjKFl4wKlqwkQsVx"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j

    Solutions
  • Textbooks
  • `); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(`
  • Solutions ${viewAllHTML}
  • `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+"    "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(`
  • Textbooks View All
  • `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; const user_hash = null; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_'+(is_login?user_hash:'ANON'))); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { if (is_login) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (prebooks.time && new Date().getTime()-prebooks.time<1000*60*60*6) { build_popup(); return; } } else { anon_pretype(); return; } } $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "6QszHhiLMHyrUb7ih2xh1ymdcquFyYYuhVqcwi8em8jpR7NnwjKFl4wKlqwkQsVx"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; if (is_login) { localStorage.setItem('PRETYPE_BOOKS_'+user_hash, JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books, time: new Date().getTime() })); } build_popup(); }, error: function(response){ console.log(response); } }); } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "6QszHhiLMHyrUb7ih2xh1ymdcquFyYYuhVqcwi8em8jpR7NnwjKFl4wKlqwkQsVx", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
    Using the MATLAB script disspct.m, determine and plot the magnitude and phase spectra of the periodic signal x(t) with a period of T0=4.6 and described in the interval [-2.3,2.3] by the relation x(t)=Λ(t). Plot the spectra for -24 ≤n ≤24. Now, analyticall (2024)

    FAQs

    How to find the magnitude of a signal in Matlab? ›

    [ mag , validOut ] = magAngle( X , validIn ) returns only the component magnitudes of X . To use this syntax, set OutputFormat to 'Magnitude' . Example: magAngle = dsphdl.

    How to plot periodic signal in Matlab? ›

    The periodic signal is defined by a single-cycle waveform cached as the Wavetable property of your wavetableSynthesizer object. To generate a periodic signal: Create the wavetableSynthesizer object and set its properties. Call the object with arguments, as if it were a function.

    How do you find the magnitude and phase spectrum? ›

    The magnitude and phase spectra are calculated from the complex output Xf using abs(Xf) and angle(Xf), respectively (see Example 3.3). Again, the angle routine gives phase in radians so as to convert to the more commonly used degrees scale by 360/(2π).

    How do you plot the magnitude of a signal? ›

    The two major components frequency and amplitude of a periodic signal define the Magnitude Spectrum of that signal. The frequency components of the periodic signal are plotted in the horizontal axis and amplitude component of the periodic signal is plotted in the vertical axis.

    How do you use the magnitude function in MATLAB? ›

    Explanation: abs (A) will return the absolute value or the magnitude of every element of the input array 'A'. If the input 'A' is complex, the abs function will return to a complex magnitude. Please recall that the complex magnitude for a complex number X + Yi is the square root of (X^2 + Y^2).

    How do you find the power spectrum of a signal in MATLAB? ›

    p = pspectrum( x , fs ) returns the power spectrum of a vector or matrix signal sampled at a rate fs . p = pspectrum( x , t ) returns the power spectrum of a vector or matrix signal sampled at the time instants specified in t .

    How to plot a signal in MATLAB? ›

    This should get you started:
    1. u = @(t) t>=0;
    2. x = @(t,u) cos(200*pi*t.*u(t));
    3. t = linspace(-1, 1);
    4. figure(1)
    5. plot(t, x(t,u))
    6. grid.
    Oct 19, 2019

    How to plot mass spectrum in MATLAB? ›

    Plot Mass Spectra Data

    Add a marker by pointing to a mass peak, right-clicking, and then clicking Add Marker. The File menu has the following options. Import Markers from Workspace - Opens the Import Markers From MATLAB® Workspace dialog. The dialog displays a list of double Mx1 or 1xM variables.

    How do you find if a signal is periodic or not in MATLAB? ›

    The autocorrelation sequence of a periodic signal has the same cyclic characteristics as the signal itself. Thus, autocorrelation can help verify the presence of cycles and determine their durations.

    What is magnitude and phase plot? ›

    The magnitude describes the strength of each frequency in the signal. The phase describes the sine/cosine phase of each frequency. The phase can also be thought of as the relative proportion of sines and cosines in the signal (i.e., a phase of zero contains only cosines and a phase of 90 degrees contains only sines).

    What is a magnitude spectra? ›

    The original desired magnitude spectrum (or response) is the input to a linear system having the magnitude response of a rectangular window. From: Practical Digital Signal Processing, 2003.

    What is property of magnitude and phase spectrum? ›

    This demonstration uses the one-sided, real, decaying (b > 0) exponential signal x(t) = ae-btu(t) which has Fourier transform X(w) = a/(b + jw) The magnitude spectrum of the signal is |X(w)| = |a|/(b2 + w2) 1/2 The phase spectrum is (in radians) <X(w) = tan-1(w/b), if a > 0. <X(w) = p + tan-1(w/b), if a < 0.

    What is the relationship between magnitude and phase? ›

    The magnitude is the square root of the sum of the squares of the real and imaginary parts. The phase is relative to the start of the time record or relative to a single-cycle cosine wave starting at the beginning of the time record. Single-channel phase measurements are stable only if the input signal is triggered.

    How to calculate magnitude? ›

    Thus, the formula to determine the magnitude of a vector (in two-dimensional space) v = (x, y) is: |v| =√(x2 + y2). This formula is derived from the Pythagorean theorem.

    How to find magnitude in MATLAB? ›

    MATLAB - Magnitude of a Vector
    1. Take the product of the vector with itself, using array multiplication (. *). ...
    2. Use the sum function to get the sum of squares of elements of vector v. ...
    3. Use the sqrt function to get the square root of the sum which is also the magnitude of the vector v.

    What is the magnitude of a signal? ›

    The magnitude describes the strength of each frequency in the signal. The phase describes the sine/cosine phase of each frequency. The phase can also be thought of as the relative proportion of sines and cosines in the signal (i.e., a phase of zero contains only cosines and a phase of 90 degrees contains only sines).

    What is the magnitude of the output signal? ›

    The magnitude of the output is the magnitude of the phasor representation of the transfer function (at a given frequency) multiplied by the magnitude of the input. The phase of the output is the phase of the transfer function added to the phase of the input.

    References

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