128 lines
4.1 KiB
JavaScript
128 lines
4.1 KiB
JavaScript
import { arraySize } from '../../utils/array.js';
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import { factory } from '../../utils/factory.js';
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var name = 'fft';
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var dependencies = ['typed', 'matrix', 'addScalar', 'multiplyScalar', 'divideScalar', 'exp', 'tau', 'i', 'dotDivide', 'conj', 'pow', 'ceil', 'log2'];
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export var createFft = /* #__PURE__ */factory(name, dependencies, _ref => {
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var {
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typed,
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matrix,
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addScalar,
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multiplyScalar,
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divideScalar,
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exp,
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tau,
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i: I,
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dotDivide,
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conj,
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pow,
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ceil,
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log2
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} = _ref;
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/**
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* Calculate N-dimensional Fourier transform
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*
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* Syntax:
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*
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* math.fft(arr)
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*
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* Examples:
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*
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* math.fft([[1, 0], [1, 0]]) // returns [[{re:2, im:0}, {re:2, im:0}], [{re:0, im:0}, {re:0, im:0}]]
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*
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*
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* See Also:
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*
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* ifft
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*
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* @param {Array | Matrix} arr An array or matrix
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* @return {Array | Matrix} N-dimensional Fourier transformation of the array
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*/
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return typed(name, {
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Array: _ndFft,
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Matrix: function Matrix(matrix) {
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return matrix.create(_ndFft(matrix.valueOf()), matrix.datatype());
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}
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});
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/**
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* Perform an N-dimensional Fourier transform
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*
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* @param {Array} arr The array
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* @return {Array} resulting array
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*/
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function _ndFft(arr) {
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var size = arraySize(arr);
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if (size.length === 1) return _fft(arr, size[0]);
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// ndFft along dimension 1,...,N-1 then 1dFft along dimension 0
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return _1dFft(arr.map(slice => _ndFft(slice, size.slice(1))), 0);
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}
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/**
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* Perform an 1-dimensional Fourier transform
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*
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* @param {Array} arr The array
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* @param {number} dim dimension of the array to perform on
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* @return {Array} resulting array
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*/
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function _1dFft(arr, dim) {
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var size = arraySize(arr);
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if (dim !== 0) return new Array(size[0]).fill(0).map((_, i) => _1dFft(arr[i], dim - 1));
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if (size.length === 1) return _fft(arr);
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function _transpose(arr) {
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// Swap first 2 dimensions
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var size = arraySize(arr);
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return new Array(size[1]).fill(0).map((_, j) => new Array(size[0]).fill(0).map((_, i) => arr[i][j]));
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}
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return _transpose(_1dFft(_transpose(arr), 1));
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}
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/**
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* Perform an 1-dimensional non-power-of-2 Fourier transform using Chirp-Z Transform
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*
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* @param {Array} arr The array
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* @return {Array} resulting array
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*/
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function _czt(arr) {
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var n = arr.length;
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var w = exp(divideScalar(multiplyScalar(-1, multiplyScalar(I, tau)), n));
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var chirp = [];
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for (var i = 1 - n; i < n; i++) {
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chirp.push(pow(w, divideScalar(pow(i, 2), 2)));
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}
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var N2 = pow(2, ceil(log2(n + n - 1)));
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var xp = [...new Array(n).fill(0).map((_, i) => multiplyScalar(arr[i], chirp[n - 1 + i])), ...new Array(N2 - n).fill(0)];
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var ichirp = [...new Array(n + n - 1).fill(0).map((_, i) => divideScalar(1, chirp[i])), ...new Array(N2 - (n + n - 1)).fill(0)];
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var fftXp = _fft(xp);
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var fftIchirp = _fft(ichirp);
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var fftProduct = new Array(N2).fill(0).map((_, i) => multiplyScalar(fftXp[i], fftIchirp[i]));
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var ifftProduct = dotDivide(conj(_ndFft(conj(fftProduct))), N2);
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var ret = [];
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for (var _i = n - 1; _i < n + n - 1; _i++) {
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ret.push(multiplyScalar(ifftProduct[_i], chirp[_i]));
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}
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return ret;
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}
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/**
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* Perform an 1-dimensional Fourier transform
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*
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* @param {Array} arr The array
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* @return {Array} resulting array
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*/
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function _fft(arr) {
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var len = arr.length;
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if (len === 1) return [arr[0]];
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if (len % 2 === 0) {
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var ret = [..._fft(arr.filter((_, i) => i % 2 === 0), len / 2), ..._fft(arr.filter((_, i) => i % 2 === 1), len / 2)];
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for (var k = 0; k < len / 2; k++) {
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var p = ret[k];
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var q = multiplyScalar(ret[k + len / 2], exp(multiplyScalar(multiplyScalar(tau, I), divideScalar(-k, len))));
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ret[k] = addScalar(p, q);
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ret[k + len / 2] = addScalar(p, multiplyScalar(-1, q));
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}
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return ret;
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} else {
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// use chirp-z transform for non-power-of-2 FFT
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return _czt(arr);
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}
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// throw new Error('Can only calculate FFT of power-of-two size')
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}
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}); |