/fourier.html
Created Jun 25, 2014
BetterExplained Fourier Example
| <html> | |
| <head> | |
| <script src="//cdnjs.cloudflare.com/ajax/libs/underscore.js/1.4.2/underscore-min.js"></script> | |
| <script src="//ajax.googleapis.com/ajax/libs/jquery/1.8.2/jquery.min.js"></script> | |
| <script src="//cdnjs.cloudflare.com/ajax/libs/modernizr/2.6.2/modernizr.min.js"></script> | |
| <script src="//ajax.cdnjs.com/ajax/libs/json2/20110223/json2.js"></script> | |
| <!-- | |
| TODO: | |
| DONE: Have a "details mode" where we see how we got the frequencies. | |
| - In details mode, have a table / dropdown for you to pick what frequency to analyze | |
| --> | |
| <script type="text/javascript"> | |
| // from view-source:http://treeblurb.com/dev_math/sin_canv00.html | |
| var x_size = 150; | |
| var y_size = 100; | |
| var settings = { | |
| canvas: { | |
| width: 0, // autodetected | |
| height: 0, | |
| }, | |
| timegraph_center_x: 150, | |
| timegraph_center_y: 100, | |
| timegraph_height: 60, | |
| timegraph_width: 360, | |
| circle_radius: 60, | |
| circle_center_x: 80, | |
| circle_center_y: 100, | |
| axis_margin_left: 15, | |
| axis_margin_top: 15, | |
| axis_margin_bottom: 15, | |
| axis_margin_right: 25, | |
| refresh: 50, // interval refresh in ms | |
| steps: 60, // # of intervals to divide wave into | |
| cyclegraph_dot: { | |
| strokeStyle: "#ccc", | |
| lineWidth: 1.5, | |
| radius: 3.5, | |
| fillStyle: "Orange" | |
| }, | |
| timegraph_dot: { | |
| strokeStyle: "#ccccff", | |
| lineWidth: 1.0, | |
| radius: 3.5, | |
| fillStyle: "Orange" | |
| }, | |
| axes: { | |
| strokeStyle: "#999", | |
| lineWidth: 0.5 | |
| }, | |
| wave: { | |
| fillStyle: "rgba(0,0,0,0)", | |
| strokeStyle: "#C2A7DD", | |
| lineWidth: 1.5 | |
| }, | |
| combined: { | |
| color: "#4A93FA" | |
| }, | |
| interval: { | |
| dotcolor: "rgba(255, 165, 0, 0.8)", | |
| lineStyle: "rgba(255, 165, 0, 0.5)", | |
| lineWidth: 1.0, | |
| }, | |
| unitcircle: { | |
| fillStyle: "rgba(0,0,0,0)", | |
| strokeStyle: "#999", | |
| lineWidth: 0.5 | |
| }, | |
| cycle: { | |
| poscolor: "#37B610", | |
| negcolor: "#E95C59", | |
| zerocolor: "#999" | |
| }, | |
| text: { | |
| font: "normal 12px Courier", | |
| fillStyle: "#888" | |
| } | |
| }; | |
| function getURLParameter(name) { | |
| return decodeURIComponent((new RegExp('[?|&]' + name + '=' + '([^&;]+?)(&|#|;|$)').exec(location.search)||[,""])[1].replace(/\+/g, '%20'))||null; | |
| } | |
| function roundTo(n, digits) { | |
| return Math.round(n * Math.pow(10, digits)) / Math.pow(10, digits); | |
| } | |
| // TODO: perhaps unnecessary, but good for learning: load canvas caches (if possible) and draw into the original | |
| var cachedCanvas = {}; | |
| function getCachedCanvas(key) { | |
| return cachedCanvas[key] || null; | |
| } | |
| function setCachedCanvas(key, ctx) { | |
| // flush cache | |
| if (_(cachedCanvas).keys().length > 25) { | |
| cachedCanvas = {}; | |
| } | |
| cachedCanvas[key] = ctx; | |
| } | |
| function generateCanvas() { | |
| var canvas = document.createElement('canvas'); | |
| canvas.width = settings.canvas.width; | |
| canvas.height = settings.canvas.height; | |
| return canvas; | |
| } | |
| function cachedRender(key, ctx, renderfn) { | |
| key = JSON.stringify(key); | |
| var cachedCanvas = getCachedCanvas(key); | |
| if (!cachedCanvas) { | |
| cachedCanvas = generateCanvas(); | |
| cached_ctx = cachedCanvas.getContext("2d"); | |
| resetCanvas(cached_ctx); | |
| renderfn(cached_ctx); | |
| setCachedCanvas(key, cachedCanvas); | |
| } | |
| ctx.drawImage(cachedCanvas, 0, 0); | |
| } | |
| // cycleFn: function(x) that returns value for a time point | |
| // key: unique key for this call, used for caching | |
| function timegraph_path(ctx, cycleFn, strokeStyle) | |
| { | |
| var N = settings.timegraph_width; // buttery-smooth, pixel-by-pixel | |
| var dx = 2 * (Math.PI) / N;; | |
| var x = 0; | |
| var px = settings.timegraph_center_x; | |
| var px_orig = px; | |
| var py = settings.timegraph_center_y; | |
| ctx.beginPath(); | |
| ctx.lineWidth = settings.wave.lineWidth; | |
| ctx.strokeStyle = strokeStyle || settings.wave.strokeStyle; | |
| // have one extra point so curves wrap nicely | |
| for (var i = 0; i <= N; i++) { | |
| var x = 2 * Math.PI * i/N; | |
| y = cycleFn(x); | |
| var px = settings.timegraph_center_x + x * (180 / Math.PI) * settings.timegraph_width / 360; | |
| var py = settings.timegraph_center_y - settings.timegraph_height*y; | |
| if (i == 0) { | |
| ctx.moveTo(px, py); | |
| } | |
| else { | |
| ctx.lineTo(px, py); | |
| } | |
| } | |
| ctx.stroke(); | |
| ctx.closePath(); | |
| } | |
| function path_circ(ctx, x, y, r) | |
| { | |
| ctx.beginPath(); | |
| ctx.arc(x, y, r, 0, Math.PI * 2, true); //arc(x, y, radius, startAngle, endAngle, anticlockwise) | |
| ctx.stroke(); | |
| ctx.closePath(); | |
| } | |
| function path_line(ctx, x0, y0, x1, y1) | |
| { | |
| ctx.beginPath(); | |
| ctx.moveTo(x0, y0); | |
| ctx.lineTo(x1, y1); | |
| ctx.stroke(); | |
| ctx.closePath(); | |
| } | |
| // place circle on canvas | |
| function path_dot(ctx, x, y, radius) | |
| { | |
| radius = radius || 3.5; | |
| ctx.beginPath(); | |
| ctx.arc(x, y, radius, 0, Math.PI * 2, true); // arc(x, y, radius, startAngle, endAngle, anticlockwise) | |
| ctx.fill(); | |
| ctx.closePath(); | |
| } | |
| // dot on cycle chart | |
| function cyclegraph_dot(ctx, x, y, fillStyle) | |
| { | |
| var x = settings.circle_center_x + settings.circle_radius*x; | |
| var y = settings.circle_center_y - settings.circle_radius*y; | |
| ctx.strokeStyle = settings.cyclegraph_dot.strokeStyle; | |
| ctx.lineWidth = settings.cyclegraph_dot.lineWidth; | |
| // line to origin | |
| path_line(ctx, settings.circle_center_x, settings.circle_center_y, x, y); | |
| // draw circle itself | |
| ctx.fillStyle = fillStyle || settings.cyclegraph_dot.fillStyle; | |
| path_dot(ctx, x, y, settings.cyclegraph_dot.radius); | |
| } | |
| // draw interval marker | |
| function cyclegraph_interval(ctx, x, y, color) | |
| { | |
| var x = settings.circle_center_x + settings.circle_radius*x; | |
| var y = settings.circle_center_y - settings.circle_radius*y; | |
| ctx.strokeStyle = color || settings.interval.fillStyle; | |
| ctx.lineWidth = settings.interval.lineWidth; | |
| // line to origin | |
| path_line(ctx, settings.circle_center_x, settings.circle_center_y, x, y); | |
| } | |
| function timegraph_interval(ctx, t, color) | |
| { | |
| var x = settings.timegraph_center_x + t * 180/Math.PI * settings.timegraph_width / 360; | |
| var min_y = settings.axis_margin_top; | |
| var max_y = settings.canvas.height - settings.axis_margin_bottom; | |
| ctx.fillStyle = color || settings.interval.fillStyle; | |
| ctx.lineWidth = settings.interval.lineWidth; | |
| // drop line to baseline | |
| path_line(ctx, x, min_y, x, max_y); | |
| } | |
| // dot on time chart | |
| function timegraph_dot(ctx, t, height, fillStyle) | |
| { | |
| var x = settings.timegraph_center_x + t * 180/Math.PI * settings.timegraph_width / 360; | |
| var y = settings.timegraph_center_y - settings.timegraph_height * height; | |
| ctx.fillStyle = fillStyle || settings.timegraph_dot.fillStyle; | |
| path_dot(ctx, x, y, settings.timegraph_dot.radius); | |
| ctx.strokeStyle = settings.timegraph_dot.strokeStyle; | |
| ctx.lineWidth = settings.timegraph_dot.lineWidth; | |
| } | |
| // parse cycle text and return array of cycle objects (amp, freq, phase) | |
| // cycles are 0th 1st 2nd 3rd... or 0th 1st & -1st 2nd & -2nd | |
| function getCycles() { | |
| $cycleInput = $('input[name=data-cycles]'); | |
| var text = $cycleInput.val(); | |
| text = text.replace(/\s+&\s+/g, '&'); | |
| var strings = _(text.split(/[\s,]+/)).reject(function(i){ return i == null || i == "";}); | |
| var index = 0; | |
| var cycles = []; | |
| function parseCycle(str, freq){ | |
| var matches = str.split(/[@:]/); | |
| return { | |
| freq: freq, | |
| amp: parseFloat(matches[0]), | |
| phase: parseFloat(matches[1] || 0) | |
| }; | |
| } | |
| _(strings).each(function(i){ | |
| var posneg = i.split('&'); | |
| cycles.push(parseCycle(posneg[0], index)); | |
| // specified negative cycle too | |
| if (posneg[1]) { | |
| cycles.push(parseCycle(posneg[1], -1 * index)); | |
| } | |
| index++; | |
| }); | |
| cycles = _(cycles).reject(function(i){ return _.isNaN(i.amp); }); | |
| return cycles; | |
| } | |
| function resetCanvas(ctx) { | |
| ctx.clearRect(0, 0, settings.canvas.width, settings.canvas.height); | |
| } | |
| function drawAxes(ctx, scale) { | |
| // style axes | |
| ctx.strokeStyle = settings.axes.strokeStyle; | |
| ctx.lineWidth = settings.axes.lineWidth; | |
| // x-axis both graphs | |
| path_line(ctx, | |
| settings.circle_center_x - settings.circle_radius - settings.axis_margin_left, | |
| settings.circle_center_y, | |
| settings.timegraph_center_x + settings.timegraph_width, | |
| settings.timegraph_center_y); | |
| // y-axis for circle | |
| path_line(ctx, settings.circle_center_x, settings.axis_margin_top, settings.circle_center_x,settings.canvas.height - settings.axis_margin_bottom); | |
| // y-axis for time series | |
| path_line(ctx, settings.timegraph_center_x, settings.axis_margin_top, settings.timegraph_center_x, settings.canvas.height - settings.axis_margin_bottom); | |
| // unit circle | |
| ctx.fillStyle = settings.unitcircle.fillStyle; | |
| ctx.strokeStyle = settings.unitcircle.strokeStyle; | |
| ctx.lineWidth = settings.unitcircle.lineWidth; | |
| path_circ(ctx, settings.circle_center_x, settings.circle_center_y, settings.circle_radius * scale); | |
| // line for the wave itself | |
| ctx.fillStyle = settings.wave.fillStyle; | |
| ctx.strokeStyle = settings.wave.strokeStyle; | |
| ctx.lineWidth = settings.wave.lineWidth; | |
| } | |
| function drawFourier(ctx, options) | |
| { | |
| var start = new Date(); | |
| options = options || {}; | |
| // position to move to has been scaled along a circle | |
| var r = (step/settings.steps) * 2.0 * Math.PI; | |
| var cycles = getCycles(); | |
| var N = cycles.length; | |
| var timeseries = Fourier.InverseTransform(cycles); | |
| var combined = Fourier.totalValue(r, cycles); | |
| var max_amplitude_time = _(_(timeseries).pluck('amp')).max(); | |
| var max_real = _(_(timeseries).pluck('real')).max(); | |
| // adjust scale if we are hiding the total | |
| if (!$('#showcombined').is(':checked')) { | |
| max_amplitude = _(_(cycles).pluck('amp')).max(); | |
| } | |
| var scale = max_amplitude_time > 0 ? 1 / max_amplitude_time : 1; | |
| if (scale > 1) { | |
| scale = 1; | |
| } | |
| resetCanvas(ctx); | |
| drawAxes(ctx, scale); | |
| function getCycleColor(cycle) { | |
| var color = cycle.freq > 0 ? settings.cycle.poscolor : settings.cycle.negcolor; | |
| if (cycle.freq == 0){ | |
| color = settings.cycle.zerocolor; | |
| } | |
| return color; | |
| } | |
| function drawStatus(text, color) { | |
| ctx.font = settings.text.font; | |
| ctx.fillStyle = color || settings.text.fillStyle; | |
| ctx.fillText(text, settings.timegraph_center_x + 10, canvas.height - settings.axis_margin_bottom); | |
| } | |
| function drawIntervals(){ | |
| // draw lines showing the intervals | |
| _(timeseries).each(function(point){ | |
| // ignore first interval, there's already an x-axis | |
| if (point.x > 0) { | |
| timegraph_interval(ctx, point.x, settings.interval.lineStyle); | |
| } | |
| var value = Fourier.totalValue(point.x, {freq: 1, phase: 0, amp: 1}); | |
| cyclegraph_interval(ctx, value.real * scale, value.im * scale, settings.interval.lineStyle); | |
| }); | |
| } | |
| if (!$('input[name=data-time]').is(':focus')) { | |
| var str = _(timeseries).map(function(point){return Math.round(point.real * 10) / 10;}).join(" "); | |
| $('input[name=data-time]').val(str); | |
| } | |
| if ($('#showreverse').is(':checked')) { | |
| // show only the total and the cycle we want | |
| var soloFreq = parseInt($('#reversefreq').val()); | |
| scale = 1 / max_amplitude_time; | |
| var cycle = { | |
| freq: -1 * soloFreq, | |
| phase: 0, | |
| amp: 1 | |
| }; | |
| var color = getCycleColor(cycle); | |
| var cycleTotal = Fourier.totalValue(r, cycle); | |
| drawIntervals(); | |
| cyclegraph_dot(ctx, cycleTotal.real * scale, cycleTotal.im * scale, color); | |
| timegraph_dot(ctx, r, cycleTotal.real * scale, color); | |
| cachedRender(["timegraph_path", cycle, scale, color], ctx, function(ctx){ | |
| timegraph_path(ctx, function(x){ return Fourier.totalValue(x, cycle).real * scale;}, color); | |
| }); | |
| var totalReal = 0; | |
| var totalIm = 0; | |
| _(timeseries).each(function(point, i){ | |
| // draw the multiplied signal | |
| var thisCycle = Fourier.totalValue(point.x, cycle); | |
| if (point.x < r) { | |
| timegraph_dot(ctx, point.x, point.real * thisCycle.real * scale, settings.cycle.negcolor); | |
| cyclegraph_dot(ctx, point.real * thisCycle.real * scale, point.real * thisCycle.im * scale, settings.cycle.negcolor); | |
| } | |
| totalReal += point.real * thisCycle.real; | |
| totalIm += point.real * thisCycle.im; | |
| }); | |
| if (timeseries.length > 0 && r > timeseries[timeseries.length - 1].x) { | |
| // show the final average | |
| var avgReal = totalReal / N; | |
| var avgIm = totalIm / N; | |
| var avgRealRounded = roundTo(avgReal, 2); | |
| var avgImRounded = roundTo(avgIm, 2); | |
| var ampRounded = Math.round(Math.sqrt(avgReal * avgReal + avgIm * avgIm), 2); | |
| var phase = roundTo(Math.atan2(avgImRounded, avgRealRounded) * 180/Math.PI, 0); | |
| cyclegraph_dot(ctx, avgReal * scale, avgIm * scale, settings.combined.color); | |
| var text = "avg: " + " re: " + avgRealRounded + " im: " + avgImRounded; | |
| // text += " [" + ampRounded + (ampRounded != 0 && phase != 0 ? phase : '' ) + "]"; | |
| drawStatus(text, settings.combined.color); | |
| } | |
| return; | |
| } | |
| if ($('#showparts').is(':checked')) { | |
| _(cycles).each(function(cycle){ | |
| var color = getCycleColor(cycle); | |
| var cycleTotal = Fourier.totalValue(r, cycle); | |
| cyclegraph_dot(ctx, cycleTotal.real * scale, cycleTotal.im * scale, color); | |
| timegraph_dot(ctx, r, cycleTotal.real * scale, color); | |
| timegraph_path(ctx, function(x){ return Fourier.totalValue(x, cycle).real * scale;}, color, cycle); | |
| }); | |
| } | |
| // ticks | |
| if ($('#showdiscrete').is(':checked')){ | |
| drawIntervals(); | |
| } | |
| // current combined point | |
| if ($('#showcombined').is(':checked')) { | |
| cyclegraph_dot(ctx, combined.real * scale, combined.im * scale, settings.combined.color); | |
| timegraph_path(ctx, function(x){return Fourier.totalValue(x, cycles).real * scale;}, settings.combined.color, cycles); | |
| timegraph_dot(ctx, r, combined.real * scale, settings.combined.color); | |
| _(timeseries).each(function(point){ | |
| timegraph_dot(ctx, point.x, point.real * scale, settings.interval.dotcolor); | |
| cyclegraph_dot(ctx, point.real * scale, point.im * scale, settings.interval.dotcolor); | |
| }); | |
| } | |
| // label values | |
| if ($('#running').is(':checked') == false) { | |
| var text = "t: " + roundTo(r, 1) + " re: " + roundTo(combined.real, 1) + " im: " + roundTo(combined.im, 1); | |
| } | |
| } | |
| function init() | |
| { | |
| var canvas = $('#canvas').get(0); | |
| var ctx = canvas.getContext("2d"); | |
| settings.canvas.width = canvas.width; | |
| settings.canvas.height = canvas.height; | |
| setInterval(function () { | |
| if ($('#running').is(':checked')) { | |
| drawFourier(ctx); | |
| advanceTime(); | |
| } | |
| }, settings.refresh); | |
| step = 0; | |
| function advanceTime(){ | |
| step++; | |
| if (step > settings.steps){ | |
| step=0; | |
| } | |
| } | |
| $('#reset').click(function(e){ | |
| e.preventDefault(); | |
| step = 0; | |
| drawFourier(ctx); | |
| }); | |
| $('input').not('.nochange').change(function(){drawFourier(ctx);}).keyup(function(){drawFourier(ctx);}); | |
| $('#time').css('visibility', 'hidden').change(function(){ | |
| step = ($(this).val() / 100) * settings.steps; | |
| drawFourier(ctx); | |
| }); | |
| $('#running').change(function(){ | |
| $('#time').css('visibility', $(this).is(':checked') ? 'hidden' : ''); | |
| $('#time').val((step / settings.steps) * 100); | |
| }); | |
| if (!Modernizr.inputtypes.range){ | |
| $('#time').css('width', '30px'); | |
| } | |
| $('input[name=data-time]').keyup(function(){ | |
| var timeseries = Fourier.parseTimeSeries($(this).val()); | |
| var transform = Fourier.Transform(timeseries); | |
| var newCycles = Fourier.getCyclesFromData(transform); | |
| var newString = Fourier.getStringFromCycles(newCycles); | |
| $('input[name=data-cycles]').val(newString); | |
| drawFourier(ctx, {dataupdate: false}); | |
| }); | |
| $('#canvas').click(function(){ | |
| $('#running').click(); | |
| }) | |
| $('.mrfourier').click(function(e){ | |
| e.preventDefault(); | |
| $('.fourierchart').toggleClass('theme-dark'); | |
| }); | |
| }; | |
| $(function(){ | |
| init(); | |
| var cycles = getURLParameter("cycles"); | |
| if (cycles) { | |
| cycles = cycles.replace(/,/g, " "); | |
| $('input[name=data-cycles]').val(cycles); | |
| } else { | |
| var time = getURLParameter("time"); | |
| if (time) { | |
| time = time.replace(/,/g, " "); | |
| $('input[name=data-cycles]').val(""); | |
| $('input[name=data-time]').val(time).trigger('keyup'); | |
| $('#running').trigger('click'); | |
| } | |
| } | |
| }); | |
| var Fourier = {}; | |
| /* | |
| Transform a discrete time series to frequency components | |
| @param data (array): time-series numbers | |
| @returns frequencies: array of frequency objects, indexed by frequency (f=0 ... N-1): | |
| {real part, imaginary part, magnitude (computed), phase in degrees (computed) } | |
| */ | |
| Fourier.Transform = function(data) { | |
| var N = data.length; | |
| var frequencies = []; | |
| // for every frequency... | |
| for (var freq = 0; freq < N; freq++) { | |
| var re = 0; | |
| var im = 0; | |
| // for every point in time... | |
| for (var t = 0; t < N; t++) { | |
| // Spin the signal _backwards_ at each frequency (as radians/s, not Hertz) | |
| var rate = -1 * (2 * Math.PI) * freq; | |
| // How far around the circle have we gone at time=t? | |
| var time = t / N; | |
| var distance = rate * time; | |
| // datapoint * e^(-i*2*pi*f) is complex, store each part | |
| var re_part = data[t] * Math.cos(distance); | |
| var im_part = data[t] * Math.sin(distance); | |
| // add this data point's contribution | |
| re += re_part; | |
| im += im_part; | |
| } | |
| // Close to zero? You're zero. | |
| if (Math.abs(re) < 1e-10) { re = 0; } | |
| if (Math.abs(im) < 1e-10) { im = 0; } | |
| // Average contribution at this frequency | |
| re = re / N; | |
| im = im / N; | |
| frequencies[freq] = { | |
| re: re, | |
| im: im, | |
| freq: freq, | |
| amp: Math.sqrt(re*re + im*im), | |
| phase: Math.atan2(im, re) * 180 / Math.PI // in degrees | |
| }; | |
| } | |
| return frequencies; | |
| } | |
| // return data point for all cycles {x, real, im, amp} | |
| Fourier.totalValue = function(x, cycles) { | |
| cycles = _.isArray(cycles) ? cycles : [cycles]; | |
| var real = 0; | |
| var im = 0; | |
| _(cycles).each(function(cycle){ | |
| real += cycle.amp * Math.cos(x * cycle.freq + cycle.phase * Math.PI/180); | |
| im += cycle.amp * Math.sin(x * cycle.freq + cycle.phase * Math.PI/180); | |
| }); | |
| return { | |
| x: x, | |
| real: real, | |
| im: im, | |
| amp: Math.sqrt(real*real + im*im) | |
| }; | |
| }; | |
| Fourier.realValue = function(x, cycle) { | |
| return Fourier.totalValue(x, cycle).real; | |
| }; | |
| Fourier.imaginaryValue = function(x, cycle) { | |
| return Fourier.totalValue(x, cycle).im; | |
| }; | |
| // return time series of data points {x, real, im, amp} | |
| Fourier.InverseTransform = function(cycles) { | |
| var timeseries = []; | |
| var len = cycles.length; | |
| for (var i = 0; i < len; i++) { | |
| var pos = i/len * 2 * Math.PI; | |
| var total = Fourier.totalValue(pos, cycles); | |
| timeseries.push(total); | |
| } | |
| return timeseries; | |
| }; | |
| // Do a fourier transform on this data string | |
| Fourier.getCyclesFromData = function(data, rounding){ | |
| rounding = rounding || 2; | |
| return _(data).map(function(i){ | |
| return { | |
| freq: i.freq, | |
| phase: Math.round(i.phase * Math.pow(10, 1)) / Math.pow(10, 1), | |
| amp: Math.round(i.amp * Math.pow(10, rounding)) / Math.pow(10, rounding) | |
| }; | |
| }); | |
| }; | |
| // convert cycles into parseable string | |
| Fourier.getStringFromCycles = function(cycles){ | |
| var str = ""; | |
| _(cycles).each(function(i){ | |
| str += i.amp; | |
| if (i.phase != 0 && i.amp != 0){ | |
| str += ":" + i.phase; | |
| } | |
| str += " "; | |
| }); | |
| return str; | |
| } | |
| // Return array of numbers given a time-series string ("1 2.3 -4"). Comma or space separated | |
| Fourier.parseTimeSeries = function(text) { | |
| var strings = _(text.split(/[\s,]+/)).reject(function(i){ return i == null || i == "";}); | |
| return _(strings).map(function(i){return parseFloat(i);}); | |
| } | |
| </script> | |
| </head> | |
| <style type="text/css"> | |
| input[type=text] { | |
| font-family: monospace; | |
| width: 240px; | |
| } | |
| input[name=data-time] { | |
| width: 160px; | |
| } | |
| #time { | |
| width: 100px; | |
| } | |
| .fourierchart { | |
| width: 520px; | |
| border: 1px solid #ccc; | |
| position: relative; | |
| } | |
| label[for=showcombined] { | |
| color: #4A93FA; | |
| } | |
| label[for=showparts] { | |
| color: #37B610; | |
| } | |
| label[for=showdiscrete]{ | |
| color: #E7A020; | |
| } | |
| .commands { | |
| font-family: 'Lucida Console', 'Courier New', monospace; | |
| font-size: 11px; | |
| background: #eaeaea; | |
| color: #333; | |
| padding: 1px 4px; | |
| } | |
| .gradient { | |
| background: rgb(238,238,238); /* Old browsers */ | |
| background: -moz-linear-gradient(top, rgba(238,238,238,1) 0%, rgba(204,204,204,1) 100%); /* FF3.6+ */ | |
| background: -webkit-gradient(linear, left top, left bottom, color-stop(0%,rgba(238,238,238,1)), color-stop(100%,rgba(204,204,204,1))); /* Chrome,Safari4+ */ | |
| background: -webkit-linear-gradient(top, rgba(238,238,238,1) 0%,rgba(204,204,204,1) 100%); /* Chrome10+,Safari5.1+ */ | |
| background: -o-linear-gradient(top, rgba(238,238,238,1) 0%,rgba(204,204,204,1) 100%); /* Opera 11.10+ */ | |
| background: -ms-linear-gradient(top, rgba(238,238,238,1) 0%,rgba(204,204,204,1) 100%); /* IE10+ */ | |
| background: linear-gradient(to bottom, rgba(238,238,238,1) 0%,rgba(204,204,204,1) 100%); /* W3C */ | |
| filter: progid:DXImageTransform.Microsoft.gradient( startColorstr='#eeeeee', endColorstr='#cccccc',GradientType=0 ); /* IE6-9 */ | |
| } | |
| .theme-dark #canvas { | |
| background: #0F2338; | |
| } | |
| .help { | |
| font-family: Verdana; | |
| font-size: 12px; | |
| position: absolute; | |
| background: #fafafa; | |
| padding: 5px; | |
| color: #333; | |
| border: 1px solid #ccc; | |
| top: -150px; | |
| left: -420px; | |
| display: none; | |
| width: 400px; | |
| } | |
| .mrfourier:hover .help { | |
| xdisplay: block; | |
| } | |
| .mrfourier { | |
| float: right; | |
| display: inline-block; | |
| width: 40px; | |
| height: 40px; | |
| /* image from Wikipedia: http://upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Joseph_Fourier.jpg/490px-Joseph_Fourier.jpg; */ | |
| background: url(http://betterexplained.com/examples/fourier/fourier.png); | |
| position: relative; | |
| top: -24px; | |
| left: -3px; | |
| background-size: 100%; | |
| background-repeat-x: no-repeat; | |
| background-position-x: 0px; | |
| border-radius: 81px; | |
| border: 1px solid #E5E5E5; | |
| } | |
| </style> | |
| <body> | |
| <div class="fourierchart"> | |
| <div class="commands gradient"> | |
| Cycles <input type="text" name="data-cycles" value = "1 0 0"></input> | |
| Time <input type="text" name="data-time" class="nochange"> | |
| </div> | |
| <canvas id="canvas" width="520px" height="200px" style=""> | |
| This browser doesn't support canvas! Try <a href="http://google.com/chrome">Google Chrome</a>. | |
| </canvas> | |
| <div class="commands gradient2"> | |
| <input type="checkbox" id="showcombined" checked="checked" name="showcombined"><label for="showcombined">Total</label> | |
| <input type="checkbox" id="showparts" checked="checked" name="showparts"><label for="showparts">Parts</label> | |
| <input type="checkbox" id="showdiscrete" name="showdiscrete"><label for="showdiscrete">Ticks</label> | |
| <input type="checkbox" id="showreverse" name="showreverse"><label for="showreverse">Derive</label> | |
| <input type="text" id="reversefreq" style="width: 20px" value="1"> | |
| </input> | |
| <input type="checkbox" id="running" checked="checked" name="running" class="nochange"><label for="running">Running?</label> | |
| <input type="range" id="time" min="0" max="100"></input> | |
| <a href="" class="mrfourier"> | |
| <div class="help"> | |
| Enter frequencies (cycles/sec aka Hz) and see their time values, or vice-versa | |
| <ul> | |
| <li>Frequency input: <code>1 0 2:45</code> is 0Hz (size 1) + 1Hz (size 0) + 2Hz (size 2, phase-shifted 45-degrees) </li> | |
| <li>Time input: <code>1 2 3</code> generates a wave that hits 1 2 3 | |
| </ul> | |
| Click Mr. Fourier for night mode. Have fun! | |
| <br/> | |
| </div> | |
| </a> | |
| </div> | |
| </div> | |
| </body> | |
| </html> |
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