plot spectrum of complex signal in javascript

To plot the spectrum of a complex signal in JavaScript, we first need to obtain its Fourier transform. This can be done using the Fast Fourier Transform (FFT) algorithm. There are several libraries available in JavaScript for performing FFT, such as DSP.js and Fourier.js.

Once we have obtained the Fourier transform of the complex signal, we can plot its magnitude and phase spectra using a charting library such as Chart.js or D3.js. The magnitude spectrum plots the absolute value of the Fourier transform, while the phase spectrum plots the angle of the complex numbers in the Fourier transform.

Here's an example code snippet that shows how to obtain the Fourier transform of a complex signal using DSP.js and plot its magnitude spectrum using Chart.js:


index.tsx
// Generate a complex signal
var n = 1024; // Number of samples
var signal = new Array(n); // Array to hold the signal
for (var i = 0; i < n; i++) {
  var t = i / n; // Time index
  signal[i] = math.complex(Math.sin(2 * Math.PI * 5 * t), Math.sin(2 * Math.PI * 10 * t)); // Complex signal with frequencies 5 Hz and 10 Hz
}

// Compute FFT of complex signal using DSP.js
var fft = new FFT(n); // FFT object with size n
fft.forward(signal); // Compute the Fourier transform

// Extract the magnitude spectrum
var magnitude = new Array(n / 2); // Array to hold the magnitude spectrum
for (var i = 0; i < n / 2; i++) {
  // Compute magnitude of complex number
  var re = fft.real[i];
  var im = fft.imag[i];
  magnitude[i] = Math.sqrt(re * re + im * im);
}

// Plot magnitude spectrum using Chart.js
var ctx = document.getElementById('myChart').getContext('2d');
var myChart = new Chart(ctx, {
  type: 'line',
  data: {
    labels: Array.from(Array(n / 2).keys()), // X-axis labels
    datasets: [{
      label: 'Magnitude Spectrum',
      data: magnitude,
      fill: false,
      borderColor: 'rgb(75, 192, 192)',
      tension: 0.1
    }]
  },
  options: {
    responsive: true,
    scales: {
      x: {
        title: {
          display: true,
          text: 'Frequency (Hz)'
        }
      },
      y: {
        title: {
          display: true,
          text: 'Magnitude'
        }
      }
    }
  }
});
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Note that this code uses the math.complex function from the Math.js library to create complex numbers. You can also use plain JavaScript objects with re and im properties to represent complex numbers.

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