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Revert "dsp/window: use half offset to exclude flanking zeros"

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This reverts efc4dabf2a

The reason for the reversion is confusion caused between different
approaches for window sizing and ease of use.
This commit is contained in:
Dan Kortschak
2020-09-12 19:18:12 +09:30
parent 1839007961
commit 7dc1a8963b
5 changed files with 127 additions and 131 deletions
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5
dsp/window/doc.go
View File

@@ -40,11 +40,6 @@
// //
// The ɣ_max parameter is the maximum level of the side lobes of the // The ɣ_max parameter is the maximum level of the side lobes of the
// normalized spectrum, in decibels. // normalized spectrum, in decibels.
//
// Window interval
//
// The window intervals used in the window functions are offset by a half
// to ensure that the window extends to exclude the flanking zeros.
package window // import "gonum.org/v1/gonum/dsp/window" package window // import "gonum.org/v1/gonum/dsp/window"
// The article at http://www.dsplib.ru/content/win/win.html is the origin // The article at http://www.dsplib.ru/content/win/win.html is the origin

82
dsp/window/window.go
View File

@@ -30,14 +30,14 @@ func Rectangular(seq []float64) []float64 {
// Sine window is a high-resolution window. // Sine window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = sin(π*(k+1/2)/N), // w[k] = sin(π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 { func Sine(seq []float64) []float64 {
k := math.Pi / float64(len(seq)) k := math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
seq[i] *= math.Sin(k * (float64(i) + 0.5)) seq[i] *= math.Sin(k * float64(i))
} }
return seq return seq
} }
@@ -49,14 +49,14 @@ func Sine(seq []float64) []float64 {
// The Lanczos window is a high-resolution window. // The Lanczos window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = sinc(2*(k+1/2)/N - 1), // w[k] = sinc(2*k/(N-1) - 1),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 { func Lanczos(seq []float64) []float64 {
k := 2 / float64(len(seq)) k := 2 / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := math.Pi * (k*(float64(i)+0.5) - 1) x := math.Pi * (k*float64(i) - 1)
if x == 0 { if x == 0 {
// Avoid NaN. // Avoid NaN.
continue continue
@@ -73,14 +73,14 @@ func Lanczos(seq []float64) []float64 {
// The Triangular window is a high-resolution window. // The Triangular window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 1 - |(k + 1/2 - N/2)/(N/2)|, // w[k] = 1 - |k/A -1|, A=(N-1)/2,
// for k=0,1,...,N-1 where N is the length of the window. // 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. // Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -26.5, β = -6.
func Triangular(seq []float64) []float64 { func Triangular(seq []float64) []float64 {
a := float64(len(seq)) / 2 a := float64(len(seq)-1) / 2
for i := range seq { for i := range seq {
seq[i] *= 1 - math.Abs((float64(i)+0.5-a)/a) seq[i] *= 1 - math.Abs(float64(i)/a-1)
} }
return seq return seq
} }
@@ -92,14 +92,14 @@ func Triangular(seq []float64) []float64 {
// The Hann window is a high-resolution window. // The Hann window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.5*(1 - cos(2*π*(k+1/2)/N)), // 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. // 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. // Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.5, K = 2, ɣ_max = -31.5, β = -6.
func Hann(seq []float64) []float64 { func Hann(seq []float64) []float64 {
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
seq[i] *= 0.5 * (1 - math.Cos(k*(float64(i)+0.5))) seq[i] *= 0.5 * (1 - math.Cos(k*float64(i)))
} }
return seq return seq
} }
@@ -111,7 +111,7 @@ func Hann(seq []float64) []float64 {
// The Bartlett-Hann window is a high-resolution window. // The Bartlett-Hann window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.62 - 0.48*|(k+1/2)/N-0.5| - 0.38*cos(2*π*(k+1/2)/N), // 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. // 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. // Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.45, K = 2, ɣ_max = -35.9, β = -6.
@@ -122,9 +122,9 @@ func BartlettHann(seq []float64) []float64 {
a2 = 0.38 a2 = 0.38
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
seq[i] *= a0 - a1*math.Abs((float64(i)+0.5)/float64(len(seq))-0.5) - a2*math.Cos(k*(float64(i)+0.5)) seq[i] *= a0 - a1*math.Abs(float64(i)/float64(len(seq)-1)-0.5) - a2*math.Cos(k*float64(i))
} }
return seq return seq
} }
@@ -137,7 +137,7 @@ func BartlettHann(seq []float64) []float64 {
// the highest ɣ_max. // the highest ɣ_max.
// //
// The sequence weights are // The sequence weights are
// w[k] = 25/46 - 21/46 * cos(2*π*(k+1/2)/N), // 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. // 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. // Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -42, β = -5.37.
@@ -147,9 +147,9 @@ func Hamming(seq []float64) []float64 {
a1 = 1 - a0 a1 = 1 - a0
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
seq[i] *= a0 - a1*math.Cos(k*(float64(i)+0.5)) seq[i] *= a0 - a1*math.Cos(k*float64(i))
} }
return seq return seq
} }
@@ -161,7 +161,7 @@ func Hamming(seq []float64) []float64 {
// The Blackman window is a high-resolution window. // The Blackman window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.42 - 0.5*cos(2*π*(k+1/2)/N) + 0.08*cos(4*π*(k+1/2)/N), // 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. // 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. // Spectral leakage parameters: ΔF_0 = 6, ΔF_0.5 = 1.7, K = 3, ɣ_max = -58, β = -7.54.
@@ -172,9 +172,9 @@ func Blackman(seq []float64) []float64 {
a2 = 0.08 a2 = 0.08
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x)
} }
return seq return seq
@@ -187,8 +187,8 @@ func Blackman(seq []float64) []float64 {
// The Blackman-Harris window is a low-resolution window. // The Blackman-Harris window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.35875 - 0.48829*cos(2*π*(k+1/2)/N) + // w[k] = 0.35875 - 0.48829*cos(2*π*k/(N-1)) +
// 0.14128*cos(4*π*(k+1/2)/N) - 0.01168*cos(6*π*(k+1/2)/N), // 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. // 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. // Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.97, K = 4, ɣ_max = -92, β = -8.91.
@@ -200,9 +200,9 @@ func BlackmanHarris(seq []float64) []float64 {
a3 = 0.01168 a3 = 0.01168
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x)
} }
return seq return seq
@@ -215,8 +215,8 @@ func BlackmanHarris(seq []float64) []float64 {
// The Nuttall window is a low-resolution window. // The Nuttall window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.355768 - 0.487396*cos(2*π*(k+1/2)/N) + 0.144232*cos(4*π*(k+1/2)/N) - // 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+1/2)/N), // 0.012604*cos(6*π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.98, K = 4, ɣ_max = -93, β = -9.
@@ -228,9 +228,9 @@ func Nuttall(seq []float64) []float64 {
a3 = 0.012604 a3 = 0.012604
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x)
} }
return seq return seq
@@ -243,8 +243,8 @@ func Nuttall(seq []float64) []float64 {
// The Blackman-Nuttall window is a low-resolution window. // The Blackman-Nuttall window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.3635819 - 0.4891775*cos(2*π*(k+1/2)/N) + 0.1365995*cos(4*π*(k+1/2)/N) - // 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+1/2)/N), // 0.0106411*cos(6*π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.94, K = 4, ɣ_max = -98, β = -8.8.
@@ -256,9 +256,9 @@ func BlackmanNuttall(seq []float64) []float64 {
a3 = 0.0106411 a3 = 0.0106411
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x)
} }
return seq return seq
@@ -271,9 +271,9 @@ func BlackmanNuttall(seq []float64) []float64 {
// The Flat Top window is a low-resolution window. // The Flat Top window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.21557895 - 0.41663158*cos(2*π*(k+1/2)/(N-1)) + // w[k] = 0.21557895 - 0.41663158*cos(2*π*k/(N-1)) +
// 0.277263158*cos(4*π*(k+1/2)/N) - 0.083578947*cos(6*π*(k+1/2)/N) + // 0.277263158*cos(4*π*k/(N-1)) - 0.083578947*cos(6*π*k/(N-1)) +
// 0.006947368*cos(4*π*(k+1/2)/N), // 0.006947368*cos(4*π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 FlatTop(seq []float64) []float64 {
a4 = 0.006947368 a4 = 0.006947368
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) 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) seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) + a4*math.Cos(4*x)
} }
return seq return seq
@@ -301,7 +301,7 @@ func FlatTop(seq []float64) []float64 {
// The Gaussian window is an adjustable window. // The Gaussian window is an adjustable window.
// //
// The sequence weights are // The sequence weights are
// w[k] = exp(-0.5 * ((k + 1/2 - M)/(σ*M))² ), M = N/2, // 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. // 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). // The properties of the window depend on the value of σ (sigma).
@@ -322,9 +322,9 @@ type Gaussian struct {
// Transform applies the Gaussian transformation to seq in place, using the value // Transform applies the Gaussian transformation to seq in place, using the value
// of the receiver as the sigma parameter, and returning the result. // of the receiver as the sigma parameter, and returning the result.
func (g Gaussian) Transform(seq []float64) []float64 { func (g Gaussian) Transform(seq []float64) []float64 {
a := float64(len(seq)) / 2 a := float64(len(seq)-1) / 2
for i := range seq { for i := range seq {
x := -0.5 * math.Pow(((float64(i)+0.5)-a)/(g.Sigma*a), 2) x := -0.5 * math.Pow((float64(i)-a)/(g.Sigma*a), 2)
seq[i] *= math.Exp(x) seq[i] *= math.Exp(x)
} }
return seq return seq

82
dsp/window/window_complex.go
View File

@@ -30,14 +30,14 @@ func RectangularComplex(seq []complex128) []complex128 {
// Sine window is a high-resolution window. // Sine window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = sin(π*(k+1/2)/N), // w[k] = sin(π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 { func SineComplex(seq []complex128) []complex128 {
k := math.Pi / float64(len(seq)) k := math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
seq[i] *= complex(math.Sin(k*(float64(i)+0.5)), 0) seq[i] *= complex(math.Sin(k*float64(i)), 0)
} }
return seq return seq
} }
@@ -49,14 +49,14 @@ func SineComplex(seq []complex128) []complex128 {
// The Lanczos window is a high-resolution window. // The Lanczos window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = sinc(2*(k+1/2)/N - 1), // w[k] = sinc(2*k/(N-1) - 1),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 { func LanczosComplex(seq []complex128) []complex128 {
k := 2 / float64(len(seq)) k := 2 / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := math.Pi * (k*(float64(i)+0.5) - 1) x := math.Pi * (k*float64(i) - 1)
if x == 0 { if x == 0 {
// Avoid NaN. // Avoid NaN.
continue continue
@@ -73,14 +73,14 @@ func LanczosComplex(seq []complex128) []complex128 {
// The Triangular window is a high-resolution window. // The Triangular window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 1 - |(k + 1/2 - N/2)/(N/2)|, // w[k] = 1 - |k/A -1|, A=(N-1)/2,
// for k=0,1,...,N-1 where N is the length of the window. // 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. // Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -26.5, β = -6.
func TriangularComplex(seq []complex128) []complex128 { func TriangularComplex(seq []complex128) []complex128 {
a := float64(len(seq)) / 2 a := float64(len(seq)-1) / 2
for i := range seq { for i := range seq {
seq[i] *= complex(1-math.Abs((float64(i)+0.5-a)/a), 0) seq[i] *= complex(1-math.Abs(float64(i)/a-1), 0)
} }
return seq return seq
} }
@@ -92,14 +92,14 @@ func TriangularComplex(seq []complex128) []complex128 {
// The Hann window is a high-resolution window. // The Hann window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.5*(1 - cos(2*π*(k+1/2)/N)), // 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. // 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. // Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.5, K = 2, ɣ_max = -31.5, β = -6.
func HannComplex(seq []complex128) []complex128 { func HannComplex(seq []complex128) []complex128 {
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
seq[i] *= complex(0.5*(1-math.Cos(k*(float64(i)+0.5))), 0) seq[i] *= complex(0.5*(1-math.Cos(k*float64(i))), 0)
} }
return seq return seq
} }
@@ -111,7 +111,7 @@ func HannComplex(seq []complex128) []complex128 {
// The Bartlett-Hann window is a high-resolution window. // The Bartlett-Hann window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.62 - 0.48*|(k+1/2)/N-0.5| - 0.38*cos(2*π*(k+1/2)/N), // 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. // 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. // 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 a2 = 0.38
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
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) seq[i] *= complex(a0-a1*math.Abs(float64(i)/float64(len(seq)-1)-0.5)-a2*math.Cos(k*float64(i)), 0)
} }
return seq return seq
} }
@@ -137,7 +137,7 @@ func BartlettHannComplex(seq []complex128) []complex128 {
// the highest ɣ_max. // the highest ɣ_max.
// //
// The sequence weights are // The sequence weights are
// w[k] = 25/46 - 21/46 * cos(2*π*(k+1/2)/N), // 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. // 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. // 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 a1 = 1 - a0
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
seq[i] *= complex(a0-a1*math.Cos(k*(float64(i)+0.5)), 0) seq[i] *= complex(a0-a1*math.Cos(k*float64(i)), 0)
} }
return seq return seq
} }
@@ -161,7 +161,7 @@ func HammingComplex(seq []complex128) []complex128 {
// The Blackman window is a high-resolution window. // The Blackman window is a high-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.42 - 0.5*cos(2*π*(k+1/2)/N) + 0.08*cos(4*π*(k+1/2)/N), // 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. // 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. // 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 a2 = 0.08
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x), 0) seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x), 0)
} }
return seq return seq
@@ -187,8 +187,8 @@ func BlackmanComplex(seq []complex128) []complex128 {
// The Blackman-Harris window is a low-resolution window. // The Blackman-Harris window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.35875 - 0.48829*cos(2*π*(k+1/2)/N) + // w[k] = 0.35875 - 0.48829*cos(2*π*k/(N-1)) +
// 0.14128*cos(4*π*(k+1/2)/N) - 0.01168*cos(6*π*(k+1/2)/N), // 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. // 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. // 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 a3 = 0.01168
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0) seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
} }
return seq return seq
@@ -215,8 +215,8 @@ func BlackmanHarrisComplex(seq []complex128) []complex128 {
// The Nuttall window is a low-resolution window. // The Nuttall window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.355768 - 0.487396*cos(2*π*(k+1/2)/N) + 0.144232*cos(4*π*(k+1/2)/N) - // 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+1/2)/N), // 0.012604*cos(6*π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 a3 = 0.012604
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0) seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
} }
return seq return seq
@@ -243,8 +243,8 @@ func NuttallComplex(seq []complex128) []complex128 {
// The Blackman-Nuttall window is a low-resolution window. // The Blackman-Nuttall window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.3635819 - 0.4891775*cos(2*π*(k+1/2)/N) + 0.1365995*cos(4*π*(k+1/2)/N) - // 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+1/2)/N), // 0.0106411*cos(6*π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 a3 = 0.0106411
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) x := k * float64(i)
seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0) seq[i] *= complex(a0-a1*math.Cos(x)+a2*math.Cos(2*x)-a3*math.Cos(3*x), 0)
} }
return seq return seq
@@ -271,9 +271,9 @@ func BlackmanNuttallComplex(seq []complex128) []complex128 {
// The Flat Top window is a low-resolution window. // The Flat Top window is a low-resolution window.
// //
// The sequence weights are // The sequence weights are
// w[k] = 0.21557895 - 0.41663158*cos(2*π*(k+1/2)/(N-1)) + // w[k] = 0.21557895 - 0.41663158*cos(2*π*k/(N-1)) +
// 0.277263158*cos(4*π*(k+1/2)/N) - 0.083578947*cos(6*π*(k+1/2)/N) + // 0.277263158*cos(4*π*k/(N-1)) - 0.083578947*cos(6*π*k/(N-1)) +
// 0.006947368*cos(4*π*(k+1/2)/N), // 0.006947368*cos(4*π*k/(N-1)),
// for k=0,1,...,N-1 where N is the length of the window. // 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. // 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 a4 = 0.006947368
) )
k := 2 * math.Pi / float64(len(seq)) k := 2 * math.Pi / float64(len(seq)-1)
for i := range seq { for i := range seq {
x := k * (float64(i) + 0.5) 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) 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 return seq
@@ -301,7 +301,7 @@ func FlatTopComplex(seq []complex128) []complex128 {
// The Gaussian window is an adjustable window. // The Gaussian window is an adjustable window.
// //
// The sequence weights are // The sequence weights are
// w[k] = exp(-0.5 * ((k + 1/2 - M)/(σ*M))² ), M = N/2, // 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. // 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). // The properties of the window depend on the value of σ (sigma).
@@ -322,9 +322,9 @@ type GaussianComplex struct {
// Transform applies the Gaussian transformation to seq in place, using the value // Transform applies the Gaussian transformation to seq in place, using the value
// of the receiver as the sigma parameter, and returning the result. // of the receiver as the sigma parameter, and returning the result.
func (g GaussianComplex) Transform(seq []complex128) []complex128 { func (g GaussianComplex) Transform(seq []complex128) []complex128 {
a := float64(len(seq)) / 2 a := float64(len(seq)-1) / 2
for i := range seq { for i := range seq {
x := -0.5 * math.Pow(((float64(i)+0.5)-a)/(g.Sigma*a), 2) x := -0.5 * math.Pow((float64(i)-a)/(g.Sigma*a), 2)
seq[i] *= complex(math.Exp(x), 0) seq[i] *= complex(math.Exp(x), 0)
} }
return seq return seq

26
dsp/window/window_example_test.go
View File

@@ -67,16 +67,16 @@ func Example() {
// freq=0.4500 cycles/period, magnitude=0.0707, phase=-1.7279 // freq=0.4500 cycles/period, magnitude=0.0707, phase=-1.7279
// freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000 // freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000
// Hamming window: // Hamming window:
// freq=0.0000 cycles/period, magnitude=0.0506, phase=0.0000 // freq=0.0000 cycles/period, magnitude=0.0218, phase=3.1416
// freq=0.0500 cycles/period, magnitude=0.5386, phase=-2.9845 // freq=0.0500 cycles/period, magnitude=0.8022, phase=-2.9845
// freq=0.1000 cycles/period, magnitude=7.3350, phase=0.3142 // freq=0.1000 cycles/period, magnitude=7.1723, phase=0.3142
// freq=0.1500 cycles/period, magnitude=8.9523, phase=-2.6704 // freq=0.1500 cycles/period, magnitude=8.6285, phase=-2.6704
// freq=0.2000 cycles/period, magnitude=1.7979, phase=0.6283 // freq=0.2000 cycles/period, magnitude=2.0420, phase=0.6283
// freq=0.2500 cycles/period, magnitude=0.0957, phase=0.7854 // freq=0.2500 cycles/period, magnitude=0.0702, phase=0.7854
// freq=0.3000 cycles/period, magnitude=0.0050, phase=-2.1991 // freq=0.3000 cycles/period, magnitude=0.0217, phase=-2.1991
// freq=0.3500 cycles/period, magnitude=0.0158, phase=-2.0420 // freq=0.3500 cycles/period, magnitude=0.0259, phase=-2.0420
// freq=0.4000 cycles/period, magnitude=0.0125, phase=-1.8850 // freq=0.4000 cycles/period, magnitude=0.0184, phase=-1.8850
// freq=0.4500 cycles/period, magnitude=0.0065, phase=-1.7279 // freq=0.4500 cycles/period, magnitude=0.0092, phase=-1.7279
// freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000 // freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000
} }
@@ -100,8 +100,8 @@ func ExampleHamming() {
// Output: // 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] // 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: [0.092577 0.136714 0.220669 0.336222 0.472063 0.614894 0.750735 0.866288 0.950242 0.994379 0.994379 0.950242 0.866288 0.750735 0.614894 0.472063 0.336222 0.220669 0.136714 0.092577] // srcCpy: [0.086957 0.111692 0.183218 0.293785 0.431409 0.581178 0.726861 0.852672 0.944977 0.993774 0.993774 0.944977 0.852672 0.726861 0.581178 0.431409 0.293785 0.183218 0.111692 0.086957]
// dst: [0.092577 0.136714 0.220669 0.336222 0.472063 0.614894 0.750735 0.866288 0.950242 0.994379 0.994379 0.950242 0.866288 0.750735 0.614894 0.472063 0.336222 0.220669 0.136714 0.092577] // dst: [0.086957 0.111692 0.183218 0.293785 0.431409 0.581178 0.726861 0.852672 0.944977 0.993774 0.993774 0.944977 0.852672 0.726861 0.581178 0.431409 0.293785 0.183218 0.111692 0.086957]
} }
func ExampleValues() { func ExampleValues() {
@@ -116,5 +116,5 @@ func ExampleValues() {
// Output: // Output:
// //
// dst: [0.078459 0.233445 0.382683 0.522499 0.649448 0.760406 0.852640 0.923880 0.972370 0.996917 0.996917 0.972370 0.923880 0.852640 0.760406 0.649448 0.522499 0.382683 0.233445 0.078459] // 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]
} }

63
dsp/window/window_test.go
View File

@@ -28,87 +28,87 @@ var windowTests = []struct {
{ {
name: "Sine", fn: Sine, fnCmplx: SineComplex, name: "Sine", fn: Sine, fnCmplx: SineComplex,
want: []float64{ want: []float64{
0.078459, 0.233445, 0.382683, 0.522499, 0.649448, 0.760406, 0.852640, 0.923880, 0.972370, 0.996917, 0.000000, 0.164595, 0.324699, 0.475947, 0.614213, 0.735724, 0.837166, 0.915773, 0.969400, 0.996584,
0.996917, 0.972370, 0.923880, 0.852640, 0.760406, 0.649448, 0.522499, 0.382683, 0.233445, 0.078459, 0.996584, 0.969400, 0.915773, 0.837166, 0.735724, 0.614213, 0.475947, 0.324699, 0.164595, 0.000000,
}, },
}, },
{ {
name: "Lanczos", fn: Lanczos, fnCmplx: LanczosComplex, name: "Lanczos", fn: Lanczos, fnCmplx: LanczosComplex,
want: []float64{ want: []float64{
0.052415, 0.170011, 0.300105, 0.436333, 0.57162, 0.698647, 0.810332, 0.900316, 0.963398, 0.995893, 0.000000, 0.115514, 0.247646, 0.389468, 0.532984, 0.669692, 0.791213, 0.889915, 0.959492, 0.995450,
0.995893, 0.963398, 0.900316, 0.810332, 0.698647, 0.57162, 0.436333, 0.300105, 0.170011, 0.052415, 0.995450, 0.959492, 0.889915, 0.791213, 0.669692, 0.532984, 0.389468, 0.247646, 0.115514, 0.000000,
}, },
}, },
// This case tests Lanczos for a NaN condition. The Lanczos NaN condition is k=(N-1)/2, that is when N is odd. // This case tests Lanczos for a NaN condition. The Lanczos NaN condition is k=(N-1)/2, that is when N is odd.
{ {
name: "LanczosOdd", fn: Lanczos, fnCmplx: LanczosComplex, name: "LanczosOdd", fn: Lanczos, fnCmplx: LanczosComplex,
want: []float64{ want: []float64{
0.049813, 0.161128, 0.284164, 0.413497, 0.543076, 0.666582, 0.777804, 0.871026, 0.941379, 0.985147, 0.000000, 0.109292, 0.233872, 0.367883, 0.504551, 0.636620, 0.756827, 0.858394, 0.935489, 0.983632,
1, 1.000000,
0.985147, 0.941379, 0.871026, 0.777804, 0.666582, 0.543076, 0.413497, 0.284164, 0.161128, 0.049813, 0.983632, 0.935489, 0.858394, 0.756827, 0.636620, 0.504551, 0.367883, 0.233872, 0.109292, 0.000000,
}, },
}, },
{ {
name: "Triangular", fn: Triangular, fnCmplx: TriangularComplex, name: "Triangular", fn: Triangular, fnCmplx: TriangularComplex,
want: []float64{ want: []float64{
0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, 0.000000, 0.105263, 0.210526, 0.315789, 0.421053, 0.526316, 0.631579, 0.736842, 0.842105, 0.947368,
0.95, 0.85, 0.75, 0.65, 0.55, 0.45, 0.35, 0.25, 0.15, 0.05, 0.947368, 0.842105, 0.736842, 0.631579, 0.526316, 0.421053, 0.315789, 0.210526, 0.105263, 0.000000,
}, },
}, },
{ {
name: "Hann", fn: Hann, fnCmplx: HannComplex, name: "Hann", fn: Hann, fnCmplx: HannComplex,
want: []float64{ want: []float64{
0.006155, 0.054496, 0.146447, 0.273005, 0.421783, 0.578217, 0.726995, 0.853553, 0.945503, 0.993844, 0.000000, 0.027091, 0.105430, 0.226526, 0.377257, 0.541290, 0.700848, 0.838641, 0.939737, 0.993181,
0.993844, 0.945503, 0.853553, 0.726995, 0.578217, 0.421783, 0.273005, 0.146447, 0.054496, 0.006155, 0.993181, 0.939737, 0.838641, 0.700848, 0.541290, 0.377257, 0.226526, 0.105430, 0.027091, 0.000000,
}, },
}, },
{ {
name: "BartlettHann", fn: BartlettHann, fnCmplx: BartlettHannComplex, name: "BartlettHann", fn: BartlettHann, fnCmplx: BartlettHannComplex,
want: []float64{ want: []float64{
0.016678, 0.077417, 0.171299, 0.291484, 0.428555, 0.571445, 0.708516, 0.828701, 0.922582, 0.983322, 0.000000, 0.045853, 0.130653, 0.247949, 0.387768, 0.537696, 0.684223, 0.814209, 0.916305, 0.982186,
0.983322, 0.922582, 0.828701, 0.708516, 0.571445, 0.428555, 0.291484, 0.171299, 0.077417, 0.016678, 0.982186, 0.916305, 0.814209, 0.684223, 0.537696, 0.387768, 0.247949, 0.130653, 0.045853, 0.000000,
}, },
}, },
{ {
name: "Hamming", fn: Hamming, fnCmplx: HammingComplex, name: "Hamming", fn: Hamming, fnCmplx: HammingComplex,
want: []float64{ want: []float64{
0.092577, 0.136714, 0.220669, 0.336222, 0.472063, 0.614894, 0.750735, 0.866288, 0.950242, 0.994379, 0.086957, 0.111692, 0.183218, 0.293785, 0.431408, 0.581178, 0.726861, 0.852672, 0.944977, 0.993774,
0.994379, 0.950242, 0.866288, 0.750735, 0.614894, 0.472063, 0.336222, 0.220669, 0.136714, 0.092577, 0.993774, 0.944977, 0.852672, 0.726861, 0.581178, 0.431409, 0.293785, 0.183218, 0.111692, 0.086957,
}, },
}, },
{ {
name: "Blackman", fn: Blackman, fnCmplx: BlackmanComplex, name: "Blackman", fn: Blackman, fnCmplx: BlackmanComplex,
want: []float64{ want: []float64{
0.002240, 0.021519, 0.066446, 0.145982, 0.265698, 0.422133, 0.599972, 0.773553, 0.912526, 0.989929, 0.000000, 0.010223, 0.045069, 0.114390, 0.226899, 0.382381, 0.566665, 0.752034, 0.903493, 0.988846,
0.989929, 0.912526, 0.773553, 0.599972, 0.422133, 0.265698, 0.145982, 0.066446, 0.021519, 0.002240, 0.988846, 0.903493, 0.752034, 0.566665, 0.382381, 0.226899, 0.114390, 0.045069, 0.010223, 0.000000,
}, },
}, },
{ {
name: "BlackmanHarris", fn: BlackmanHarris, fnCmplx: BlackmanHarrisComplex, name: "BlackmanHarris", fn: BlackmanHarris, fnCmplx: BlackmanHarrisComplex,
want: []float64{ want: []float64{
0.000429, 0.004895, 0.021735, 0.065564, 0.153302, 0.295468, 0.485851, 0.695764, 0.878689, 0.985801, 0.000060, 0.002018, 0.012795, 0.046450, 0.122540, 0.256852, 0.448160, 0.668576, 0.866426, 0.984278,
0.985801, 0.878689, 0.695764, 0.485851, 0.295468, 0.153302, 0.065564, 0.021735, 0.004895, 0.000429, 0.984278, 0.866426, 0.668576, 0.448160, 0.256852, 0.122540, 0.046450, 0.012795, 0.002018, 0.000060,
}, },
}, },
{ {
name: "Nuttall", fn: Nuttall, fnCmplx: NuttallComplex, name: "Nuttall", fn: Nuttall, fnCmplx: NuttallComplex,
want: []float64{ want: []float64{
0.000315, 0.004300, 0.020039, 0.062166, 0.148072, 0.289119, 0.479815, 0.691497, 0.876790, 0.985566, 0.000000, 0.001706, 0.011614, 0.043682, 0.117808, 0.250658, 0.441946, 0.664015, 0.864348, 0.984019,
0.985566, 0.876790, 0.691497, 0.479815, 0.289119, 0.148072, 0.062166, 0.020039, 0.004300, 0.000315, 0.984019, 0.864348, 0.664015, 0.441946, 0.250658, 0.117808, 0.043682, 0.011614, 0.001706, 0.000000,
}, },
}, },
{ {
name: "BlackmanNuttall", fn: BlackmanNuttall, fnCmplx: BlackmanNuttallComplex, name: "BlackmanNuttall", fn: BlackmanNuttall, fnCmplx: BlackmanNuttallComplex,
want: []float64{ want: []float64{
0.000859, 0.006348, 0.025205, 0.071718, 0.161975, 0.305361, 0.494863, 0.701958, 0.881398, 0.986132, 0.000363, 0.002885, 0.015360, 0.051652, 0.130567, 0.266629, 0.457501, 0.675215, 0.869392, 0.984644,
0.986132, 0.881398, 0.701958, 0.494863, 0.305361, 0.161975, 0.071718, 0.025205, 0.006348, 0.000859, 0.984644, 0.869392, 0.675215, 0.457501, 0.266629, 0.130567, 0.051652, 0.015360, 0.002885, 0.000363,
}, },
}, },
{ {
name: "FlatTop", fn: FlatTop, fnCmplx: FlatTopComplex, name: "FlatTop", fn: FlatTop, fnCmplx: FlatTopComplex,
want: []float64{ want: []float64{
-0.001079, -0.007892, -0.026872, -0.056135, -0.069724, -0.015262, 0.157058, 0.444135, 0.760699, 0.970864, -0.000421, -0.003687, -0.017675, -0.045939, -0.070137, -0.037444, 0.115529, 0.402051, 0.737755, 0.967756,
0.970864, 0.760699, 0.444135, 0.157058, -0.015262, -0.069724, -0.056135, -0.026872, -0.007892, -0.001079, 0.967756, 0.737755, 0.402051, 0.115529, -0.037444, -0.070137, -0.045939, -0.017675, -0.003687, -0.000421,
}, },
}, },
} }
@@ -121,21 +121,22 @@ var gausWindowTests = []struct {
{ {
name: "Gaussian", sigma: 0.3, name: "Gaussian", sigma: 0.3,
want: []float64{ want: []float64{
0.006645, 0.018063, 0.043936, 0.095634, 0.186270, 0.324652, 0.506336, 0.706648, 0.882497, 0.986207, 0.003866, 0.011708, 0.031348, 0.074214, 0.155344, 0.287499, 0.470444, 0.680632, 0.870660, 0.984728,
0.986207, 0.882497, 0.706648, 0.506336, 0.324652, 0.186270, 0.095634, 0.043936, 0.018063, 0.006645}, 0.984728, 0.870660, 0.680632, 0.470444, 0.287499, 0.155344, 0.074214, 0.031348, 0.011708, 0.003866,
},
}, },
{ {
name: "Gaussian", sigma: 0.5, name: "Gaussian", sigma: 0.5,
want: []float64{ want: []float64{
0.164474, 0.235746, 0.324652, 0.429557, 0.546074, 0.666977, 0.782705, 0.882497, 0.955997, 0.995012, 0.135335, 0.201673, 0.287499, 0.392081, 0.511524, 0.638423, 0.762260, 0.870660, 0.951361, 0.994475,
0.995012, 0.955997, 0.882497, 0.782705, 0.666977, 0.546074, 0.429557, 0.324652, 0.235746, 0.164474, 0.994475, 0.951361, 0.870660, 0.762260, 0.638423, 0.511524, 0.392081, 0.287499, 0.201673, 0.135335,
}, },
}, },
{ {
name: "Gaussian", sigma: 1.2, name: "Gaussian", sigma: 1.2,
want: []float64{ want: []float64{
0.730981, 0.778125, 0.822578, 0.863552, 0.900293, 0.932102, 0.958357, 0.978532, 0.992218, 0.999132, 0.706648, 0.757319, 0.805403, 0.849974, 0.890135, 0.925049, 0.953963, 0.976241, 0.991381, 0.999039,
0.999132, 0.992218, 0.978532, 0.958357, 0.932102, 0.900293, 0.863552, 0.822578, 0.778125, 0.730981, 0.999039, 0.991381, 0.976241, 0.953963, 0.925049, 0.890135, 0.849974, 0.805403, 0.757319, 0.706648,
}, },
}, },
} }