mirror of
https://github.com/gonum/gonum.git
synced 2025-10-05 15:16:59 +08:00
404 lines
13 KiB
Go
404 lines
13 KiB
Go
// Copyright ©2020 The Gonum Authors. All rights reserved.
|
||
// Use of this source code is governed by a BSD-style
|
||
// license that can be found in the LICENSE file.
|
||
|
||
package window
|
||
|
||
import "math"
|
||
|
||
// 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(seq []complex128) []complex128 {
|
||
return seq
|
||
}
|
||
|
||
// 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 SineComplex(seq []complex128) []complex128 {
|
||
k := math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
seq[i] *= complex(math.Sin(k*float64(i)), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 LanczosComplex(seq []complex128) []complex128 {
|
||
k := 2 / float64(len(seq)-1)
|
||
for i := range seq {
|
||
x := math.Pi * (k*float64(i) - 1)
|
||
if x == 0 {
|
||
// Avoid NaN.
|
||
continue
|
||
}
|
||
seq[i] *= complex(math.Sin(x)/x, 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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.
|
||
func TriangularComplex(seq []complex128) []complex128 {
|
||
a := float64(len(seq)-1) / 2
|
||
for i := range seq {
|
||
seq[i] *= complex(1-math.Abs(float64(i)/a-1), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 HannComplex(seq []complex128) []complex128 {
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
seq[i] *= complex(0.5*(1-math.Cos(k*float64(i))), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 BartlettHannComplex(seq []complex128) []complex128 {
|
||
const (
|
||
a0 = 0.62
|
||
a1 = 0.48
|
||
a2 = 0.38
|
||
)
|
||
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
seq[i] *= complex(a0-a1*math.Abs(float64(i)/float64(len(seq)-1)-0.5)-a2*math.Cos(k*float64(i)), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 HammingComplex(seq []complex128) []complex128 {
|
||
const (
|
||
a0 = 25.0 / 46.0
|
||
a1 = 1 - a0
|
||
)
|
||
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
seq[i] *= complex(a0-a1*math.Cos(k*float64(i)), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 BlackmanComplex(seq []complex128) []complex128 {
|
||
const (
|
||
a0 = 0.42
|
||
a1 = 0.5
|
||
a2 = 0.08
|
||
)
|
||
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
x := k * float64(i)
|
||
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 BlackmanHarrisComplex(seq []complex128) []complex128 {
|
||
const (
|
||
a0 = 0.35875
|
||
a1 = 0.48829
|
||
a2 = 0.14128
|
||
a3 = 0.01168
|
||
)
|
||
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
x := k * float64(i)
|
||
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 NuttallComplex(seq []complex128) []complex128 {
|
||
const (
|
||
a0 = 0.355768
|
||
a1 = 0.487396
|
||
a2 = 0.144232
|
||
a3 = 0.012604
|
||
)
|
||
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
x := k * float64(i)
|
||
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 BlackmanNuttallComplex(seq []complex128) []complex128 {
|
||
const (
|
||
a0 = 0.3635819
|
||
a1 = 0.4891775
|
||
a2 = 0.1365995
|
||
a3 = 0.0106411
|
||
)
|
||
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
x := k * float64(i)
|
||
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// 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 FlatTopComplex(seq []complex128) []complex128 {
|
||
const (
|
||
a0 = 0.21557895
|
||
a1 = 0.41663158
|
||
a2 = 0.277263158
|
||
a3 = 0.083578947
|
||
a4 = 0.006947368
|
||
)
|
||
|
||
k := 2 * math.Pi / float64(len(seq)-1)
|
||
for i := range seq {
|
||
x := k * float64(i)
|
||
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x)+a4*math.Cos(4*x), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// GaussianComplex can modify a sequence by 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 |
|
||
type GaussianComplex struct {
|
||
Sigma float64
|
||
}
|
||
|
||
// Transform applies the Gaussian transformation to seq in place, using the value
|
||
// of the receiver as the sigma parameter, and returning the result.
|
||
func (g GaussianComplex) Transform(seq []complex128) []complex128 {
|
||
a := float64(len(seq)-1) / 2
|
||
for i := range seq {
|
||
x := -0.5 * math.Pow((float64(i)-a)/(g.Sigma*a), 2)
|
||
seq[i] *= complex(math.Exp(x), 0)
|
||
}
|
||
return seq
|
||
}
|
||
|
||
// TukeyComplex 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 |
|
||
type TukeyComplex struct {
|
||
Alpha float64
|
||
}
|
||
|
||
// Transform applies the Tukey transformation to seq in place, using the value
|
||
// of the receiver as the Alpha parameter, and returning the result
|
||
func (t TukeyComplex) Transform(seq []complex128) []complex128 {
|
||
switch {
|
||
case t.Alpha <= 0:
|
||
return RectangularComplex(seq)
|
||
case t.Alpha >= 1:
|
||
return HannComplex(seq)
|
||
default:
|
||
alphaL := t.Alpha * float64(len(seq)-1)
|
||
width := int(0.5*alphaL) + 1
|
||
for i := range seq[:width] {
|
||
w := complex(0.5*(1-math.Cos(2*math.Pi*float64(i)/alphaL)), 0)
|
||
seq[i] *= w
|
||
seq[len(seq)-1-i] *= w
|
||
}
|
||
return seq
|
||
}
|
||
}
|
||
|
||
// ValuesComplex is an arbitrary complex window function.
|
||
type ValuesComplex []complex128
|
||
|
||
// NewValuesComplex returns a ValuesComplex of length n with weights corresponding
|
||
// to the provided window function.
|
||
func NewValuesComplex(window func([]complex128) []complex128, n int) ValuesComplex {
|
||
v := make(ValuesComplex, n)
|
||
for i := range v {
|
||
v[i] = 1
|
||
}
|
||
return window(v)
|
||
}
|
||
|
||
// 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 (v ValuesComplex) Transform(seq []complex128) []complex128 {
|
||
if v == nil {
|
||
return seq
|
||
}
|
||
if len(v) != len(seq) {
|
||
panic("window: length mismatch")
|
||
}
|
||
for i, w := range v {
|
||
seq[i] *= w
|
||
}
|
||
return seq
|
||
}
|