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224 lines
6.4 KiB
Go
224 lines
6.4 KiB
Go
// Copyright ©2018 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package fourier_test
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import (
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"fmt"
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"math"
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"math/cmplx"
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"gonum.org/v1/gonum/floats"
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"gonum.org/v1/gonum/fourier"
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"gonum.org/v1/gonum/mat"
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)
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func ExampleFFT_Coefficients() {
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// Period is a set of samples over a given period.
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period := []float64{1, 0, 2, 0, 4, 0, 2, 0}
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// Initialize an FFT and perform the analysis.
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fft := fourier.NewFFT(len(period))
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coeff := fft.Coefficients(nil, period)
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for i, c := range coeff {
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fmt.Printf("freq=%v cycles/period, magnitude=%v, phase=%.4g\n",
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fft.Freq(i), cmplx.Abs(c), cmplx.Phase(c))
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}
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// Output:
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//
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// freq=0 cycles/period, magnitude=9, phase=0
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// freq=0.125 cycles/period, magnitude=3, phase=3.142
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// freq=0.25 cycles/period, magnitude=1, phase=-0
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// freq=0.375 cycles/period, magnitude=3, phase=3.142
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// freq=0.5 cycles/period, magnitude=9, phase=0
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}
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func ExampleFFT_Coefficients_tone() {
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// Tone is a set of samples over a second of a pure Middle C.
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const (
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mC = 261.625565 // Hz
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samples = 44100
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)
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tone := make([]float64, samples)
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for i := range tone {
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tone[i] = math.Sin(mC * 2 * math.Pi * float64(i) / samples)
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}
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// Initialize an FFT and perform the analysis.
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fft := fourier.NewFFT(samples)
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coeff := fft.Coefficients(nil, tone)
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var maxFreq, magnitude, mean float64
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for i, c := range coeff {
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m := cmplx.Abs(c)
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mean += m
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if m > magnitude {
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magnitude = m
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maxFreq = fft.Freq(i) * samples
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}
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}
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fmt.Printf("freq=%v Hz, magnitude=%.0f, mean=%.4f\n", maxFreq, magnitude, mean/samples)
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// Output:
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//
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// freq=262 Hz, magnitude=17296, mean=2.7835
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}
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func ExampleCmplxFFT_Coefficients() {
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// Period is a set of samples over a given period.
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period := []complex128{1, 0, 2, 0, 4, 0, 2, 0}
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// Initialize a complex FFT and perform the analysis.
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fft := fourier.NewCmplxFFT(len(period))
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coeff := fft.Coefficients(nil, period)
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for i := range coeff {
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// Center the spectrum.
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i = fft.ShiftIdx(i)
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fmt.Printf("freq=%v cycles/period, magnitude=%v, phase=%.4g\n",
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fft.Freq(i), cmplx.Abs(coeff[i]), cmplx.Phase(coeff[i]))
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}
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// Output:
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//
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// freq=-0.5 cycles/period, magnitude=9, phase=0
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// freq=-0.375 cycles/period, magnitude=3, phase=3.142
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// freq=-0.25 cycles/period, magnitude=1, phase=0
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// freq=-0.125 cycles/period, magnitude=3, phase=3.142
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// freq=0 cycles/period, magnitude=9, phase=0
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// freq=0.125 cycles/period, magnitude=3, phase=3.142
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// freq=0.25 cycles/period, magnitude=1, phase=0
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// freq=0.375 cycles/period, magnitude=3, phase=3.142
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}
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func Example_fFT2() {
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// This example shows how to perform a 2D fourier transform
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// on an image. The transform identifies the lines present
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// in the image.
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// Image is a set of diagonal lines.
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image := mat.NewDense(11, 11, []float64{
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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})
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// Make appropriately sized real and complex FFT types.
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r, c := image.Dims()
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fft := fourier.NewFFT(c)
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cfft := fourier.NewCmplxFFT(r)
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// Only c/2+1 coefficients will be returned for
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// the real FFT.
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c = c/2 + 1
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// Perform the first axis transform.
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rows := make([]complex128, r*c)
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for i := 0; i < r; i++ {
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fft.Coefficients(rows[c*i:c*(i+1)], image.RawRowView(i))
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}
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// Perform the second axis transform, storing
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// the result in freqs.
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freqs := mat.NewDense(c, c, nil)
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column := make([]complex128, r)
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for j := 0; j < c; j++ {
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for i := 0; i < r; i++ {
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column[i] = rows[i*c+j]
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}
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cfft.Coefficients(column, column)
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for i, v := range column[:c] {
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freqs.Set(i, j, floats.Round(cmplx.Abs(v), 1))
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}
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}
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fmt.Printf("%v\n", mat.Formatted(freqs))
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// Output:
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//
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// ⎡ 40 0.4 0.5 1.4 3.2 1.1⎤
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// ⎢ 0.4 0.5 0.7 1.8 4 1.2⎥
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// ⎢ 0.5 0.7 1.1 2.8 5.9 1.7⎥
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// ⎢ 1.4 1.8 2.8 6.8 14.1 3.8⎥
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// ⎢ 3.2 4 5.9 14.1 27.5 6.8⎥
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// ⎣ 1.1 1.2 1.7 3.8 6.8 1.6⎦
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}
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func Example_cmplxFFT2() {
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// Image is a set of diagonal lines.
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image := mat.NewDense(11, 11, []float64{
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0,
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0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1,
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})
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// Make appropriately sized complex FFT.
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// Rows and columns are the same, so the same
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// CmplxFFT can be used for both axes.
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r, c := image.Dims()
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cfft := fourier.NewCmplxFFT(r)
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// Perform the first axis transform.
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rows := make([]complex128, r*c)
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for i := 0; i < r; i++ {
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row := rows[c*i : c*(i+1)]
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for j, v := range image.RawRowView(i) {
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row[j] = complex(v, 0)
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}
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cfft.Coefficients(row, row)
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}
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// Perform the second axis transform, storing
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// the result in freqs.
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freqs := mat.NewDense(c, c, nil)
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column := make([]complex128, r)
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for j := 0; j < c; j++ {
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for i := 0; i < r; i++ {
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column[i] = rows[i*c+j]
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}
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cfft.Coefficients(column, column)
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for i, v := range column {
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// Center the frequencies.
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freqs.Set(cfft.UnshiftIdx(i), cfft.UnshiftIdx(j), floats.Round(cmplx.Abs(v), 1))
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}
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}
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fmt.Printf("%v\n", mat.Formatted(freqs))
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// Output:
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//
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// ⎡ 1.6 6.8 3.8 1.7 1.2 1.1 1.1 1.4 2.6 3.9 1.1⎤
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// ⎢ 6.8 27.5 14.1 5.9 4 3.2 3 3 3.9 3.2 3.9⎥
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// ⎢ 3.8 14.1 6.8 2.8 1.8 1.4 1.2 1.1 1.4 3.9 2.6⎥
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// ⎢ 1.7 5.9 2.8 1.1 0.7 0.5 0.5 0.5 1.1 3 1.4⎥
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// ⎢ 1.2 4 1.8 0.7 0.5 0.4 0.4 0.5 1.2 3 1.1⎥
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// ⎢ 1.1 3.2 1.4 0.5 0.4 40 0.4 0.5 1.4 3.2 1.1⎥
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// ⎢ 1.1 3 1.2 0.5 0.4 0.4 0.5 0.7 1.8 4 1.2⎥
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// ⎢ 1.4 3 1.1 0.5 0.5 0.5 0.7 1.1 2.8 5.9 1.7⎥
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// ⎢ 2.6 3.9 1.4 1.1 1.2 1.4 1.8 2.8 6.8 14.1 3.8⎥
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// ⎢ 3.9 3.2 3.9 3 3 3.2 4 5.9 14.1 27.5 6.8⎥
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// ⎣ 1.1 3.9 2.6 1.4 1.1 1.1 1.2 1.7 3.8 6.8 1.6⎦
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}
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