| // 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 Rectangular(seq []float64) []float64 { |
| return seq |
| } |
| |
| // 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 Sine(seq []float64) []float64 { |
| k := math.Pi / float64(len(seq)-1) |
| for i := range seq { |
| seq[i] *= math.Sin(k * float64(i)) |
| } |
| return seq |
| } |
| |
| // 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 Lanczos(seq []float64) []float64 { |
| 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] *= math.Sin(x) / x |
| } |
| return seq |
| } |
| |
| // 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 Triangular(seq []float64) []float64 { |
| a := float64(len(seq)-1) / 2 |
| for i := range seq { |
| seq[i] *= 1 - math.Abs(float64(i)/a-1) |
| } |
| return seq |
| } |
| |
| // 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 Hann(seq []float64) []float64 { |
| k := 2 * math.Pi / float64(len(seq)-1) |
| for i := range seq { |
| seq[i] *= 0.5 * (1 - math.Cos(k*float64(i))) |
| } |
| return seq |
| } |
| |
| // 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 BartlettHann(seq []float64) []float64 { |
| const ( |
| a0 = 0.62 |
| a1 = 0.48 |
| a2 = 0.38 |
| ) |
| |
| k := 2 * math.Pi / float64(len(seq)-1) |
| for i := range seq { |
| seq[i] *= a0 - a1*math.Abs(float64(i)/float64(len(seq)-1)-0.5) - a2*math.Cos(k*float64(i)) |
| } |
| return seq |
| } |
| |
| // 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. |
| func Hamming(seq []float64) []float64 { |
| const ( |
| a0 = 0.54 |
| a1 = 0.46 |
| ) |
| |
| k := 2 * math.Pi / float64(len(seq)-1) |
| for i := range seq { |
| seq[i] *= a0 - a1*math.Cos(k*float64(i)) |
| } |
| return seq |
| } |
| |
| // 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 Blackman(seq []float64) []float64 { |
| 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] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) |
| } |
| return seq |
| } |
| |
| // 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 BlackmanHarris(seq []float64) []float64 { |
| 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] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) |
| } |
| return seq |
| } |
| |
| // 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 Nuttall(seq []float64) []float64 { |
| 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] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) |
| } |
| return seq |
| } |
| |
| // 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 BlackmanNuttall(seq []float64) []float64 { |
| 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] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) |
| } |
| return seq |
| } |
| |
| // 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 FlatTop(seq []float64) []float64 { |
| 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] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) + a4*math.Cos(4*x) |
| } |
| return seq |
| } |
