/
fft_test.go
162 lines (131 loc) · 3.48 KB
/
fft_test.go
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package fnt
import (
"fmt"
"math"
"math/cmplx"
"testing"
)
func TestFFTLength(t *testing.T) {
bits := uint(4)
blockSize := 1 << bits
samples := randBlockC128(blockSize)
fft := NewFFT(blockSize)
defer func() {
if r := recover(); r == nil {
t.Fatal("failed to fail: " + r.(string))
}
}()
fft.Execute(samples[1:], DIT, Forward, false)
fft.Execute(samples[1:], DIF, Forward, false)
}
func TestFFTIdentity(t *testing.T) {
bits := uint(14)
blockSize := 1 << bits
for _, d := range div {
input := randBlockC128(blockSize)
output := make([]complex128, blockSize)
copy(output, input)
fft := NewFFT(blockSize)
fft.Execute(output, d, Forward, false)
fft.Execute(output, d, Backward, true)
for i := range output {
expected := input[i]
received := output[i]
diff := cmplx.Abs(expected - received)
if diff >= Tolerance {
t.Fatalf("%f %f %f\n", diff, expected, received)
}
}
}
}
func TestFFTConstant(t *testing.T) {
bits := uint(4)
blockSize := 1 << bits
fft := NewFFT(blockSize)
for d := range div {
input := make([]complex128, blockSize)
output := make([]complex128, blockSize)
for i := range input {
input[i] = 1.0
output[i] = 1.0
}
fft.Execute(output, div[d], Forward, false)
if output[0] != complex(float64(blockSize), 0) {
t.Fatalf("%f %f\n", float64(blockSize), output[0])
}
for i := 1; i < len(output)-1; i++ {
if output[i] != 0.0 {
t.Fatalf("%f %f\n", 0.0, output[i])
}
}
}
}
func TestFFTDirect(t *testing.T) {
bits := uint(7)
blockSize := 1 << bits
for _, d := range div {
f0 := randBlockC128(blockSize)
f1 := make([]complex128, blockSize)
copy(f1, f0)
directFourierTransform(f0, -1.0)
fft := NewFFT(blockSize)
fft.Execute(f1, d, Forward, false)
for i := range f0 {
if cmplx.Abs(f0[i]-f1[i]) > Tolerance {
t.Fatalf("%f %f\n", f0[i], f1[i])
}
}
}
}
func directFourierTransform(f []complex128, sign float64) {
n := len(f)
h := make([]complex128, n)
phi := sign * 2.0 * math.Pi / float64(n)
for w := 0; w < n; w++ {
var t complex128
for k := 0; k < n; k++ {
t += f[k] * cmplx.Rect(1, phi*float64(k)*float64(w))
}
h[w] = t
}
copy(f, h)
}
func BenchmarkFFTRadix2DIT(b *testing.B) {
bits := uint(14)
blockSize := 1 << bits
fft := NewFFT(blockSize)
samples := randBlockC128(blockSize)
b.SetBytes(int64(blockSize))
b.ReportAllocs()
b.ResetTimer()
for n := 0; n < b.N; n++ {
fft.Execute(samples, DIT, Forward, false)
}
}
func BenchmarkFFTRadix2DIF(b *testing.B) {
bits := uint(14)
blockSize := 1 << bits
fft := NewFFT(blockSize)
samples := randBlockC128(blockSize)
b.SetBytes(int64(blockSize))
b.ReportAllocs()
b.ResetTimer()
for n := 0; n < b.N; n++ {
fft.Execute(samples, DIF, Forward, false)
}
}
func Example_fourier() {
fft := NewFFT(8)
samples := []complex128{1, 1, 1, 1, 0, 0, 0, 0}
fmt.Printf("%+0.3f\n", samples)
// Transform to Fourier domain.
fft.Execute(samples, DIT, Forward, false)
fmt.Printf("%+0.3f\n", samples)
// Transform back to time-domain and normalize.
fft.Execute(samples, DIT, Backward, true)
fmt.Printf("%+0.3f\n", samples)
// Output:
// [(+1.000+0.000i) (+1.000+0.000i) (+1.000+0.000i) (+1.000+0.000i) (+0.000+0.000i) (+0.000+0.000i) (+0.000+0.000i) (+0.000+0.000i)]
// [(+4.000+0.000i) (+1.000-2.414i) (+0.000+0.000i) (+1.000-0.414i) (+0.000+0.000i) (+1.000+0.414i) (+0.000+0.000i) (+1.000+2.414i)]
// [(+1.000+0.000i) (+1.000+0.000i) (+1.000-0.000i) (+1.000-0.000i) (+0.000+0.000i) (+0.000-0.000i) (+0.000+0.000i) (+0.000+0.000i)]
}