Chris@25: require('./test_helper')
Chris@25: 
Chris@25: var ComplexArray = require('../lib/complex_array').ComplexArray
Chris@25: 
Chris@25: describe('fft', function() {
Chris@25:   describe('#FFT()', function() {
Chris@25:     describe('on N=4 Arrays', function() {
Chris@25:       it('should return a single frequency given a constant array', function() {
Chris@25:         assertFFTMatches([1, 1, 1, 1], new ComplexArray([2, 0, 0, 0]))
Chris@25:       })
Chris@25: 
Chris@25:       it('should return flat with a delta function input', function() {
Chris@25:         assertFFTMatches([1, 0, 0, 0], new ComplexArray([0.5, 0.5, 0.5, 0.5]))
Chris@25:       })
Chris@25: 
Chris@25:       it('should return a single high freq', function() {
Chris@25:         assertFFTMatches([1, -1, 1, -1], new ComplexArray([0, 0, 2, 0]))
Chris@25:       })
Chris@25: 
Chris@25:       it('should return a single low freq', function() {
Chris@25:         assertFFTMatches([1, 0, -1, -0], new ComplexArray([0, 1, 0, 1]))
Chris@25:       })
Chris@25: 
Chris@25:       it('should return a high freq and DC', function() {
Chris@25:         assertFFTMatches([1, 0, 1, 0], new ComplexArray([1, 0, 1, 0]))
Chris@25:       })
Chris@25:     })
Chris@25: 
Chris@25:     describe('on N=6 Arrays', function() {
Chris@25:       it('should return a single frequency given a constant array', function() {
Chris@25:         assertFFTMatches(
Chris@25:           [1, 1, 1, 1, 1, 1],
Chris@25:           new ComplexArray([Math.sqrt(6), 0, 0, 0, 0, 0])
Chris@25:         )
Chris@25:       })
Chris@25: 
Chris@25:       it('should return flat with a delta function input', function() {
Chris@25:         var a = 1 / Math.sqrt(6)
Chris@25:         assertFFTMatches(
Chris@25:           [1, 0, 0, 0, 0, 0],
Chris@25:           new ComplexArray([a, a, a, a, a, a])
Chris@25:         )
Chris@25:       })
Chris@25:     })
Chris@25: 
Chris@25:     describe('on N=`prime` Arrays', function() {
Chris@25:       it('should match the DFT', function() {
Chris@25:         var a = new ComplexArray(13)
Chris@25: 
Chris@25:         a.map(function(value) {
Chris@25:           value.real = Math.random()
Chris@25:           value.imag = Math.random()
Chris@25:         })
Chris@25: 
Chris@25:         assertFFTMatchesDFT(a)
Chris@25:       })
Chris@25:     })
Chris@25: 
Chris@25:     describe('on N=512 Arrays', function() {
Chris@25:       it('should match the DFT', function() {
Chris@25:         var a = new ComplexArray(512)
Chris@25: 
Chris@25:         a.map(function(value) {
Chris@25:           value.real = Math.random()
Chris@25:           value.imag = Math.random()
Chris@25:         })
Chris@25: 
Chris@25:         assertFFTMatchesDFT(a)
Chris@25:       })
Chris@25:     })
Chris@25: 
Chris@25:     describe('on N=900 Arrays', function() {
Chris@25:       it('should match the DFT', function() {
Chris@25:         var a = new ComplexArray(900)
Chris@25: 
Chris@25:         a.map(function(value) {
Chris@25:           value.real = Math.random()
Chris@25:           value.imag = Math.random()
Chris@25:         })
Chris@25: 
Chris@25:         assertFFTMatchesDFT(a)
Chris@25:       })
Chris@25:     })
Chris@25:   })
Chris@25: 
Chris@25:   describe('#frequencyMap()', function() {
Chris@25:     it('should not modify the original', function() {
Chris@25:       var
Chris@25:         original = new ComplexArray([1, 2, 3, 4]),
Chris@25:         filtered = original.frequencyMap(function() {})
Chris@25: 
Chris@25:       assertComplexArraysAlmostEqual(original, filtered)
Chris@25:     })
Chris@25: 
Chris@25:     it('should halve the original', function() {
Chris@25:       var
Chris@25:         original = new ComplexArray([1, 2, 3, 4]),
Chris@25:         filtered = original.frequencyMap(function(value, i) {
Chris@25:           value.real /= 2
Chris@25:           value.imag /= 2
Chris@25:         })
Chris@25: 
Chris@25:       assertComplexArraysAlmostEqual(
Chris@25:           new ComplexArray([0.5, 1, 1.5, 2]), filtered)
Chris@25:     })
Chris@25: 
Chris@25:     it('should return zeroed ComplexArray', function() {
Chris@25:       var
Chris@25:         original = new ComplexArray([1, 2, 3, 4]),
Chris@25:         filtered = original.frequencyMap(function(value, i) {
Chris@25:           value.real = value.imag = 0
Chris@25:         })
Chris@25: 
Chris@25:       assertComplexArraysAlmostEqual(new ComplexArray([0, 0, 0, 0]), filtered)
Chris@25:     })
Chris@25: 
Chris@25:     it('should shift the original', function() {
Chris@25:       var
Chris@25:         original = new ComplexArray([1, 2, 3, 4]),
Chris@25:         filtered = original.frequencyMap(function(value, i) {
Chris@25:           var
Chris@25:             // Multiply by a phase to shift the original.
Chris@25:             real_multiplier = i % 2 ? 0 : (1 - i),
Chris@25:             imag_multiplier = i % 2 ? (2 - i) : 0,
Chris@25:             swap_real = value.real,
Chris@25:             swap_imag = value.imag
Chris@25: 
Chris@25:           value.real = real_multiplier * swap_real - imag_multiplier * swap_imag
Chris@25:           value.imag = real_multiplier * swap_imag + imag_multiplier * swap_real
Chris@25:         })
Chris@25: 
Chris@25:       assertComplexArraysAlmostEqual(new ComplexArray([4, 1, 2, 3]), filtered)
Chris@25:     })
Chris@25:   })
Chris@25: })
Chris@25: