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Update FFT tests.

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This commit is contained in:
Oleksii Trekhleb
2018-08-15 17:47:32 +03:00
parent c2f7e49f07
commit 13ed5061a3
3 changed files with 20 additions and 19 deletions
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5
src/algorithms/math/fourier-transform/README.md
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@ -120,8 +120,9 @@ Stuart Riffle has a great interpretation of the Fourier Transform:
## References ## References
- [An Interactive Guide To The Fourier Transform](https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/) - [An Interactive Guide To The Fourier Transform](https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/)
- [YouTube by Better Explained](https://www.youtube.com/watch?v=iN0VG9N2q0U&t=0s&index=77&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - [DFT on YouTube by Better Explained](https://www.youtube.com/watch?v=iN0VG9N2q0U&t=0s&index=77&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
- [YouTube by 3Blue1Brown](https://www.youtube.com/watch?v=spUNpyF58BY&t=0s&index=76&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - [FT on YouTube by 3Blue1Brown](https://www.youtube.com/watch?v=spUNpyF58BY&t=0s&index=76&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
- [FFT on YouTube by Simon Xu](https://www.youtube.com/watch?v=htCj9exbGo0&index=78&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&t=0s)
- Wikipedia - Wikipedia
- [FT](https://en.wikipedia.org/wiki/Fourier_transform) - [FT](https://en.wikipedia.org/wiki/Fourier_transform)
- [DFT](https://www.wikiwand.com/en/Discrete_Fourier_transform) - [DFT](https://www.wikiwand.com/en/Discrete_Fourier_transform)

4
src/algorithms/math/fourier-transform/__test__/fastFourierTransform.test.js
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@ -53,10 +53,10 @@ describe('fastFourierTransform', () => {
]; ];
const output = fastFourierTransform(input); const output = fastFourierTransform(input);
const invertedOut = fastFourierTransform(output, true); const invertedOutput = fastFourierTransform(output, true);
expect(sequencesApproximatelyEqual(expectedOutput, output, delta)).toBe(true); expect(sequencesApproximatelyEqual(expectedOutput, output, delta)).toBe(true);
expect(sequencesApproximatelyEqual(input, invertedOut, delta)).toBe(true); expect(sequencesApproximatelyEqual(input, invertedOutput, delta)).toBe(true);
}); });
it('should calculate the radix-2 discrete fourier transform #3', () => { it('should calculate the radix-2 discrete fourier transform #3', () => {

30
src/algorithms/math/fourier-transform/fastFourierTransform.js
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@ -4,17 +4,17 @@ import bitLength from '../bits/bitLength';
/** /**
* Returns the number which is the flipped binary representation of input. * Returns the number which is the flipped binary representation of input.
* *
* @param {Number} [input] * @param {number} input
* @param {Number} [bitsCount] * @param {number} bitsCount
* @return {Number} * @return {number}
*/ */
function reverseBits(input, bitsCount) { function reverseBits(input, bitsCount) {
let reversedBits = 0; let reversedBits = 0;
for (let i = 0; i < bitsCount; i += 1) { for (let bitIndex = 0; bitIndex < bitsCount; bitIndex += 1) {
reversedBits *= 2; reversedBits *= 2;
if (Math.floor(input / (1 << i)) % 2 === 1) { if (Math.floor(input / (1 << bitIndex)) % 2 === 1) {
reversedBits += 1; reversedBits += 1;
} }
} }
@ -39,8 +39,8 @@ export default function fastFourierTransform(inputData, inverse = false) {
} }
const output = []; const output = [];
for (let i = 0; i < N; i += 1) { for (let dataSampleIndex = 0; dataSampleIndex < N; dataSampleIndex += 1) {
output[i] = inputData[reverseBits(i, bitsCount)]; output[dataSampleIndex] = inputData[reverseBits(dataSampleIndex, bitsCount)];
} }
for (let blockLength = 2; blockLength <= N; blockLength *= 2) { for (let blockLength = 2; blockLength <= N; blockLength *= 2) {
@ -53,14 +53,14 @@ export default function fastFourierTransform(inputData, inverse = false) {
for (let blockStart = 0; blockStart < N; blockStart += blockLength) { for (let blockStart = 0; blockStart < N; blockStart += blockLength) {
let phase = new ComplexNumber({ re: 1, im: 0 }); let phase = new ComplexNumber({ re: 1, im: 0 });
for (let idx = blockStart; idx < blockStart + blockLength / 2; idx += 1) { for (let signalId = blockStart; signalId < (blockStart + blockLength / 2); signalId += 1) {
const component = output[idx + blockLength / 2].multiply(phase); const component = output[signalId + blockLength / 2].multiply(phase);
const upd1 = output[idx].add(component); const upd1 = output[signalId].add(component);
const upd2 = output[idx].subtract(component); const upd2 = output[signalId].subtract(component);
output[idx] = upd1; output[signalId] = upd1;
output[idx + blockLength / 2] = upd2; output[signalId + blockLength / 2] = upd2;
phase = phase.multiply(phaseStep); phase = phase.multiply(phaseStep);
} }
@ -68,8 +68,8 @@ export default function fastFourierTransform(inputData, inverse = false) {
} }
if (inverse) { if (inverse) {
for (let idx = 0; idx < N; idx += 1) { for (let signalId = 0; signalId < N; signalId += 1) {
output[idx] /= N; output[signalId] /= N;
} }
} }