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dsp/window: use half offset to exclude flanking zeros

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This commit is contained in:
Dan Kortschak
2020-02-20 19:30:39 +10:30
committed by GitHub
parent 43ba13d1a9
commit efc4dabf2a
6 changed files with 245 additions and 320 deletions
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84
dsp/window/window_complex.go
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@@ -30,14 +30,14 @@ func RectangularComplex(seq []complex128) []complex128 {
// Sine window is a high-resolution window.
//
// The sequence weights are
// w[k] = sin(π*k/(N-1)),
// w[k] = sin(π*(k+1/2)/N),
// 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)
k := math.Pi / float64(len(seq))
for i := range seq {
seq[i] *= complex(math.Sin(k*float64(i)), 0)
seq[i] *= complex(math.Sin(k*(float64(i)+0.5)), 0)
}
return seq
}
@@ -49,14 +49,14 @@ func SineComplex(seq []complex128) []complex128 {
// The Lanczos window is a high-resolution window.
//
// The sequence weights are
// w[k] = sinc(2*k/(N-1) - 1),
// w[k] = sinc(2*(k+1/2)/N - 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)
k := 2 / float64(len(seq))
for i := range seq {
x := math.Pi * (k*float64(i) - 1)
x := math.Pi * (k*(float64(i)+0.5) - 1)
if x == 0 {
// Avoid NaN.
continue
@@ -73,14 +73,14 @@ func LanczosComplex(seq []complex128) []complex128 {
// The Triangular window is a high-resolution window.
//
// The sequence weights are
// w[k] = 1 - |k/A -1|, A=(N-1)/2,
// w[k] = 1 - |(k + 1/2 - N/2)/(N/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
a := float64(len(seq)) / 2
for i := range seq {
seq[i] *= complex(1-math.Abs(float64(i)/a-1), 0)
seq[i] *= complex(1-math.Abs((float64(i)+0.5-a)/a), 0)
}
return seq
}
@@ -92,14 +92,14 @@ func TriangularComplex(seq []complex128) []complex128 {
// The Hann window is a high-resolution window.
//
// The sequence weights are
// w[k] = 0.5*(1 - cos(2*π*k/(N-1))),
// w[k] = 0.5*(1 - cos(2*π*(k+1/2)/N)),
// 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)
k := 2 * math.Pi / float64(len(seq))
for i := range seq {
seq[i] *= complex(0.5*(1-math.Cos(k*float64(i))), 0)
seq[i] *= complex(0.5*(1-math.Cos(k*(float64(i)+0.5))), 0)
}
return seq
}
@@ -111,7 +111,7 @@ func HannComplex(seq []complex128) []complex128 {
// 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)),
// w[k] = 0.62 - 0.48*|(k+1/2)/N-0.5| - 0.38*cos(2*π*(k+1/2)/N),
// 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.
@@ -122,9 +122,9 @@ func BartlettHannComplex(seq []complex128) []complex128 {
a2 = 0.38
)
k := 2 * math.Pi / float64(len(seq)-1)
k := 2 * math.Pi / float64(len(seq))
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)
seq[i] *= complex(a0-a1*math.Abs((float64(i)+0.5)/float64(len(seq))-0.5)-a2*math.Cos(k*(float64(i)+0.5)), 0)
}
return seq
}
@@ -137,7 +137,7 @@ func BartlettHannComplex(seq []complex128) []complex128 {
// the highest ɣ_max.
//
// The sequence weights are
// w[k] = 25/46 - 21/46 * cos(2*π*k/(N-1)),
// w[k] = 25/46 - 21/46 * cos(2*π*(k+1/2)/N),
// 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.
@@ -147,9 +147,9 @@ func HammingComplex(seq []complex128) []complex128 {
a1 = 1 - a0
)
k := 2 * math.Pi / float64(len(seq)-1)
k := 2 * math.Pi / float64(len(seq))
for i := range seq {
seq[i] *= complex(a0-a1*math.Cos(k*float64(i)), 0)
seq[i] *= complex(a0-a1*math.Cos(k*(float64(i)+0.5)), 0)
}
return seq
}
@@ -161,7 +161,7 @@ func HammingComplex(seq []complex128) []complex128 {
// 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)),
// w[k] = 0.42 - 0.5*cos(2*π*(k+1/2)/N) + 0.08*cos(4*π*(k+1/2)/N),
// 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.
@@ -172,9 +172,9 @@ func BlackmanComplex(seq []complex128) []complex128 {
a2 = 0.08
)
k := 2 * math.Pi / float64(len(seq)-1)
k := 2 * math.Pi / float64(len(seq))
for i := range seq {
x := k * float64(i)
x := k * (float64(i) + 0.5)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x), 0)
}
return seq
@@ -187,8 +187,8 @@ func BlackmanComplex(seq []complex128) []complex128 {
// 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)),
// w[k] = 0.35875 - 0.48829*cos(2*π*(k+1/2)/N) +
// 0.14128*cos(4*π*(k+1/2)/N) - 0.01168*cos(6*π*(k+1/2)/N),
// 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.
@@ -200,9 +200,9 @@ func BlackmanHarrisComplex(seq []complex128) []complex128 {
a3 = 0.01168
)
k := 2 * math.Pi / float64(len(seq)-1)
k := 2 * math.Pi / float64(len(seq))
for i := range seq {
x := k * float64(i)
x := k * (float64(i) + 0.5)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
}
return seq
@@ -215,8 +215,8 @@ func BlackmanHarrisComplex(seq []complex128) []complex128 {
// 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)),
// w[k] = 0.355768 - 0.487396*cos(2*π*(k+1/2)/N) + 0.144232*cos(4*π*(k+1/2)/N) -
// 0.012604*cos(6*π*(k+1/2)/N),
// 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.
@@ -228,9 +228,9 @@ func NuttallComplex(seq []complex128) []complex128 {
a3 = 0.012604
)
k := 2 * math.Pi / float64(len(seq)-1)
k := 2 * math.Pi / float64(len(seq))
for i := range seq {
x := k * float64(i)
x := k * (float64(i) + 0.5)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
}
return seq
@@ -243,8 +243,8 @@ func NuttallComplex(seq []complex128) []complex128 {
// 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)),
// w[k] = 0.3635819 - 0.4891775*cos(2*π*(k+1/2)/N) + 0.1365995*cos(4*π*(k+1/2)/N) -
// 0.0106411*cos(6*π*(k+1/2)/N),
// 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.
@@ -256,9 +256,9 @@ func BlackmanNuttallComplex(seq []complex128) []complex128 {
a3 = 0.0106411
)
k := 2 * math.Pi / float64(len(seq)-1)
k := 2 * math.Pi / float64(len(seq))
for i := range seq {
x := k * float64(i)
x := k * (float64(i) + 0.5)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
}
return seq
@@ -271,9 +271,9 @@ func BlackmanNuttallComplex(seq []complex128) []complex128 {
// 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)),
// w[k] = 0.21557895 - 0.41663158*cos(2*π*(k+1/2)/(N-1)) +
// 0.277263158*cos(4*π*(k+1/2)/N) - 0.083578947*cos(6*π*(k+1/2)/N) +
// 0.006947368*cos(4*π*(k+1/2)/N),
// 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.
@@ -286,9 +286,9 @@ func FlatTopComplex(seq []complex128) []complex128 {
a4 = 0.006947368
)
k := 2 * math.Pi / float64(len(seq)-1)
k := 2 * math.Pi / float64(len(seq))
for i := range seq {
x := k * float64(i)
x := k * (float64(i) + 0.5)
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
@@ -301,10 +301,10 @@ func FlatTopComplex(seq []complex128) []complex128 {
// 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,
// w[k] = exp(-0.5 * ((k + 1/2 - M)/(σ*M))² ), M = N/2,
// for k=0,1,...,N-1 where N is the length of the window.
//
// The properties of window depends on the σ (sigma) argument.
// The properties of the window depend on the σ (sigma) argument.
// It can be used as high or low resolution window, depending of the σ value.
//
// Spectral leakage parameters are summarized in the table:
@@ -316,9 +316,9 @@ func FlatTopComplex(seq []complex128) []complex128 {
// ɣ_max | -65 | -31.5 | -15.5 |
// β | -8.52 | -4.48 | -0.96 |
func GaussianComplex(seq []complex128, sigma float64) []complex128 {
a := float64(len(seq)-1) / 2
a := float64(len(seq)) / 2
for i := range seq {
x := -0.5 * math.Pow((float64(i)-a)/(sigma*a), 2)
x := -0.5 * math.Pow(((float64(i)+0.5)-a)/(sigma*a), 2)
seq[i] *= complex(math.Exp(x), 0)
}
return seq