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 // 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, v := range seq { w := math.Sin(k * float64(i)) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { x := math.Pi * (k*float64(i) - 1) if x == 0 { // Avoid NaN. continue } w := math.Sin(x) / x seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { w := 1 - math.Abs(float64(i)/a-1) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { w := 0.5 * (1 - math.Cos(k*float64(i))) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { w := a0 - a1*math.Abs(float64(i)/float64(len(seq)-1)-0.5) - a2*math.Cos(k*float64(i)) seq[i] = complex(w*real(v), w*imag(v)) } 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 = 0.54 a1 = 0.46 ) k := 2 * math.Pi / float64(len(seq)-1) for i, v := range seq { w := a0 - a1*math.Cos(k*float64(i)) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { x := k * float64(i) w := a0 - a1*math.Cos(x) + a2*math.Cos(2*x) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { x := k * float64(i) w := a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { x := k * float64(i) w := a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { x := k * float64(i) w := a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) seq[i] = complex(w*real(v), w*imag(v)) } 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, v := range seq { x := k * float64(i) w := a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) + a4*math.Cos(4*x) seq[i] = complex(w*real(v), w*imag(v)) } return seq }