fourier transform formula matlab in javascript

The general formula for the Fourier Transform can be written as follows:

$$\large X(\omega)=\int_{-\infty}^{\infty} x(t)e^{-i\omega t} dt$$

Where x(t) is the input signal, X(ω) is the frequency domain representation of the signal, and ω is the frequency.

In MATLAB, you can use the fft function to perform the Fourier Transform. In JavaScript, you can use the Fourier Transform library like fft.js. Here's how to implement the Fourier Transform formula in JavaScript using the fft.js library:

index.tsx
const fft = require('fft.js');

// input signal
const x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9];

// number of samples
const N = x.length;

// initialize Fourier Transform
const fourier = new fft(N);

// calculate the Fourier Transform (output in complex domain)
const Xc = fourier.createComplexArray();
fourier.realTransform(Xc, x);

// convert the Fourier Transform to frequency domain (output in magnitude domain)
const X = new Array(N);
for (let i = 0; i < N / 2; i++) {
  X[i] = Math.sqrt(Xc[i * 2] ** 2 + Xc[i * 2 + 1] ** 2);
  X[i] *= 2 / N;
}
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In this code, we first define our input signal x. Then, we create a new instance of the Fourier Transform object with the size of the input signal N. We create a new complex array Xc to store the Fourier Transform in the complex domain.

Next, we use the realTransform method to calculate the Fourier Transform of the input signal x. This method takes the complex array Xc as the output parameter.

Finally, we convert the Fourier Transform from the complex domain to frequency domain by calculating the magnitude of the complex numbers in Xc. We store the output in an array X with the same size as x.

Note that the above code is simplified for demonstration purposes, and in practice, you may need to apply a window function to the input signal x before performing the Fourier Transform.