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fft_test.go
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fft_test.go
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package fourier
import (
"fmt"
"math"
"testing"
"github.com/stretchr/testify/assert"
"github.com/stretchr/testify/require"
)
var epsilon = 0.0000001
func TestBitReversal(t *testing.T) {
b16 := "%016b"
require.Equal(t, "0000000000000100", fmt.Sprintf(b16, reverseBits(2, 4)))
require.Equal(t, "0000000001000000", fmt.Sprintf(b16, reverseBits(2, 8)))
require.Equal(t, "0000000010000000", fmt.Sprintf(b16, reverseBits(1, 8)))
require.Equal(t, "0000000000100000", fmt.Sprintf(b16, reverseBits(1, 6)))
require.Equal(t, "1000000000000000", fmt.Sprintf(b16, reverseBits(1, 16)))
require.Equal(t, "0000000000000001", fmt.Sprintf(b16, reverseBits(1, 1)))
require.Equal(t, "0000000000000001", fmt.Sprintf(b16, reverseBits(1, 0)))
}
func TestLog2(t *testing.T) {
require.Equal(t, uint(1), log2(3))
require.Equal(t, uint(4), log2(16))
require.Equal(t, uint(5), log2(32))
}
func TestIsPowerOf2(t *testing.T) {
require.True(t, isPowerOfTwo(2))
require.True(t, isPowerOfTwo(4))
require.True(t, isPowerOfTwo(8))
require.True(t, isPowerOfTwo(1))
require.False(t, isPowerOfTwo(5))
require.False(t, isPowerOfTwo(7))
}
func TestNextPowerOfTwo(t *testing.T) {
require.Equal(t, 1, nextPowerOfTwo(1))
require.Equal(t, 8, nextPowerOfTwo(5))
require.Equal(t, 64, nextPowerOfTwo(50))
require.Equal(t, 64, nextPowerOfTwo(64))
}
func TestButterflyReorder(t *testing.T) {
buf := []complex128{
complex(1, 0),
complex(2, 0),
complex(3, 0),
complex(4, 0),
complex(5, 0),
complex(6, 0),
complex(7, 0),
complex(8, 0),
}
reorder(buf)
require.Equal(t, []complex128{
complex(1, 0),
complex(5, 0),
complex(3, 0),
complex(7, 0),
complex(2, 0),
complex(6, 0),
complex(4, 0),
complex(8, 0),
}, buf)
}
func TestForwardTransform(t *testing.T) {
buf := make([]complex128, 8)
for i := 0; i < 4; i++ {
buf[i] = complex(1, 0)
}
Forward(buf)
cmplxEqualEpsilon(t, []complex128{
(4 + 0i),
(1 - 2.414213562373095i),
(0 + 0i),
(1 - 0.4142135623730949i),
(0 + 0i),
(0.9999999999999999 + 0.4142135623730949i),
(0 + 0i),
(0.9999999999999997 + 2.414213562373095i),
}, buf, epsilon)
}
func TestRoundTripTransform(t *testing.T) {
buf := make([]complex128, 4)
for i := range buf {
buf[i] = complex(float64(i)+1, 0)
}
Forward(buf)
cmplxEqualEpsilon(t, []complex128{
(10 + 0i),
(-2 + 2i),
(-2 + 0i),
(-2 - 2i),
}, buf, epsilon)
Inverse(buf)
cmplxEqualEpsilon(t, []complex128{
(1 + 0i),
(2 + 0i),
(3 + 0i),
(4 + 0i),
}, buf, epsilon)
}
func TestFrequencyDomainZeroPaddingResample(t *testing.T) {
for _, tt := range []struct {
src []float64
scale int
expected []float64
}{
{
src: []float64{1, 0.5, 1.0, 0.5, 1.0, 0.5, 1.0, 0.5},
scale: 1,
expected: []float64{1, 0.5, 1.0, 0.5, 1.0, 0.5, 1.0, 0.5},
},
{
src: []float64{1, 0.5, 1.0, 0.5, 1.0, 0.5, 1.0, 0.5},
scale: 2,
expected: []float64{1, 0.75, 0.5, 0.75, 1.0, 0.75, 0.5, 0.75, 1.0, 0.75, 0.5, 0.75, 1.0, 0.75, 0.5, 0.75},
},
{
src: []float64{1, 0.5, 1.0, 0.5, 1.0, 0.5, 1.0, 0.5},
scale: 8,
expected: []float64{1, 0.9809698831278217, 0.9267766952966369, 0.8456708580912724, 0.75, 0.6543291419087276, 0.5732233047033631, 0.5190301168721783, 0.5, 0.5190301168721783, 0.5732233047033631, 0.6543291419087276, 0.75, 0.8456708580912724, 0.9267766952966369, 0.9809698831278217, 1, 0.9809698831278217, 0.9267766952966369, 0.8456708580912724, 0.75, 0.6543291419087276, 0.5732233047033631, 0.5190301168721783, 0.5, 0.5190301168721783, 0.5732233047033631, 0.6543291419087276, 0.75, 0.8456708580912724, 0.9267766952966369, 0.9809698831278217, 1, 0.9809698831278217, 0.9267766952966369, 0.8456708580912724, 0.75, 0.6543291419087276, 0.5732233047033631, 0.5190301168721783, 0.5, 0.5190301168721783, 0.5732233047033631, 0.6543291419087276, 0.75, 0.8456708580912724, 0.9267766952966369, 0.9809698831278217, 1, 0.9809698831278217, 0.9267766952966369, 0.8456708580912724, 0.75, 0.6543291419087276, 0.5732233047033631, 0.5190301168721783, 0.5, 0.5190301168721783, 0.5732233047033631, 0.6543291419087276, 0.75, 0.8456708580912724, 0.9267766952966369, 0.9809698831278217},
},
} {
var (
l = len(tt.src)
ln = l * tt.scale
csrc = make([]complex128, l)
cpadded = make([]complex128, ln)
out = make([]float64, ln)
)
for i, v := range tt.src {
csrc[i] = complex(v*float64(tt.scale), 0)
}
require.NoError(t, Forward(csrc))
// Split the spectral content down the middle and copy both ends into the
// ends of a new upscaled buffer. This will leave the zeros in the center.
for i := 0; i < l/2; i++ {
cpadded[i] = csrc[i]
cpadded[len(cpadded)-1-i] = csrc[len(csrc)-1-i]
}
require.NoError(t, Inverse(cpadded))
for i, v := range cpadded {
out[i] = real(v)
}
assert.Equal(t, tt.expected, out)
}
}
func TestMagnitude(t *testing.T) {
const fc = 10.0
const fs = 32.0 * fc
const size = 256
carrier := make([]complex128, size)
cmplxCarrier(carrier, fc, fs)
err := Forward(carrier)
require.NoError(t, err)
abs := make([]float64, len(carrier))
err = Magnitude(abs, carrier)
require.NoError(t, err)
// Carrier Frequency = 10Hz
// Resolution = 1.25Hz
// Spike @ Carrier Frequency / Resolution = 8
assert.Equal(t, 1.0, abs[8])
// Spike in negative frequencies
assert.Equal(t, 1.0, abs[248])
// Other parts should be close to zero
assert.Equal(t, 0.0, math.Round(abs[0]))
assert.Equal(t, 0.0, math.Round(abs[10]))
}
func cmplxEqualEpsilon(t *testing.T, expected, actual []complex128, epsilon float64) {
t.Helper()
for i := range expected {
if real(expected[i]) == 0 {
assert.Equal(t, 0.0, real(actual[i]))
} else {
assert.InEpsilon(t, real(expected[i]), real(actual[i]), epsilon)
}
if imag(expected[i]) == 0 {
assert.Equal(t, 0.0, imag(actual[i]))
} else {
assert.InEpsilon(t, imag(expected[i]), imag(actual[i]), epsilon)
}
}
}
func BenchmarkFFT(b *testing.B) {
b.ReportAllocs()
b.StopTimer()
src := make([]complex128, 64)
for i := range src {
src[i] = complex(float64(i)+1, 0)
}
buf := make([]complex128, len(src))
for i := 0; i < b.N; i++ {
copy(buf, src)
b.StartTimer()
Forward(buf)
b.StopTimer()
}
}
func BenchmarkIFFT(b *testing.B) {
b.ReportAllocs()
b.StopTimer()
src := make([]complex128, 64)
for i := range src {
src[i] = complex(float64(i)+1, 0)
}
Forward(src)
buf := make([]complex128, len(src))
for i := 0; i < b.N; i++ {
copy(buf, src)
b.StartTimer()
Inverse(buf)
b.StopTimer()
}
}
func ExampleForward_roundtrip() {
buf := make([]complex128, 8)
for i := range buf {
buf[i] = complex(float64(i+1), 0)
}
fmt.Println("time:", buf)
// Transform to the frequency domain
Forward(buf)
fmt.Println("frequency:", buf)
// Transform back to the time domain
Inverse(buf)
fmt.Println("time:", buf)
// Output: time: [(1+0i) (2+0i) (3+0i) (4+0i) (5+0i) (6+0i) (7+0i) (8+0i)]
// frequency: [(36+0i) (-4+9.65685424949238i) (-4+4i) (-4+1.6568542494923797i) (-4+0i) (-3.9999999999999996-1.6568542494923797i) (-3.9999999999999996-4i) (-3.9999999999999987-9.65685424949238i)]
// time: [(1.0000000000000002+0i) (2+0i) (3+0i) (4+0i) (5+0i) (6+0i) (7+0i) (8+0i)]
}