dist-javascript-algorithms-and-data-structures/dist/algorithms/math/fourier-transform/inverseDiscreteFourierTransform.js

Algorithms and data-structures implemented on JavaScript

"use strict";

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.default = inverseDiscreteFourierTransform;

var _ComplexNumber = _interopRequireDefault(require("../complex-number/ComplexNumber"));

function _interopRequireDefault(obj) { return obj && obj.__esModule ? obj : { default: obj }; }

const CLOSE_TO_ZERO_THRESHOLD = 1e-10;
/**
 * Inverse Discrete Fourier Transform (IDFT): frequencies to time.
 *
 * Time complexity: O(N^2)
 *
 * @param {ComplexNumber[]} frequencies - Frequencies summands of the final signal.
 * @param {number} zeroThreshold - Threshold that is used to convert real and imaginary numbers
 * to zero in case if they are smaller then this.
 *
 * @return {number[]} - Discrete amplitudes distributed in time.
 */

function inverseDiscreteFourierTransform(frequencies, zeroThreshold = CLOSE_TO_ZERO_THRESHOLD) {
  const N = frequencies.length;
  const amplitudes = []; // Go through every discrete point of time.

  for (let timer = 0; timer < N; timer += 1) {
    // Compound amplitude at current time.
    let amplitude = new _ComplexNumber.default(); // Go through all discrete frequencies.

    for (let frequency = 0; frequency < N; frequency += 1) {
      const currentFrequency = frequencies[frequency]; // Calculate rotation angle.

      const rotationAngle = 2 * Math.PI * frequency * (timer / N); // Remember that e^ix = cos(x) + i * sin(x);

      const frequencyContribution = new _ComplexNumber.default({
        re: Math.cos(rotationAngle),
        im: Math.sin(rotationAngle)
      }).multiply(currentFrequency);
      amplitude = amplitude.add(frequencyContribution);
    } // Close to zero? You're zero.


    if (Math.abs(amplitude.re) < zeroThreshold) {
      amplitude.re = 0;
    }

    if (Math.abs(amplitude.im) < zeroThreshold) {
      amplitude.im = 0;
    } // Add current frequency signal to the list of compound signals.


    amplitudes[timer] = amplitude.re;
  }

  return amplitudes;
}