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FFT.js\n[![Build Status](https://secure.travis-ci.org/indutny/fft.js.svg)](http://travis-ci.org/indutny/fft.js)\n[![NPM version](https://badge.fury.io/js/fft.js.svg)](https://badge.fury.io/js/fft.js)\n\nImplementation of Radix-4 FFT.\n\n## Usage\n\n```js\nconst FFT = require('fft.js');\n\nconst f = new FFT(4096);\n\nconst input = new Array(4096);\ninput.fill(0);\n\nconst out = f.createComplexArray();\n```\n\nIf `data` has just real numbers as is the case when `toComplexArray` is\nused - real FFT may be run to compute it 25% faster:\n```js\nconst realInput = new Array(f.size);\nf.realTransform(out, realInput);\n```\n\n`realTransform` fills just the left half of the `out`, so if the full\nspectrum is needed (which is symmetric), do the following:\n```js\nf.completeSpectrum(out);\n```\n\nIf `data` on other hand is a complex array:\n```js\nconst data = f.toComplexArray(input);\nf.transform(out, data);\n```\n\nInverse fourier transform:\n```js\nf.inverseTransform(data, out);\n```\n\n## Benchmarks\n\n```\n$ npm run bench\n===== table construction =====\n    fft.js x 1,426 ops/sec ±0.70% (93 runs sampled)\n  Fastest is fft.js\n===== transform size=2048 =====\n    fft.js x 35,153 ops/sec ±0.83% (94 runs sampled)\n    jensnockert x 5,037 ops/sec ±0.98% (91 runs sampled)\n    dsp.js x 23,143 ops/sec ±0.64% (96 runs sampled)\n    drom x 14,372 ops/sec ±0.76% (92 runs sampled)\n  Fastest is fft.js\n===== transform size=4096 =====\n    fft.js x 15,676 ops/sec ±0.76% (94 runs sampled)\n    jensnockert x 3,864 ops/sec ±1.02% (93 runs sampled)\n    dsp.js x 7,905 ops/sec ±0.50% (97 runs sampled)\n    drom x 6,718 ops/sec ±0.78% (96 runs sampled)\n  Fastest is fft.js\n===== transform size=8192 =====\n    fft.js x 6,896 ops/sec ±0.79% (96 runs sampled)\n    jensnockert x 1,193 ops/sec ±0.73% (94 runs sampled)\n    dsp.js x 2,300 ops/sec ±0.74% (95 runs sampled)\n    drom x 3,164 ops/sec ±0.67% (95 runs sampled)\n  Fastest is fft.js\n===== transform size=16384 =====\n    fft.js x 3,123 ops/sec ±0.84% (95 runs sampled)\n    jensnockert x 855 ops/sec ±1.02% (92 runs sampled)\n    dsp.js x 948 ops/sec ±0.70% (94 runs sampled)\n    drom x 1,428 ops/sec ±0.56% (93 runs sampled)\n  Fastest is fft.js\n===== realTransform size=2048 =====\n    fft.js x 47,511 ops/sec ±0.93% (91 runs sampled)\n    fourier-transform x 34,859 ops/sec ±0.77% (93 runs sampled)\n  Fastest is fft.js\n===== realTransform size=4096 =====\n    fft.js x 21,841 ops/sec ±0.70% (94 runs sampled)\n    fourier-transform x 16,135 ops/sec ±0.39% (93 runs sampled)\n  Fastest is fft.js\n===== realTransform size=8192 =====\n    fft.js x 9,665 ops/sec ±0.65% (95 runs sampled)\n    fourier-transform x 6,456 ops/sec ±0.83% (93 runs sampled)\n  Fastest is fft.js\n===== realTransform size=16384 =====\n    fft.js x 4,399 ops/sec ±0.82% (93 runs sampled)\n    fourier-transform x 2,745 ops/sec ±0.68% (94 runs sampled)\n  Fastest is fft.js\n```\n\n## API Details\n\n### Constructor\n\n```js\nconst FFT = require('fft.js');\n\nconst fft = new FFT(size);\n```\n\nNOTE: `size` MUST be a power of two and MUST be bigger than 1.\n\nIf you are looking to find the nearest power of 2 given the size of your dataset, here is a [good tutorial](https://stackoverflow.com/questions/466204/rounding-up-to-next-power-of-2/466256#466256)\n\n### Input/Output formats and helper methods.\n\n#### `fft.createComplexArray()`\n\nCreate an array of size equal to `fft.size * 2`.\nThis array contains `fft.size` complex numbers whose real and imaginary parts\nare interleaved like this:\n\n```js\nconst complexArray = [ real0, imaginary0, real1, imaginary1, ... ];\n```\n\n#### `fft.toComplexArray(realInput, /* optional */ storage)`\n\nUse provided `storage` or create a new complex array and fill all\nreal slots with values from `realInput` array, and all imaginary slots with\nzeroes.\n\n_NOTE: Always provide `storage` for better performance and to avoid extra time\nin Garbage Collection._\n\n#### `fft.fromComplexArray(complexInput, /* optional */ storage)`\n\nUse provided `storage` or create an array of size `fft.size` and fill it with\nreal values from the `complexInput`.\n\n_NOTE: Imaginary values from `complexInput` are ignored. This is a convenience\nmethod._\n\n_NOTE: Always provide `storage` for better performance and to avoid extra time\nin Garbage Collection._\n\n#### `fft.completeSpectrum(spectrum)`\n\nFill the right half of `spectrum` complex array (See:\n`fft.createComplexArray()`) with the complex conjugates of the left half:\n\n```js\nfor (every every `i` between 1 and (N / 2 - 1))\n  spectrum[N - i] = spectrum*[i]\n```\n\n_NOTE: This method may be used with `fft.realTransform()` if full output is\ndesired._\n\n### FFT Methods\n\n#### `fft.realTransform(output, input)`\n\nTake array of real numbers `input` and perform FFT transformation on it, filling\nthe left half of the `output` with the real part of the Fourier Transform's complex output (See:\n`fft.completeSpectrum()`).\n\n_NOTE: Always use this method if the input for FFT transformation is real (has\nno imaginary parts). It is about 40% faster to do such transformation this way._\n\n_NOTE: `input` - real array of size `fft.size`, `output` - complex array (See:\n`fft.createComplexArray()`)._\n\n#### `fft.transform(output, input)`\n\nPerform transformation on complex `input` array and store results in\nthe complex `output` array.\n\n_NOTE: `input` and `output` are complex arrays (See:\n`fft.createComplexArray()`)._\n\n#### `fft.inverseTransform(output, input)`\n\nPerform inverse Fourier transform on complex `input` array and store results in\nthe complex `output` array.\n\n_NOTE: `input` and `output` are complex arrays (See:\n`fft.createComplexArray()`)._\n\n#### LICENSE\n\nThis software is licensed under the MIT License.\n\nCopyright Fedor Indutny, 2017.\n\nPermission is hereby granted, free of charge, to any person obtaining a\ncopy of this software and associated documentation files (the\n\"Software\"), to deal in the Software without restriction, including\nwithout limitation the rights to use, copy, modify, merge, publish,\ndistribute, sublicense, and/or sell copies of the Software, and to permit\npersons to whom the Software is furnished to do so, subject to the\nfollowing conditions:\n\nThe above copyright notice and this permission notice shall be included\nin all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS\nOR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\nMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN\nNO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,\nDAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR\nOTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE\nUSE OR OTHER DEALINGS IN THE SOFTWARE.","users":{}}