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Refactor DFT and add common tests for Fourier.
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‎src/algorithms/math/fourier-transform/__test__/FourierTester.js

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import ComplexNumber from '../../complex-number/ComplexNumber';
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export const fourierDirectTestCases = [
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{
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input: [
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{ amplitude: 1 },
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],
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output: [
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{
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frequency: 0, amplitude: 1, phase: 0, re: 1, im: 0,
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},
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],
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},
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{
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input: [
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{ amplitude: 1 },
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{ amplitude: 0 },
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],
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output: [
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{
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frequency: 0, amplitude: 0.5, phase: 0, re: 0.5, im: 0,
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},
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{
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frequency: 1, amplitude: 0.5, phase: 0, re: 0.5, im: 0,
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},
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],
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},
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{
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input: [
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{ amplitude: 2 },
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{ amplitude: 0 },
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],
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output: [
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{
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frequency: 0, amplitude: 1, phase: 0, re: 1, im: 0,
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},
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{
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frequency: 1, amplitude: 1, phase: 0, re: 1, im: 0,
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},
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],
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},
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{
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input: [
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{ amplitude: 1 },
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{ amplitude: 0 },
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{ amplitude: 0 },
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],
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output: [
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{
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frequency: 0, amplitude: 0.3333, phase: 0, re: 0.3333, im: 0,
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},
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{
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frequency: 1, amplitude: 0.3333, phase: 0, re: 0.3333, im: 0,
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},
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{
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frequency: 2, amplitude: 0.3333, phase: 0, re: 0.3333, im: 0,
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},
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],
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},
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{
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input: [
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{ amplitude: 1 },
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{ amplitude: 0 },
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{ amplitude: 0 },
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{ amplitude: 0 },
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],
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output: [
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{
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frequency: 0, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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{
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frequency: 1, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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{
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frequency: 2, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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{
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frequency: 3, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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],
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},
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{
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input: [
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{ amplitude: 0 },
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{ amplitude: 1 },
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{ amplitude: 0 },
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{ amplitude: 0 },
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],
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output: [
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{
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frequency: 0, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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{
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frequency: 1, amplitude: 0.25, phase: -90, re: 0, im: -0.25,
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},
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{
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frequency: 2, amplitude: 0.25, phase: 180, re: -0.25, im: 0,
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},
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{
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frequency: 3, amplitude: 0.25, phase: 90, re: 0, im: 0.25,
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},
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],
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},
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{
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input: [
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{ amplitude: 0 },
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{ amplitude: 0 },
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{ amplitude: 1 },
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{ amplitude: 0 },
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],
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output: [
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{
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frequency: 0, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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{
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frequency: 1, amplitude: 0.25, phase: 180, re: -0.25, im: 0,
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},
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{
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frequency: 2, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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{
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frequency: 3, amplitude: 0.25, phase: 180, re: -0.25, im: 0,
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},
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],
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},
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{
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input: [
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{ amplitude: 0 },
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{ amplitude: 0 },
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{ amplitude: 0 },
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{ amplitude: 2 },
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],
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output: [
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{
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frequency: 0, amplitude: 0.5, phase: 0, re: 0.5, im: 0,
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},
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{
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frequency: 1, amplitude: 0.5, phase: 90, re: 0, im: 0.5,
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},
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{
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frequency: 2, amplitude: 0.5, phase: 180, re: -0.5, im: 0,
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},
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{
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frequency: 3, amplitude: 0.5, phase: -90, re: 0, im: -0.5,
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},
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],
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},
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{
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input: [
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{ amplitude: 0 },
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{ amplitude: 1 },
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{ amplitude: 0 },
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{ amplitude: 2 },
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],
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output: [
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{
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frequency: 0, amplitude: 0.75, phase: 0, re: 0.75, im: 0,
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},
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{
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frequency: 1, amplitude: 0.25, phase: 90, re: 0, im: 0.25,
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},
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{
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frequency: 2, amplitude: 0.75, phase: 180, re: -0.75, im: 0,
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},
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{
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frequency: 3, amplitude: 0.25, phase: -90, re: 0, im: -0.25,
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},
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],
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},
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{
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input: [
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{ amplitude: 4 },
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{ amplitude: 1 },
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{ amplitude: 0 },
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{ amplitude: 2 },
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],
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output: [
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{
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frequency: 0, amplitude: 1.75, phase: 0, re: 1.75, im: 0,
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},
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{
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frequency: 1, amplitude: 1.03077, phase: 14.0362, re: 0.99999, im: 0.25,
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},
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{
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frequency: 2, amplitude: 0.25, phase: 0, re: 0.25, im: 0,
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},
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{
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frequency: 3, amplitude: 1.03077, phase: -14.0362, re: 1, im: -0.25,
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},
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],
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},
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{
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input: [
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{ amplitude: 4 },
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{ amplitude: 1 },
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{ amplitude: -3 },
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{ amplitude: 2 },
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],
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output: [
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{
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frequency: 0, amplitude: 1, phase: 0, re: 1, im: 0,
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},
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{
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frequency: 1, amplitude: 1.76776, phase: 8.1301, re: 1.75, im: 0.25,
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},
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{
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frequency: 2, amplitude: 0.5, phase: 180, re: -0.5, im: 0,
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},
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{
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frequency: 3, amplitude: 1.76776, phase: -8.13010, re: 1.75, im: -0.24999,
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},
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],
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},
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{
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input: [
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{ amplitude: 1 },
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{ amplitude: 2 },
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{ amplitude: 3 },
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{ amplitude: 4 },
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],
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output: [
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{
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frequency: 0, amplitude: 2.5, phase: 0, re: 2.5, im: 0,
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},
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{
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frequency: 1, amplitude: 0.70710, phase: 135, re: -0.5, im: 0.49999,
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},
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{
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frequency: 2, amplitude: 0.5, phase: 180, re: -0.5, im: 0,
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},
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{
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frequency: 3, amplitude: 0.70710, phase: -134.99999, re: -0.49999, im: -0.5,
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},
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],
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},
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];
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export default class FourierTester {
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/**
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* @param {function} fourierTransform
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*/
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static testDirectFourierTransform(fourierTransform) {
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fourierDirectTestCases.forEach((testCase) => {
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const { input, output: expectedOutput } = testCase;
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// Convert input into complex numbers.
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const complexInput = input.map(sample => new ComplexNumber({ re: sample.amplitude }));
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// Try to split input signal into sequence of pure sinusoids.
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const currentOutput = fourierTransform(complexInput);
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// Check the signal has been split into proper amount of sub-signals.
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expect(currentOutput.length).toBeGreaterThanOrEqual(complexInput.length);
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// Now go through all the signals and check their frequency, amplitude and phase.
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expectedOutput.forEach((expectedSignal, frequency) => {
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// Get template data we want to test against.
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const currentSignal = currentOutput[frequency];
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const currentPolarSignal = currentSignal.getPolarForm(false);
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// Check all signal parameters.
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expect(frequency).toBe(expectedSignal.frequency);
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expect(currentSignal.re).toBeCloseTo(expectedSignal.re, 4);
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expect(currentSignal.im).toBeCloseTo(expectedSignal.im, 4);
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expect(currentPolarSignal.phase).toBeCloseTo(expectedSignal.phase, 4);
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expect(currentPolarSignal.radius).toBeCloseTo(expectedSignal.amplitude, 4);
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});
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});
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}
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}

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