50ohm-contents-dl/contents/html/applet_rectangle.html

<html>
  <script src="https://www.50ohm.de/assets/jquery/3.7.1/jquery.min.js"></script>
  <script src="https://www.50ohm.de/assets/chartjs/4.4.1/chart.min.js"></script>

  <p>Hier kann die Fourier-Näherung eines symmetrischen Rechtecksignals mit einer variablen Anzahl ungerader Harmonischer untersucht werden. Die Schalter erlauben Werte von 1 bis 500.</p>

  <table>
    <tr>
      <td>Harmonische $N$:</td>
      <td>
        <input type="range" id="harmonicsRange" min="1" max="499" value="1" step="2">
      </td>
      <td>
        <input type="number" id="harmonicsInput" min="1" max="499" value="1" step="2" style="width: 6em;">
      </td>
    </tr>
  </table>

  <canvas id="rectangleFourierChart" style="width:100%; height:260px;"></canvas>

  <script>
    const chartCanvas = document.getElementById('rectangleFourierChart');
    const harmonicsRange = document.getElementById('harmonicsRange');
    const harmonicsInput = document.getElementById('harmonicsInput');
    const xMin = -1.5 * Math.PI;
    const xMax = 1.5 * Math.PI;

    const rectangleChart = new Chart(chartCanvas, {
      type: 'line',
      data: {
        datasets: [
          {
            label: 'Rechteck ideal',
            borderColor: '#ED7D71',
            backgroundColor: 'transparent',
            pointRadius: 0,
            borderDash: [6, 4],
            data: []
          },
          {
            label: 'Fourier-Näherung',
            borderColor: '#00AEDF',
            backgroundColor: 'transparent',
            pointRadius: 0,
            tension: 0.15,
            data: []
          }
        ]
      },
      options: {
        responsive: true,
        animation: false,
        plugins: {
          legend: {
            display: true
          }
        },
        scales: {
          x: {
            type: 'linear',
            min: xMin,
            max: xMax,
            title: {
              display: true,
              text: 't'
            },
            ticks: {
              callback: function(value) {
                if (Math.abs(value) < 1e-8) return '0';
                if (Math.abs(value - Math.PI) < 1e-8) return 'π';
                if (Math.abs(value + Math.PI) < 1e-8) return '-π';
                if (Math.abs(value - 1.5 * Math.PI) < 1e-8) return '3π/2';
                if (Math.abs(value + 1.5 * Math.PI) < 1e-8) return '-3π/2';
                return value.toFixed(2);
              }
            }
          },
          y: {
            min: -1.3,
            max: 1.3,
            title: {
              display: true,
              text: 'f(t)'
            },
            ticks: {
              stepSize: 0.5,
              callback: function(value) {
                return value.toFixed(1);
              }
            }
          }
        }
      }
    });

    function clampHarmonics(value) {
      const parsed = Number.parseInt(value, 10);
      if (Number.isNaN(parsed)) return 1;
      const clamped = Math.max(1, Math.min(499, parsed));
      return clamped % 2 === 0 ? clamped - 1 : clamped;
    }

    function buildFourierSeries(n) {
      const samples = [];
      const sampleCount = Math.max(1200, n * 40);
      const step = (xMax - xMin) / sampleCount;

      for (let x = xMin; x <= xMax + 1e-9; x += step) {
        let y = 0;
        for (let k = 1; k <= n; k += 2) {
          y += (4 / Math.PI) * Math.sin(k * x) / k;
        }
        samples.push({ x, y });
      }

      const idealPoints = [
        { x: xMin, y: 1 },
        { x: -Math.PI, y: 1 },
        { x: -Math.PI, y: -1 },
        { x: 0, y: -1 },
        { x: 0, y: 1 },
        { x: Math.PI, y: 1 },
        { x: Math.PI, y: -1 },
        { x: xMax, y: -1 }
      ];

      return { samples, idealPoints };
    }

    function updateChart() {
      const n = clampHarmonics(harmonicsInput.value);
      harmonicsRange.value = n;
      harmonicsInput.value = n;

      const { samples, idealPoints } = buildFourierSeries(n);

      rectangleChart.data.datasets[0].data = idealPoints.map(point => ({ x: point.x, y: point.y }));
      rectangleChart.data.datasets[1].data = samples.map(point => ({ x: point.x, y: point.y }));
      rectangleChart.update();
    }

    harmonicsRange.addEventListener('input', function() {
      harmonicsInput.value = this.value;
      updateChart();
    });

    harmonicsInput.addEventListener('input', function() {
      harmonicsRange.value = this.value;
      updateChart();
    });

    harmonicsInput.addEventListener('change', function() {
      harmonicsRange.value = this.value;
      updateChart();
    });

    updateChart();
  </script>
</html>