Documentation
¶
Overview ¶
Package window provides a set of functions to perform the transformation of sequence by different window functions.
Window functions can be used to control spectral leakage parameters when performing a Fourier transform on a signal of limited length. See https://en.wikipedia.org/wiki/Window_function for more details.
Spectral leakage parameters ¶
Application of window functions to an input will result in changes to the frequency content of the signal in an effect called spectral leakage. See https://en.wikipedia.org/wiki/Spectral_leakage.
The characteristic changes associated with each window function may be described using a set of spectral leakage parameters; β, ΔF_0, ΔF_0.5, K and ɣ_max.
The β, attenuation, coefficient of a window is the ratio of the constant component of the spectrum resulting from use of the window compared to that produced using the rectangular window, expressed in a logarithmic scale.
β_w = 20 log10(A_w / A_rect) dB
The ΔF_0 parameter describes the normalized width of the main lobe of the frequency spectrum at zero amplitude.
The ΔF_0.5 parameter describes the normalized width of the main lobe of the frequency spectrum at -3 dB (half maximum amplitude).
The K parameter describes the relative width of the main lobe of the frequency spectrum produced by the window compared with the rectangular window. The rectangular window has the lowest ΔF_0 at a value of 2.
K_w = ΔF_0_w/ΔF_0_rect.
The value of K divides windows into high resolution windows (K≤3) and low resolution windows (K>3).
The ɣ_max parameter is the maximum level of the side lobes of the normalized spectrum, in decibels.
Example ¶
package main
import (
"fmt"
"math"
"math/cmplx"
"gonum.org/v1/gonum/dsp/fourier"
"gonum.org/v1/gonum/dsp/window"
)
func main() {
// The input sequence is a 2.5 period of the Sin function.
src := make([]float64, 20)
k := 5 * math.Pi / float64(len(src)-1)
for i := range src {
src[i] = math.Sin(k * float64(i))
}
// Initialize an FFT and perform the analysis.
fft := fourier.NewFFT(len(src))
coeff := fft.Coefficients(nil, src)
// The result shows that width of the main lobe with center
// between frequencies 0.1 and 0.15 is small, but that the
// height of the side lobes is large.
fmt.Println("Rectangular window (or no window):")
for i, c := range coeff {
fmt.Printf("freq=%.4f\tcycles/period, magnitude=%.4f,\tphase=%.4f\n",
fft.Freq(i), cmplx.Abs(c), cmplx.Phase(c))
}
// Initialize an FFT and perform the analysis on a sequence
// transformed by the Hamming window function.
fft = fourier.NewFFT(len(src))
coeff = fft.Coefficients(nil, window.Hamming(src))
// The result shows that width of the main lobe is wider,
// but height of the side lobes is lower.
fmt.Println("Hamming window:")
// The magnitude of all bins has been decreased by β.
// Generally in an analysis amplification may be omitted, but to
// make a comparable data, the result should be amplified by -β
// of the window function — +5.37 dB for the Hamming window.
// -β = 20 log_10(amplifier).
amplifier := math.Pow(10, 5.37/20.0)
for i, c := range coeff {
fmt.Printf("freq=%.4f\tcycles/period, magnitude=%.4f,\tphase=%.4f\n",
fft.Freq(i), amplifier*cmplx.Abs(c), cmplx.Phase(c))
}
}
Output: Rectangular window (or no window): freq=0.0000 cycles/period, magnitude=2.2798, phase=0.0000 freq=0.0500 cycles/period, magnitude=2.6542, phase=0.1571 freq=0.1000 cycles/period, magnitude=5.3115, phase=0.3142 freq=0.1500 cycles/period, magnitude=7.3247, phase=-2.6704 freq=0.2000 cycles/period, magnitude=1.6163, phase=-2.5133 freq=0.2500 cycles/period, magnitude=0.7681, phase=-2.3562 freq=0.3000 cycles/period, magnitude=0.4385, phase=-2.1991 freq=0.3500 cycles/period, magnitude=0.2640, phase=-2.0420 freq=0.4000 cycles/period, magnitude=0.1530, phase=-1.8850 freq=0.4500 cycles/period, magnitude=0.0707, phase=-1.7279 freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000 Hamming window: freq=0.0000 cycles/period, magnitude=0.0542, phase=3.1416 freq=0.0500 cycles/period, magnitude=0.8458, phase=-2.9845 freq=0.1000 cycles/period, magnitude=7.1519, phase=0.3142 freq=0.1500 cycles/period, magnitude=8.5907, phase=-2.6704 freq=0.2000 cycles/period, magnitude=2.0804, phase=0.6283 freq=0.2500 cycles/period, magnitude=0.0816, phase=0.7854 freq=0.3000 cycles/period, magnitude=0.0156, phase=-2.1991 freq=0.3500 cycles/period, magnitude=0.0224, phase=-2.0420 freq=0.4000 cycles/period, magnitude=0.0163, phase=-1.8850 freq=0.4500 cycles/period, magnitude=0.0083, phase=-1.7279 freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000
Index ¶
- func BartlettHann(seq []float64) []float64
- func BartlettHannComplex(seq []complex128) []complex128
- func Blackman(seq []float64) []float64
- func BlackmanComplex(seq []complex128) []complex128
- func BlackmanHarris(seq []float64) []float64
- func BlackmanHarrisComplex(seq []complex128) []complex128
- func BlackmanNuttall(seq []float64) []float64
- func BlackmanNuttallComplex(seq []complex128) []complex128
- func FlatTop(seq []float64) []float64
- func FlatTopComplex(seq []complex128) []complex128
- func Hamming(seq []float64) []float64
- func HammingComplex(seq []complex128) []complex128
- func Hann(seq []float64) []float64
- func HannComplex(seq []complex128) []complex128
- func Lanczos(seq []float64) []float64
- func LanczosComplex(seq []complex128) []complex128
- func Nuttall(seq []float64) []float64
- func NuttallComplex(seq []complex128) []complex128
- func Rectangular(seq []float64) []float64
- func RectangularComplex(seq []complex128) []complex128
- func Sine(seq []float64) []float64
- func SineComplex(seq []complex128) []complex128
- func Triangular(seq []float64) []float64
- func TriangularComplex(seq []complex128) []complex128
- type Gaussian
- type Tukey
- type Values
Examples ¶
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func BartlettHann ¶
BartlettHann modifies seq in place by the Bartlett-Hann window and returns result. See https://en.wikipedia.org/wiki/Window_function#Bartlett%E2%80%93Hann_window and https://www.recordingblogs.com/wiki/bartlett-hann-window for details.
The Bartlett-Hann window is a high-resolution window.
The sequence weights are
w[k] = 0.62 - 0.48*|k/(N-1)-0.5| - 0.38*cos(2*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.45, K = 2, ɣ_max = -35.9, β = -6.
func BartlettHannComplex ¶
func BartlettHannComplex(seq []complex128) []complex128
BartlettHannComplex modifies seq in place by the Bartlett-Hann window and returns result. See https://en.wikipedia.org/wiki/Window_function#Bartlett%E2%80%93Hann_window and https://www.recordingblogs.com/wiki/bartlett-hann-window for details.
The Bartlett-Hann window is a high-resolution window.
The sequence weights are
w[k] = 0.62 - 0.48*|k/(N-1)-0.5| - 0.38*cos(2*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.45, K = 2, ɣ_max = -35.9, β = -6.
func Blackman ¶
Blackman modifies seq in place by the Blackman window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Blackman_window and https://www.recordingblogs.com/wiki/blackman-window for details.
The Blackman window is a high-resolution window.
The sequence weights are
w[k] = 0.42 - 0.5*cos(2*π*k/(N-1)) + 0.08*cos(4*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 6, ΔF_0.5 = 1.7, K = 3, ɣ_max = -58, β = -7.54.
func BlackmanComplex ¶
func BlackmanComplex(seq []complex128) []complex128
BlackmanComplex modifies seq in place by the Blackman window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Blackman_window and https://www.recordingblogs.com/wiki/blackman-window for details.
The Blackman window is a high-resolution window.
The sequence weights are
w[k] = 0.42 - 0.5*cos(2*π*k/(N-1)) + 0.08*cos(4*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 6, ΔF_0.5 = 1.7, K = 3, ɣ_max = -58, β = -7.54.
func BlackmanHarris ¶
BlackmanHarris modifies seq in place by the Blackman-Harris window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Harris_window and https://www.recordingblogs.com/wiki/blackman-harris-window for details.
The Blackman-Harris window is a low-resolution window.
The sequence weights are
w[k] = 0.35875 - 0.48829*cos(2*π*k/(N-1)) +
0.14128*cos(4*π*k/(N-1)) - 0.01168*cos(6*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.97, K = 4, ɣ_max = -92, β = -8.91.
func BlackmanHarrisComplex ¶
func BlackmanHarrisComplex(seq []complex128) []complex128
BlackmanHarrisComplex modifies seq in place by the Blackman-Harris window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Harris_window and https://www.recordingblogs.com/wiki/blackman-harris-window for details.
The Blackman-Harris window is a low-resolution window.
The sequence weights are
w[k] = 0.35875 - 0.48829*cos(2*π*k/(N-1)) +
0.14128*cos(4*π*k/(N-1)) - 0.01168*cos(6*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.97, K = 4, ɣ_max = -92, β = -8.91.
func BlackmanNuttall ¶
BlackmanNuttall modifies seq in place by the Blackman-Nuttall window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Nuttall_window and https://www.recordingblogs.com/wiki/blackman-nuttall-window for details.
The Blackman-Nuttall window is a low-resolution window.
The sequence weights are
w[k] = 0.3635819 - 0.4891775*cos(2*π*k/(N-1)) + 0.1365995*cos(4*π*k/(N-1)) -
0.0106411*cos(6*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.94, K = 4, ɣ_max = -98, β = -8.8.
func BlackmanNuttallComplex ¶
func BlackmanNuttallComplex(seq []complex128) []complex128
BlackmanNuttallComplex modifies seq in place by the Blackman-Nuttall window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Nuttall_window and https://www.recordingblogs.com/wiki/blackman-nuttall-window for details.
The Blackman-Nuttall window is a low-resolution window.
The sequence weights are
w[k] = 0.3635819 - 0.4891775*cos(2*π*k/(N-1)) + 0.1365995*cos(4*π*k/(N-1)) -
0.0106411*cos(6*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.94, K = 4, ɣ_max = -98, β = -8.8.
func FlatTop ¶
FlatTop modifies seq in place by the Flat Top window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Flat_top_window and https://www.recordingblogs.com/wiki/flat-top-window for details.
The Flat Top window is a low-resolution window.
The sequence weights are
w[k] = 0.21557895 - 0.41663158*cos(2*π*k/(N-1)) +
0.277263158*cos(4*π*k/(N-1)) - 0.083578947*cos(6*π*k/(N-1)) +
0.006947368*cos(4*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 10, ΔF_0.5 = 3.72, K = 5, ɣ_max = -93.0, β = -13.34.
func FlatTopComplex ¶
func FlatTopComplex(seq []complex128) []complex128
FlatTopComplex modifies seq in place by the Flat Top window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Flat_top_window and https://www.recordingblogs.com/wiki/flat-top-window for details.
The Flat Top window is a low-resolution window.
The sequence weights are
w[k] = 0.21557895 - 0.41663158*cos(2*π*k/(N-1)) +
0.277263158*cos(4*π*k/(N-1)) - 0.083578947*cos(6*π*k/(N-1)) +
0.006947368*cos(4*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 10, ΔF_0.5 = 3.72, K = 5, ɣ_max = -93.0, β = -13.34.
func Hamming ¶
Hamming modifies seq in place by the Hamming window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows and https://www.recordingblogs.com/wiki/hamming-window for details.
The Hamming window is a high-resolution window. Among K=2 windows it has the highest ɣ_max.
The sequence weights are
w[k] = 25/46 - 21/46 * cos(2*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -42, β = -5.37.
Example ¶
package main
import (
"fmt"
"gonum.org/v1/gonum/dsp/window"
)
func main() {
src := []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
// Window functions change data in place. So, if input data
// needs to stay unchanged, it must be copied.
srcCpy := append([]float64(nil), src...)
// Apply window function to srcCpy.
dst := window.Hamming(srcCpy)
// src is unchanged.
fmt.Printf("src: %f\n", src)
// srcCpy is altered.
fmt.Printf("srcCpy: %f\n", srcCpy)
// dst mirrors the srcCpy slice.
fmt.Printf("dst: %f\n", dst)
}
Output: src: [1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000] srcCpy: [0.080000 0.104924 0.176995 0.288404 0.427077 0.577986 0.724780 0.851550 0.944558 0.993726 0.993726 0.944558 0.851550 0.724780 0.577986 0.427077 0.288404 0.176995 0.104924 0.080000] dst: [0.080000 0.104924 0.176995 0.288404 0.427077 0.577986 0.724780 0.851550 0.944558 0.993726 0.993726 0.944558 0.851550 0.724780 0.577986 0.427077 0.288404 0.176995 0.104924 0.080000]
func HammingComplex ¶
func HammingComplex(seq []complex128) []complex128
HammingComplex modifies seq in place by the Hamming window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows and https://www.recordingblogs.com/wiki/hamming-window for details.
The Hamming window is a high-resolution window. Among K=2 windows it has the highest ɣ_max.
The sequence weights are
w[k] = 25/46 - 21/46 * cos(2*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -42, β = -5.37.
func Hann ¶
Hann modifies seq in place by the Hann window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows and https://www.recordingblogs.com/wiki/hann-window for details.
The Hann window is a high-resolution window.
The sequence weights are
w[k] = 0.5*(1 - cos(2*π*k/(N-1))),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.5, K = 2, ɣ_max = -31.5, β = -6.
func HannComplex ¶
func HannComplex(seq []complex128) []complex128
HannComplex modifies seq in place by the Hann window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows and https://www.recordingblogs.com/wiki/hann-window for details.
The Hann window is a high-resolution window.
The sequence weights are
w[k] = 0.5*(1 - cos(2*π*k/(N-1))),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.5, K = 2, ɣ_max = -31.5, β = -6.
func Lanczos ¶
Lanczos modifies seq in place by the Lanczos window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Lanczos_window and https://www.recordingblogs.com/wiki/lanczos-window for details.
The Lanczos window is a high-resolution window.
The sequence weights are
w[k] = sinc(2*k/(N-1) - 1),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 3.24, ΔF_0.5 = 1.3, K = 1.62, ɣ_max = -26.4, β = -4.6.
func LanczosComplex ¶
func LanczosComplex(seq []complex128) []complex128
LanczosComplex modifies seq in place by the Lanczos window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Lanczos_window and https://www.recordingblogs.com/wiki/lanczos-window for details.
The Lanczos window is a high-resolution window.
The sequence weights are
w[k] = sinc(2*k/(N-1) - 1),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 3.24, ΔF_0.5 = 1.3, K = 1.62, ɣ_max = -26.4, β = -4.6.
func Nuttall ¶
Nuttall modifies seq in place by the Nuttall window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Nuttall_window,_continuous_first_derivative and https://www.recordingblogs.com/wiki/nuttall-window for details.
The Nuttall window is a low-resolution window.
The sequence weights are
w[k] = 0.355768 - 0.487396*cos(2*π*k/(N-1)) + 0.144232*cos(4*π*k/(N-1)) -
0.012604*cos(6*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.98, K = 4, ɣ_max = -93, β = -9.
func NuttallComplex ¶
func NuttallComplex(seq []complex128) []complex128
NuttallComplex modifies seq in place by the Nuttall window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Nuttall_window,_continuous_first_derivative and https://www.recordingblogs.com/wiki/nuttall-window for details.
The Nuttall window is a low-resolution window.
The sequence weights are
w[k] = 0.355768 - 0.487396*cos(2*π*k/(N-1)) + 0.144232*cos(4*π*k/(N-1)) -
0.012604*cos(6*π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.98, K = 4, ɣ_max = -93, β = -9.
func Rectangular ¶
Rectangular modifies seq in place by the Rectangular window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Rectangular_window and https://www.recordingblogs.com/wiki/rectangular-window for details.
The rectangular window has the lowest width of the main lobe and largest level of the side lobes. The result corresponds to a selection of limited length sequence of values without any modification.
The sequence weights are
w[k] = 1,
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 2, ΔF_0.5 = 0.89, K = 1, ɣ_max = -13, β = 0.
func RectangularComplex ¶
func RectangularComplex(seq []complex128) []complex128
RectangularComplex modifies seq in place by the Rectangular window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Rectangular_window and https://www.recordingblogs.com/wiki/rectangular-window for details.
The rectangular window has the lowest width of the main lobe and largest level of the side lobes. The result corresponds to a selection of limited length sequence of values without any modification.
The sequence weights are
w[k] = 1,
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 2, ΔF_0.5 = 0.89, K = 1, ɣ_max = -13, β = 0.
func Sine ¶
Sine modifies seq in place by the Sine window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Sine_window and https://www.recordingblogs.com/wiki/sine-window for details.
Sine window is a high-resolution window.
The sequence weights are
w[k] = sin(π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 3, ΔF_0.5 = 1.23, K = 1.5, ɣ_max = -23, β = -3.93.
func SineComplex ¶
func SineComplex(seq []complex128) []complex128
SineComplex modifies seq in place by the Sine window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Sine_window and https://www.recordingblogs.com/wiki/sine-window for details.
Sine window is a high-resolution window.
The sequence weights are
w[k] = sin(π*k/(N-1)),
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 3, ΔF_0.5 = 1.23, K = 1.5, ɣ_max = -23, β = -3.93.
func Triangular ¶
Triangular modifies seq in place by the Triangular window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Triangular_window and https://www.recordingblogs.com/wiki/triangular-window for details.
The Triangular window is a high-resolution window.
The sequence weights are
w[k] = 1 - |k/A -1|, A=(N-1)/2,
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -26.5, β = -6.
func TriangularComplex ¶
func TriangularComplex(seq []complex128) []complex128
TriangularComplex modifies seq in place by the Triangular window and returns the result. See https://en.wikipedia.org/wiki/Window_function#Triangular_window and https://www.recordingblogs.com/wiki/triangular-window for details.
The Triangular window is a high-resolution window.
The sequence weights are
w[k] = 1 - |k/A -1|, A=(N-1)/2,
for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -26.5, β = -6.
Types ¶
type Gaussian ¶
type Gaussian struct {
Sigma float64
}
Gaussian can modify a sequence using the Gaussian window and return the result. See https://en.wikipedia.org/wiki/Window_function#Gaussian_window and https://www.recordingblogs.com/wiki/gaussian-window for details.
The Gaussian window is an adjustable window.
The sequence weights are
w[k] = exp(-0.5 * ((k-M)/(σ*M))² ), M = (N-1)/2,
for k=0,1,...,N-1 where N is the length of the window.
The properties of the window depend on the value of σ (sigma). It can be used as high or low resolution window, depending of the σ value.
Spectral leakage parameters are summarized in the table:
| σ=0.3 | σ=0.5 | σ=1.2 | -------|---------------------------| ΔF_0 | 8 | 3.4 | 2.2 | ΔF_0.5 | 1.82 | 1.2 | 0.94 | K | 4 | 1.7 | 1.1 | ɣ_max | -65 | -31.5 | -15.5 | β | -8.52 | -4.48 | -0.96 |
func (Gaussian) Transform ¶
Transform applies the Gaussian transformation to seq in place, using the value of the receiver as the sigma parameter, and returning the result.
func (Gaussian) TransformComplex ¶ added in v0.9.0
func (g Gaussian) TransformComplex(seq []complex128) []complex128
TransformComplex applies the Gaussian transformation to seq in place, using the value of the receiver as the sigma parameter, and returning the result.
type Tukey ¶ added in v0.9.0
type Tukey struct {
Alpha float64
}
Tukey can modify a sequence using the Tukey window and return the result. See https://en.wikipedia.org/wiki/Window_function#Tukey_window and https://www.recordingblogs.com/wiki/tukey-window for details.
The Tukey window is an adjustable window.
The sequence weights are
w[k] = 0.5 * (1 + cos(π*(|k - M| - αM)/((1-α) * M))), |k - M| ≥ αM
= 1, |k - M| < αM
with M = (N - 1)/2 for k=0,1,...,N-1 where N is the length of the window.
Spectral leakage parameters are summarized in the table:
| α=0.3 | α=0.5 | α=0.7 | -------|--------------------------| ΔF_0 | 1.33 | 1.22 | 1.13 | ΔF_0.5 | 1.28 | 1.16 | 1.04 | K | 0.67 | 0.61 | 0.57 | ɣ_max | -18.2 | -15.1 | -13.8 | β | -1.41 | -2.50 | -3.74 |
func (Tukey) Transform ¶ added in v0.9.0
Transform applies the Tukey transformation to seq in place, using the value of the receiver as the Alpha parameter, and returning the result.
func (Tukey) TransformComplex ¶ added in v0.9.0
func (t Tukey) TransformComplex(seq []complex128) []complex128
TransformComplex applies the Tukey transformation to seq in place, using the value of the receiver as the Alpha parameter, and returning the result.
type Values ¶
type Values []float64
Values is an arbitrary real window function.
Example ¶
package main
import (
"fmt"
"gonum.org/v1/gonum/dsp/window"
)
func main() {
src := []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
// Create a Sine Window lookup table.
sine := window.NewValues(window.Sine, len(src))
// Apply the transformation to the src.
fmt.Printf("dst: %f\n", sine.Transform(src))
}
Output: dst: [0.000000 0.164595 0.324699 0.475947 0.614213 0.735724 0.837166 0.915773 0.969400 0.996584 0.996584 0.969400 0.915773 0.837166 0.735724 0.614213 0.475947 0.324699 0.164595 0.000000]
func NewValues ¶
NewValues returns a Values of length n with weights corresponding to the provided window function.
func (Values) Transform ¶
Transform applies the weights in the receiver to seq in place, returning the result. If v is nil, Transform is a no-op, otherwise the length of v must match the length of seq.
func (Values) TransformComplex ¶ added in v0.9.0
func (v Values) TransformComplex(seq []complex128) []complex128
TransformComplex applies the weights in the receiver to seq in place, returning the result. If v is nil, TransformComplex is a no-op, otherwise the length of v must match the length of seq.
func (Values) TransformComplexTo ¶ added in v0.9.0
func (v Values) TransformComplexTo(dst, src []complex128)
TransformComplexTo applies the weights in the receiver to src placing the result in dst. If v is nil, TransformComplexTo is a no-op, otherwise the length of v must match the length of src and dst.
func (Values) TransformTo ¶ added in v0.9.0
TransformTo applies the weights in the receiver to src placing the result in dst. If v is nil, TransformTo is a no-op, otherwise the length of v must match the length of src and dst.
Example (Gabor) ¶
package main
import (
"fmt"
"gonum.org/v1/gonum/dsp/window"
)
func main() {
src := []float64{1, 2, 1, 0, -1, -1, -2, -2, -1, -1,
0, 1, 1, 2, 1, 0, -1, -2, -1, 0}
// Create a Gaussian Window lookup table for 4 samples.
gaussian := window.NewValues(window.Gaussian{0.5}.Transform, 4)
// Prepare a destination.
dst := make([]float64, 8)
// Apply the transformation to the src, placing it in dst.
for i := 0; i < len(src)-len(gaussian); i++ {
gaussian.TransformTo(dst[0:len(gaussian)], src[i:i+len(gaussian)])
// To perform the Gabor transform, we would calculate
// the FFT on dst for each iteration.
fmt.Printf("FFT(%f)\n", dst)
}
}
Output: FFT([0.135335 1.601475 0.800737 0.000000 0.000000 0.000000 0.000000 0.000000]) FFT([0.270671 0.800737 0.000000 -0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([0.135335 0.000000 -0.800737 -0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([0.000000 -0.800737 -0.800737 -0.270671 0.000000 0.000000 0.000000 0.000000]) FFT([-0.135335 -0.800737 -1.601475 -0.270671 0.000000 0.000000 0.000000 0.000000]) FFT([-0.135335 -1.601475 -1.601475 -0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([-0.270671 -1.601475 -0.800737 -0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([-0.270671 -0.800737 -0.800737 0.000000 0.000000 0.000000 0.000000 0.000000]) FFT([-0.135335 -0.800737 0.000000 0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([-0.135335 0.000000 0.800737 0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([0.000000 0.800737 0.800737 0.270671 0.000000 0.000000 0.000000 0.000000]) FFT([0.135335 0.800737 1.601475 0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([0.135335 1.601475 0.800737 0.000000 0.000000 0.000000 0.000000 0.000000]) FFT([0.270671 0.800737 0.000000 -0.135335 0.000000 0.000000 0.000000 0.000000]) FFT([0.135335 0.000000 -0.800737 -0.270671 0.000000 0.000000 0.000000 0.000000]) FFT([0.000000 -0.800737 -1.601475 -0.135335 0.000000 0.000000 0.000000 0.000000])
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