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dsp/window: use half offset to exclude flanking zeros
This commit is contained in:
Dan Kortschak
@@ -40,4 +40,9 @@
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//
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// The ɣ_max parameter is the maximum level of the side lobes of the
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// normalized spectrum, in decibels.
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//
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// Window interval
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//
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// The window intervals used in the window functions are offset by a half
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// to ensure that the window extends to exclude the flanking zeros.
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package window // import "gonum.org/v1/gonum/dsp/window"
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@@ -30,14 +30,14 @@ func Rectangular(seq []float64) []float64 {
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// Sine window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = sin(π*k/(N-1)),
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// w[k] = sin(π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 3, ΔF_0.5 = 1.23, K = 1.5, ɣ_max = -23, β = -3.93.
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func Sine(seq []float64) []float64 {
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k := math.Pi / float64(len(seq)-1)
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k := math.Pi / float64(len(seq))
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for i := range seq {
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seq[i] *= math.Sin(k * float64(i))
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seq[i] *= math.Sin(k * (float64(i) + 0.5))
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}
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return seq
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}
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@@ -49,14 +49,14 @@ func Sine(seq []float64) []float64 {
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// The Lanczos window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = sinc(2*k/(N-1) - 1),
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// w[k] = sinc(2*(k+1/2)/N - 1),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 3.24, ΔF_0.5 = 1.3, K = 1.62, ɣ_max = -26.4, β = -4.6.
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func Lanczos(seq []float64) []float64 {
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k := 2 / float64(len(seq)-1)
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k := 2 / float64(len(seq))
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for i := range seq {
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x := math.Pi * (k*float64(i) - 1)
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x := math.Pi * (k*(float64(i)+0.5) - 1)
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if x == 0 {
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// Avoid NaN.
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continue
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@@ -73,14 +73,14 @@ func Lanczos(seq []float64) []float64 {
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// The Triangular window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = 1 - |k/A -1|, A=(N-1)/2,
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// w[k] = 1 - |(k + 1/2 - N/2)/(N/2)|,
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -26.5, β = -6.
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func Triangular(seq []float64) []float64 {
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a := float64(len(seq)-1) / 2
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a := float64(len(seq)) / 2
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for i := range seq {
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seq[i] *= 1 - math.Abs(float64(i)/a-1)
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seq[i] *= 1 - math.Abs((float64(i)+0.5-a)/a)
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}
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return seq
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}
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@@ -92,14 +92,14 @@ func Triangular(seq []float64) []float64 {
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// The Hann window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = 0.5*(1 - cos(2*π*k/(N-1))),
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// w[k] = 0.5*(1 - cos(2*π*(k+1/2)/N)),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.5, K = 2, ɣ_max = -31.5, β = -6.
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func Hann(seq []float64) []float64 {
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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seq[i] *= 0.5 * (1 - math.Cos(k*float64(i)))
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seq[i] *= 0.5 * (1 - math.Cos(k*(float64(i)+0.5)))
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}
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return seq
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}
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@@ -111,7 +111,7 @@ func Hann(seq []float64) []float64 {
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// The Bartlett-Hann window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = 0.62 - 0.48*|k/(N-1)-0.5| - 0.38*cos(2*π*k/(N-1)),
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// w[k] = 0.62 - 0.48*|(k+1/2)/N-0.5| - 0.38*cos(2*π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.45, K = 2, ɣ_max = -35.9, β = -6.
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@@ -122,9 +122,9 @@ func BartlettHann(seq []float64) []float64 {
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a2 = 0.38
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)
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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seq[i] *= a0 - a1*math.Abs(float64(i)/float64(len(seq)-1)-0.5) - a2*math.Cos(k*float64(i))
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seq[i] *= a0 - a1*math.Abs((float64(i)+0.5)/float64(len(seq))-0.5) - a2*math.Cos(k*(float64(i)+0.5))
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}
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return seq
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}
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@@ -137,7 +137,7 @@ func BartlettHann(seq []float64) []float64 {
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// the highest ɣ_max.
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//
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// The sequence weights are
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// w[k] = 25/46 - 21/46 * cos(2*π*k/(N-1)),
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// w[k] = 25/46 - 21/46 * cos(2*π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -42, β = -5.37.
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@@ -147,9 +147,9 @@ func Hamming(seq []float64) []float64 {
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a1 = 1 - a0
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)
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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seq[i] *= a0 - a1*math.Cos(k*float64(i))
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seq[i] *= a0 - a1*math.Cos(k*(float64(i)+0.5))
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}
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return seq
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}
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@@ -161,7 +161,7 @@ func Hamming(seq []float64) []float64 {
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// The Blackman window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = 0.42 - 0.5*cos(2*π*k/(N-1)) + 0.08*cos(4*π*k/(N-1)),
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// w[k] = 0.42 - 0.5*cos(2*π*(k+1/2)/N) + 0.08*cos(4*π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 6, ΔF_0.5 = 1.7, K = 3, ɣ_max = -58, β = -7.54.
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@@ -172,9 +172,9 @@ func Blackman(seq []float64) []float64 {
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a2 = 0.08
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)
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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x := k * float64(i)
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x := k * (float64(i) + 0.5)
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seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x)
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}
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return seq
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@@ -187,8 +187,8 @@ func Blackman(seq []float64) []float64 {
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// The Blackman-Harris window is a low-resolution window.
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//
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// The sequence weights are
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// w[k] = 0.35875 - 0.48829*cos(2*π*k/(N-1)) +
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// 0.14128*cos(4*π*k/(N-1)) - 0.01168*cos(6*π*k/(N-1)),
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// w[k] = 0.35875 - 0.48829*cos(2*π*(k+1/2)/N) +
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// 0.14128*cos(4*π*(k+1/2)/N) - 0.01168*cos(6*π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.97, K = 4, ɣ_max = -92, β = -8.91.
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@@ -200,9 +200,9 @@ func BlackmanHarris(seq []float64) []float64 {
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a3 = 0.01168
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)
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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x := k * float64(i)
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x := k * (float64(i) + 0.5)
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seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x)
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}
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return seq
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@@ -215,8 +215,8 @@ func BlackmanHarris(seq []float64) []float64 {
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// The Nuttall window is a low-resolution window.
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//
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// The sequence weights are
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// w[k] = 0.355768 - 0.487396*cos(2*π*k/(N-1)) + 0.144232*cos(4*π*k/(N-1)) -
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// 0.012604*cos(6*π*k/(N-1)),
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// w[k] = 0.355768 - 0.487396*cos(2*π*(k+1/2)/N) + 0.144232*cos(4*π*(k+1/2)/N) -
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// 0.012604*cos(6*π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.98, K = 4, ɣ_max = -93, β = -9.
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@@ -228,9 +228,9 @@ func Nuttall(seq []float64) []float64 {
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a3 = 0.012604
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)
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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x := k * float64(i)
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x := k * (float64(i) + 0.5)
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seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x)
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}
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return seq
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@@ -243,8 +243,8 @@ func Nuttall(seq []float64) []float64 {
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// The Blackman-Nuttall window is a low-resolution window.
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//
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// The sequence weights are
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// w[k] = 0.3635819 - 0.4891775*cos(2*π*k/(N-1)) + 0.1365995*cos(4*π*k/(N-1)) -
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// 0.0106411*cos(6*π*k/(N-1)),
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// w[k] = 0.3635819 - 0.4891775*cos(2*π*(k+1/2)/N) + 0.1365995*cos(4*π*(k+1/2)/N) -
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// 0.0106411*cos(6*π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 8, ΔF_0.5 = 1.94, K = 4, ɣ_max = -98, β = -8.8.
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@@ -256,9 +256,9 @@ func BlackmanNuttall(seq []float64) []float64 {
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a3 = 0.0106411
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)
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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x := k * float64(i)
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x := k * (float64(i) + 0.5)
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seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x)
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}
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return seq
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@@ -271,9 +271,9 @@ func BlackmanNuttall(seq []float64) []float64 {
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// The Flat Top window is a low-resolution window.
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//
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// The sequence weights are
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// w[k] = 0.21557895 - 0.41663158*cos(2*π*k/(N-1)) +
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// 0.277263158*cos(4*π*k/(N-1)) - 0.083578947*cos(6*π*k/(N-1)) +
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// 0.006947368*cos(4*π*k/(N-1)),
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// w[k] = 0.21557895 - 0.41663158*cos(2*π*(k+1/2)/(N-1)) +
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// 0.277263158*cos(4*π*(k+1/2)/N) - 0.083578947*cos(6*π*(k+1/2)/N) +
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// 0.006947368*cos(4*π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 10, ΔF_0.5 = 3.72, K = 5, ɣ_max = -93.0, β = -13.34.
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@@ -286,9 +286,9 @@ func FlatTop(seq []float64) []float64 {
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a4 = 0.006947368
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)
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k := 2 * math.Pi / float64(len(seq)-1)
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k := 2 * math.Pi / float64(len(seq))
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for i := range seq {
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x := k * float64(i)
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x := k * (float64(i) + 0.5)
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seq[i] *= a0 - a1*math.Cos(x) + a2*math.Cos(2*x) - a3*math.Cos(3*x) + a4*math.Cos(4*x)
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}
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return seq
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@@ -301,10 +301,10 @@ func FlatTop(seq []float64) []float64 {
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// The Gaussian window is an adjustable window.
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//
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// The sequence weights are
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// w[k] = exp(-0.5 * ((k-M)/(σ*M))² ), M = (N-1)/2,
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// w[k] = exp(-0.5 * ((k + 1/2 - M)/(σ*M))² ), M = N/2,
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// The properties of window depends on the σ (sigma) argument.
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// The properties of the window depend on the σ (sigma) argument.
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// It can be used as high or low resolution window, depending of the σ value.
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//
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// Spectral leakage parameters are summarized in the table:
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@@ -316,9 +316,9 @@ func FlatTop(seq []float64) []float64 {
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// ɣ_max | -65 | -31.5 | -15.5 |
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// β | -8.52 | -4.48 | -0.96 |
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func Gaussian(seq []float64, sigma float64) []float64 {
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a := float64(len(seq)-1) / 2
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a := float64(len(seq)) / 2
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for i := range seq {
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x := -0.5 * math.Pow((float64(i)-a)/(sigma*a), 2)
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x := -0.5 * math.Pow(((float64(i)+0.5)-a)/(sigma*a), 2)
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seq[i] *= math.Exp(x)
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}
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return seq
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@@ -30,14 +30,14 @@ func RectangularComplex(seq []complex128) []complex128 {
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// Sine window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = sin(π*k/(N-1)),
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// w[k] = sin(π*(k+1/2)/N),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 3, ΔF_0.5 = 1.23, K = 1.5, ɣ_max = -23, β = -3.93.
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func SineComplex(seq []complex128) []complex128 {
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k := math.Pi / float64(len(seq)-1)
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k := math.Pi / float64(len(seq))
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for i := range seq {
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seq[i] *= complex(math.Sin(k*float64(i)), 0)
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seq[i] *= complex(math.Sin(k*(float64(i)+0.5)), 0)
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}
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return seq
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}
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@@ -49,14 +49,14 @@ func SineComplex(seq []complex128) []complex128 {
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// The Lanczos window is a high-resolution window.
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//
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// The sequence weights are
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// w[k] = sinc(2*k/(N-1) - 1),
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// w[k] = sinc(2*(k+1/2)/N - 1),
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 3.24, ΔF_0.5 = 1.3, K = 1.62, ɣ_max = -26.4, β = -4.6.
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func LanczosComplex(seq []complex128) []complex128 {
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k := 2 / float64(len(seq)-1)
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k := 2 / float64(len(seq))
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for i := range seq {
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x := math.Pi * (k*float64(i) - 1)
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x := math.Pi * (k*(float64(i)+0.5) - 1)
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if x == 0 {
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// Avoid NaN.
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continue
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@@ -73,14 +73,14 @@ func LanczosComplex(seq []complex128) []complex128 {
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// The Triangular window is a high-resolution window.
|
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//
|
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// The sequence weights are
|
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// w[k] = 1 - |k/A -1|, A=(N-1)/2,
|
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// w[k] = 1 - |(k + 1/2 - N/2)/(N/2)|,
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// for k=0,1,...,N-1 where N is the length of the window.
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//
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// Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.33, K = 2, ɣ_max = -26.5, β = -6.
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func TriangularComplex(seq []complex128) []complex128 {
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a := float64(len(seq)-1) / 2
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a := float64(len(seq)) / 2
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for i := range seq {
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seq[i] *= complex(1-math.Abs(float64(i)/a-1), 0)
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seq[i] *= complex(1-math.Abs((float64(i)+0.5-a)/a), 0)
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}
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return seq
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}
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@@ -92,14 +92,14 @@ func TriangularComplex(seq []complex128) []complex128 {
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// The Hann window is a high-resolution window.
|
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//
|
||||
// The sequence weights are
|
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// 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.
|
||||
//
|
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// Spectral leakage parameters: ΔF_0 = 4, ΔF_0.5 = 1.5, K = 2, ɣ_max = -31.5, β = -6.
|
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func HannComplex(seq []complex128) []complex128 {
|
||||
k := 2 * math.Pi / float64(len(seq)-1)
|
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k := 2 * math.Pi / float64(len(seq))
|
||||
for i := range seq {
|
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seq[i] *= complex(0.5*(1-math.Cos(k*float64(i))), 0)
|
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seq[i] *= complex(0.5*(1-math.Cos(k*(float64(i)+0.5))), 0)
|
||||
}
|
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return seq
|
||||
}
|
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@@ -111,7 +111,7 @@ func HannComplex(seq []complex128) []complex128 {
|
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// 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
|
||||
|
||||
@@ -1,167 +0,0 @@
|
||||
// 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 (
|
||||
"testing"
|
||||
|
||||
"gonum.org/v1/gonum/floats"
|
||||
)
|
||||
|
||||
// want the same value in imag part as in real part,
|
||||
// so use one float64 for both
|
||||
var complexWindowTests = []struct {
|
||||
name string
|
||||
fn func([]complex128) []complex128
|
||||
want []float64
|
||||
winLen int
|
||||
}{
|
||||
{
|
||||
name: "RectangularComplex", fn: RectangularComplex, winLen: 20,
|
||||
want: []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
||||
1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
|
||||
},
|
||||
{
|
||||
name: "SineComplex", fn: SineComplex, winLen: 20,
|
||||
want: []float64{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},
|
||||
},
|
||||
{
|
||||
name: "LanczosComplex", fn: LanczosComplex, winLen: 20,
|
||||
want: []float64{0.000000, 0.115514, 0.247646, 0.389468, 0.532984, 0.669692, 0.791213, 0.889915, 0.959492, 0.995450,
|
||||
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.
|
||||
{
|
||||
name: "LanczosComplexOdd", fn: LanczosComplex, winLen: 21,
|
||||
want: []float64{0.000000, 0.109292, 0.233872, 0.367883, 0.504551, 0.636620, 0.756827, 0.858394, 0.935489, 0.983632,
|
||||
1.000000, 0.983632, 0.935489, 0.858394, 0.756827, 0.636620, 0.504551, 0.367883, 0.233872, 0.109292, 0.000000},
|
||||
},
|
||||
{
|
||||
name: "TriangularComplex", fn: TriangularComplex, winLen: 20,
|
||||
want: []float64{0.000000, 0.105263, 0.210526, 0.315789, 0.421053, 0.526316, 0.631579, 0.736842, 0.842105, 0.947368,
|
||||
0.947368, 0.842105, 0.736842, 0.631579, 0.526316, 0.421053, 0.315789, 0.210526, 0.105263, 0.000000},
|
||||
},
|
||||
{
|
||||
name: "HannComplex", fn: HannComplex, winLen: 20,
|
||||
want: []float64{0.000000, 0.027091, 0.105430, 0.226526, 0.377257, 0.541290, 0.700848, 0.838641, 0.939737, 0.993181,
|
||||
0.993181, 0.939737, 0.838641, 0.700848, 0.541290, 0.377257, 0.226526, 0.105430, 0.027091, 0.000000},
|
||||
},
|
||||
{
|
||||
name: "BartlettHannComplex", fn: BartlettHannComplex, winLen: 20,
|
||||
want: []float64{0.000000, 0.045853, 0.130653, 0.247949, 0.387768, 0.537696, 0.684223, 0.814209, 0.916305, 0.982186,
|
||||
0.982186, 0.916305, 0.814209, 0.684223, 0.537696, 0.387768, 0.247949, 0.130653, 0.045853, 0.000000},
|
||||
},
|
||||
{
|
||||
name: "HammingComplex", fn: HammingComplex, winLen: 20,
|
||||
want: []float64{0.086957, 0.111692, 0.183218, 0.293785, 0.431408, 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},
|
||||
},
|
||||
{
|
||||
name: "BlackmanComplex", fn: BlackmanComplex, winLen: 20,
|
||||
want: []float64{0.000000, 0.010223, 0.045069, 0.114390, 0.226899, 0.382381, 0.566665, 0.752034, 0.903493, 0.988846,
|
||||
0.988846, 0.903493, 0.752034, 0.566665, 0.382381, 0.226899, 0.114390, 0.045069, 0.010223, 0.000000},
|
||||
},
|
||||
{
|
||||
name: "BlackmanHarrisComplex", fn: BlackmanHarrisComplex, winLen: 20,
|
||||
want: []float64{0.000060, 0.002018, 0.012795, 0.046450, 0.122540, 0.256852, 0.448160, 0.668576, 0.866426, 0.984278,
|
||||
0.984278, 0.866426, 0.668576, 0.448160, 0.256852, 0.122540, 0.046450, 0.012795, 0.002018, 0.000060},
|
||||
},
|
||||
{
|
||||
name: "NuttallComplex", fn: NuttallComplex, winLen: 20,
|
||||
want: []float64{0.000000, 0.001706, 0.011614, 0.043682, 0.117808, 0.250658, 0.441946, 0.664015, 0.864348, 0.984019,
|
||||
0.984019, 0.864348, 0.664015, 0.441946, 0.250658, 0.117808, 0.043682, 0.011614, 0.001706, 0.000000},
|
||||
},
|
||||
{
|
||||
name: "BlackmanNuttallComplex", fn: BlackmanNuttallComplex, winLen: 20,
|
||||
want: []float64{0.000363, 0.002885, 0.015360, 0.051652, 0.130567, 0.266629, 0.457501, 0.675215, 0.869392, 0.984644,
|
||||
0.984644, 0.869392, 0.675215, 0.457501, 0.266629, 0.130567, 0.051652, 0.015360, 0.002885, 0.000363},
|
||||
},
|
||||
{
|
||||
name: "FlatTopComplex", fn: FlatTopComplex, winLen: 20,
|
||||
want: []float64{-0.000421, -0.003687, -0.017675, -0.045939, -0.070137, -0.037444, 0.115529, 0.402051, 0.737755, 0.967756,
|
||||
0.967756, 0.737755, 0.402051, 0.115529, -0.037444, -0.070137, -0.045939, -0.017675, -0.003687, -0.000421},
|
||||
},
|
||||
}
|
||||
|
||||
// want the same value in imag part as in real part,
|
||||
// so use one float64 for both
|
||||
var complexGausWindowTests = []struct {
|
||||
name string
|
||||
sigma float64
|
||||
want []float64
|
||||
}{
|
||||
{
|
||||
name: "GaussianComplex (sigma=0.3)", sigma: 0.3,
|
||||
want: []float64{0.003866, 0.011708, 0.031348, 0.074214, 0.155344, 0.287499, 0.470444, 0.680632, 0.870660, 0.984728,
|
||||
0.984728, 0.870660, 0.680632, 0.470444, 0.287499, 0.155344, 0.074214, 0.031348, 0.011708, 0.003866},
|
||||
},
|
||||
{
|
||||
name: "GaussianComplex (sigma=0.5)", sigma: 0.5,
|
||||
want: []float64{0.135335, 0.201673, 0.287499, 0.392081, 0.511524, 0.638423, 0.762260, 0.870660, 0.951361, 0.994475,
|
||||
0.994475, 0.951361, 0.870660, 0.762260, 0.638423, 0.511524, 0.392081, 0.287499, 0.201673, 0.135335},
|
||||
},
|
||||
{
|
||||
name: "GaussianComplex (sigma=1.2)", sigma: 1.2,
|
||||
want: []float64{0.706648, 0.757319, 0.805403, 0.849974, 0.890135, 0.925049, 0.953963, 0.976241, 0.991381, 0.999039,
|
||||
0.999039, 0.991381, 0.976241, 0.953963, 0.925049, 0.890135, 0.849974, 0.805403, 0.757319, 0.706648},
|
||||
},
|
||||
}
|
||||
|
||||
func TestWindowsComplex(t *testing.T) {
|
||||
const tol = 1e-6
|
||||
|
||||
for _, test := range complexWindowTests {
|
||||
t.Run(test.name, func(t *testing.T) {
|
||||
src := make([]complex128, test.winLen)
|
||||
for i := range src {
|
||||
src[i] = complex(1, 1)
|
||||
}
|
||||
|
||||
dst := test.fn(src)
|
||||
|
||||
if !equalApprox(dst, test.want, tol) {
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%v\nwant:%v", test.name, dst, test.want)
|
||||
}
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
func TestGausWindowComplex(t *testing.T) {
|
||||
const tol = 1e-6
|
||||
|
||||
src := make([]complex128, 20)
|
||||
for i := range src {
|
||||
src[i] = complex(1, 1)
|
||||
}
|
||||
|
||||
for _, test := range complexGausWindowTests {
|
||||
t.Run(test.name, func(t *testing.T) {
|
||||
// Copy the input since we are mutating it.
|
||||
srcCpy := make([]complex128, len(src))
|
||||
copy(srcCpy, src)
|
||||
dst := GaussianComplex(srcCpy, test.sigma)
|
||||
|
||||
if !equalApprox(dst, test.want, tol) {
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%v\nwant:%v", test.name, dst, test.want)
|
||||
}
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
func equalApprox(seq1 []complex128, seq2 []float64, tol float64) bool {
|
||||
if len(seq1) != len(seq2) {
|
||||
return false
|
||||
}
|
||||
for i := range seq1 {
|
||||
if !floats.EqualWithinAbsOrRel(real(seq1[i]), seq2[i], tol, tol) {
|
||||
return false
|
||||
}
|
||||
if !floats.EqualWithinAbsOrRel(imag(seq1[i]), seq2[i], tol, tol) {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
@@ -67,16 +67,16 @@ func Example() {
|
||||
// freq=0.4500 cycles/period, magnitude=0.0707, phase=-1.7279
|
||||
// freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000
|
||||
// Hamming window:
|
||||
// freq=0.0000 cycles/period, magnitude=0.0218, phase=3.1416
|
||||
// freq=0.0500 cycles/period, magnitude=0.8022, phase=-2.9845
|
||||
// freq=0.1000 cycles/period, magnitude=7.1723, phase=0.3142
|
||||
// freq=0.1500 cycles/period, magnitude=8.6285, phase=-2.6704
|
||||
// freq=0.2000 cycles/period, magnitude=2.0420, phase=0.6283
|
||||
// freq=0.2500 cycles/period, magnitude=0.0702, phase=0.7854
|
||||
// freq=0.3000 cycles/period, magnitude=0.0217, phase=-2.1991
|
||||
// freq=0.3500 cycles/period, magnitude=0.0259, phase=-2.0420
|
||||
// freq=0.4000 cycles/period, magnitude=0.0184, phase=-1.8850
|
||||
// freq=0.4500 cycles/period, magnitude=0.0092, phase=-1.7279
|
||||
// freq=0.0000 cycles/period, magnitude=0.0506, phase=0.0000
|
||||
// freq=0.0500 cycles/period, magnitude=0.5386, phase=-2.9845
|
||||
// freq=0.1000 cycles/period, magnitude=7.3350, phase=0.3142
|
||||
// freq=0.1500 cycles/period, magnitude=8.9523, phase=-2.6704
|
||||
// freq=0.2000 cycles/period, magnitude=1.7979, phase=0.6283
|
||||
// freq=0.2500 cycles/period, magnitude=0.0957, phase=0.7854
|
||||
// freq=0.3000 cycles/period, magnitude=0.0050, phase=-2.1991
|
||||
// freq=0.3500 cycles/period, magnitude=0.0158, phase=-2.0420
|
||||
// freq=0.4000 cycles/period, magnitude=0.0125, phase=-1.8850
|
||||
// freq=0.4500 cycles/period, magnitude=0.0065, phase=-1.7279
|
||||
// freq=0.5000 cycles/period, magnitude=0.0000, phase=0.0000
|
||||
}
|
||||
|
||||
@@ -100,6 +100,6 @@ func ExampleHamming() {
|
||||
// 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]
|
||||
// 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: [0.086957 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]
|
||||
// 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]
|
||||
// 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]
|
||||
}
|
||||
|
||||
@@ -5,6 +5,7 @@
|
||||
package window
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"testing"
|
||||
|
||||
"gonum.org/v1/gonum/floats"
|
||||
@@ -13,74 +14,101 @@ import (
|
||||
var windowTests = []struct {
|
||||
name string
|
||||
fn func([]float64) []float64
|
||||
fnCmplx func([]complex128) []complex128
|
||||
want []float64
|
||||
winLen int
|
||||
}{
|
||||
{
|
||||
name: "Rectangular", fn: Rectangular, winLen: 20,
|
||||
want: []float64{1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
||||
1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
|
||||
name: "Rectangular", fn: Rectangular, fnCmplx: RectangularComplex,
|
||||
want: []float64{
|
||||
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
||||
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Sine", fn: Sine, winLen: 20,
|
||||
want: []float64{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},
|
||||
name: "Sine", fn: Sine, fnCmplx: SineComplex,
|
||||
want: []float64{
|
||||
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,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Lanczos", fn: Lanczos, winLen: 20,
|
||||
want: []float64{0.000000, 0.115514, 0.247646, 0.389468, 0.532984, 0.669692, 0.791213, 0.889915, 0.959492, 0.995450,
|
||||
0.995450, 0.959492, 0.889915, 0.791213, 0.669692, 0.532984, 0.389468, 0.247646, 0.115514, 0.000000},
|
||||
name: "Lanczos", fn: Lanczos, fnCmplx: LanczosComplex,
|
||||
want: []float64{
|
||||
0.052415, 0.170011, 0.300105, 0.436333, 0.57162, 0.698647, 0.810332, 0.900316, 0.963398, 0.995893,
|
||||
0.995893, 0.963398, 0.900316, 0.810332, 0.698647, 0.57162, 0.436333, 0.300105, 0.170011, 0.052415,
|
||||
},
|
||||
},
|
||||
// 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, winLen: 21,
|
||||
want: []float64{0.000000, 0.109292, 0.233872, 0.367883, 0.504551, 0.636620, 0.756827, 0.858394, 0.935489, 0.983632,
|
||||
1.000000, 0.983632, 0.935489, 0.858394, 0.756827, 0.636620, 0.504551, 0.367883, 0.233872, 0.109292, 0.000000},
|
||||
name: "LanczosOdd", fn: Lanczos, fnCmplx: LanczosComplex,
|
||||
want: []float64{
|
||||
0.049813, 0.161128, 0.284164, 0.413497, 0.543076, 0.666582, 0.777804, 0.871026, 0.941379, 0.985147,
|
||||
1,
|
||||
0.985147, 0.941379, 0.871026, 0.777804, 0.666582, 0.543076, 0.413497, 0.284164, 0.161128, 0.049813,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Triangular", fn: Triangular, winLen: 20,
|
||||
want: []float64{0.000000, 0.105263, 0.210526, 0.315789, 0.421053, 0.526316, 0.631579, 0.736842, 0.842105, 0.947368,
|
||||
0.947368, 0.842105, 0.736842, 0.631579, 0.526316, 0.421053, 0.315789, 0.210526, 0.105263, 0.000000},
|
||||
name: "Triangular", fn: Triangular, fnCmplx: TriangularComplex,
|
||||
want: []float64{
|
||||
0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95,
|
||||
0.95, 0.85, 0.75, 0.65, 0.55, 0.45, 0.35, 0.25, 0.15, 0.05,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Hann", fn: Hann, winLen: 20,
|
||||
want: []float64{0.000000, 0.027091, 0.105430, 0.226526, 0.377257, 0.541290, 0.700848, 0.838641, 0.939737, 0.993181,
|
||||
0.993181, 0.939737, 0.838641, 0.700848, 0.541290, 0.377257, 0.226526, 0.105430, 0.027091, 0.000000},
|
||||
name: "Hann", fn: Hann, fnCmplx: HannComplex,
|
||||
want: []float64{
|
||||
0.006155, 0.054496, 0.146447, 0.273005, 0.421783, 0.578217, 0.726995, 0.853553, 0.945503, 0.993844,
|
||||
0.993844, 0.945503, 0.853553, 0.726995, 0.578217, 0.421783, 0.273005, 0.146447, 0.054496, 0.006155,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "BartlettHann", fn: BartlettHann, winLen: 20,
|
||||
want: []float64{0.000000, 0.045853, 0.130653, 0.247949, 0.387768, 0.537696, 0.684223, 0.814209, 0.916305, 0.982186,
|
||||
0.982186, 0.916305, 0.814209, 0.684223, 0.537696, 0.387768, 0.247949, 0.130653, 0.045853, 0.000000},
|
||||
name: "BartlettHann", fn: BartlettHann, fnCmplx: BartlettHannComplex,
|
||||
want: []float64{
|
||||
0.016678, 0.077417, 0.171299, 0.291484, 0.428555, 0.571445, 0.708516, 0.828701, 0.922582, 0.983322,
|
||||
0.983322, 0.922582, 0.828701, 0.708516, 0.571445, 0.428555, 0.291484, 0.171299, 0.077417, 0.016678,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Hamming", fn: Hamming, winLen: 20,
|
||||
want: []float64{0.086957, 0.111692, 0.183218, 0.293785, 0.431408, 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},
|
||||
name: "Hamming", fn: Hamming, fnCmplx: HammingComplex,
|
||||
want: []float64{
|
||||
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,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Blackman", fn: Blackman, winLen: 20,
|
||||
want: []float64{0.000000, 0.010223, 0.045069, 0.114390, 0.226899, 0.382381, 0.566665, 0.752034, 0.903493, 0.988846,
|
||||
0.988846, 0.903493, 0.752034, 0.566665, 0.382381, 0.226899, 0.114390, 0.045069, 0.010223, 0.000000},
|
||||
name: "Blackman", fn: Blackman, fnCmplx: BlackmanComplex,
|
||||
want: []float64{
|
||||
0.002240, 0.021519, 0.066446, 0.145982, 0.265698, 0.422133, 0.599972, 0.773553, 0.912526, 0.989929,
|
||||
0.989929, 0.912526, 0.773553, 0.599972, 0.422133, 0.265698, 0.145982, 0.066446, 0.021519, 0.002240,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "BlackmanHarris", fn: BlackmanHarris, winLen: 20,
|
||||
want: []float64{0.000060, 0.002018, 0.012795, 0.046450, 0.122540, 0.256852, 0.448160, 0.668576, 0.866426, 0.984278,
|
||||
0.984278, 0.866426, 0.668576, 0.448160, 0.256852, 0.122540, 0.046450, 0.012795, 0.002018, 0.000060},
|
||||
name: "BlackmanHarris", fn: BlackmanHarris, fnCmplx: BlackmanHarrisComplex,
|
||||
want: []float64{
|
||||
0.000429, 0.004895, 0.021735, 0.065564, 0.153302, 0.295468, 0.485851, 0.695764, 0.878689, 0.985801,
|
||||
0.985801, 0.878689, 0.695764, 0.485851, 0.295468, 0.153302, 0.065564, 0.021735, 0.004895, 0.000429,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Nuttall", fn: Nuttall, winLen: 20,
|
||||
want: []float64{0.000000, 0.001706, 0.011614, 0.043682, 0.117808, 0.250658, 0.441946, 0.664015, 0.864348, 0.984019,
|
||||
0.984019, 0.864348, 0.664015, 0.441946, 0.250658, 0.117808, 0.043682, 0.011614, 0.001706, 0.000000},
|
||||
name: "Nuttall", fn: Nuttall, fnCmplx: NuttallComplex,
|
||||
want: []float64{
|
||||
0.000315, 0.004300, 0.020039, 0.062166, 0.148072, 0.289119, 0.479815, 0.691497, 0.876790, 0.985566,
|
||||
0.985566, 0.876790, 0.691497, 0.479815, 0.289119, 0.148072, 0.062166, 0.020039, 0.004300, 0.000315,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "BlackmanNuttall", fn: BlackmanNuttall, winLen: 20,
|
||||
want: []float64{0.000363, 0.002885, 0.015360, 0.051652, 0.130567, 0.266629, 0.457501, 0.675215, 0.869392, 0.984644,
|
||||
0.984644, 0.869392, 0.675215, 0.457501, 0.266629, 0.130567, 0.051652, 0.015360, 0.002885, 0.000363},
|
||||
name: "BlackmanNuttall", fn: BlackmanNuttall, fnCmplx: BlackmanNuttallComplex,
|
||||
want: []float64{
|
||||
0.000859, 0.006348, 0.025205, 0.071718, 0.161975, 0.305361, 0.494863, 0.701958, 0.881398, 0.986132,
|
||||
0.986132, 0.881398, 0.701958, 0.494863, 0.305361, 0.161975, 0.071718, 0.025205, 0.006348, 0.000859,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "FlatTop", fn: FlatTop, winLen: 20,
|
||||
want: []float64{-0.000421, -0.003687, -0.017675, -0.045939, -0.070137, -0.037444, 0.115529, 0.402051, 0.737755, 0.967756,
|
||||
0.967756, 0.737755, 0.402051, 0.115529, -0.037444, -0.070137, -0.045939, -0.017675, -0.003687, -0.000421},
|
||||
name: "FlatTop", fn: FlatTop, fnCmplx: FlatTopComplex,
|
||||
want: []float64{
|
||||
-0.001079, -0.007892, -0.026872, -0.056135, -0.069724, -0.015262, 0.157058, 0.444135, 0.760699, 0.970864,
|
||||
0.970864, 0.760699, 0.444135, 0.157058, -0.015262, -0.069724, -0.056135, -0.026872, -0.007892, -0.001079,
|
||||
},
|
||||
},
|
||||
}
|
||||
|
||||
@@ -90,19 +118,24 @@ var gausWindowTests = []struct {
|
||||
want []float64
|
||||
}{
|
||||
{
|
||||
name: "Gaussian (sigma=0.3)", sigma: 0.3,
|
||||
want: []float64{0.003866, 0.011708, 0.031348, 0.074214, 0.155344, 0.287499, 0.470444, 0.680632, 0.870660, 0.984728,
|
||||
0.984728, 0.870660, 0.680632, 0.470444, 0.287499, 0.155344, 0.074214, 0.031348, 0.011708, 0.003866},
|
||||
name: "Gaussian", sigma: 0.3,
|
||||
want: []float64{
|
||||
0.006645, 0.018063, 0.043936, 0.095634, 0.186270, 0.324652, 0.506336, 0.706648, 0.882497, 0.986207,
|
||||
0.986207, 0.882497, 0.706648, 0.506336, 0.324652, 0.186270, 0.095634, 0.043936, 0.018063, 0.006645},
|
||||
},
|
||||
{
|
||||
name: "Gaussian (sigma=0.5)", sigma: 0.5,
|
||||
want: []float64{0.135335, 0.201673, 0.287499, 0.392081, 0.511524, 0.638423, 0.762260, 0.870660, 0.951361, 0.994475,
|
||||
0.994475, 0.951361, 0.870660, 0.762260, 0.638423, 0.511524, 0.392081, 0.287499, 0.201673, 0.135335},
|
||||
name: "Gaussian", sigma: 0.5,
|
||||
want: []float64{
|
||||
0.164474, 0.235746, 0.324652, 0.429557, 0.546074, 0.666977, 0.782705, 0.882497, 0.955997, 0.995012,
|
||||
0.995012, 0.955997, 0.882497, 0.782705, 0.666977, 0.546074, 0.429557, 0.324652, 0.235746, 0.164474,
|
||||
},
|
||||
},
|
||||
{
|
||||
name: "Gaussian (sigma=1.2)", sigma: 1.2,
|
||||
want: []float64{0.706648, 0.757319, 0.805403, 0.849974, 0.890135, 0.925049, 0.953963, 0.976241, 0.991381, 0.999039,
|
||||
0.999039, 0.991381, 0.976241, 0.953963, 0.925049, 0.890135, 0.849974, 0.805403, 0.757319, 0.706648},
|
||||
name: "Gaussian", sigma: 1.2,
|
||||
want: []float64{
|
||||
0.730981, 0.778125, 0.822578, 0.863552, 0.900293, 0.932102, 0.958357, 0.978532, 0.992218, 0.999132,
|
||||
0.999132, 0.992218, 0.978532, 0.958357, 0.932102, 0.900293, 0.863552, 0.822578, 0.778125, 0.730981,
|
||||
},
|
||||
},
|
||||
}
|
||||
|
||||
@@ -111,7 +144,7 @@ func TestWindows(t *testing.T) {
|
||||
|
||||
for _, test := range windowTests {
|
||||
t.Run(test.name, func(t *testing.T) {
|
||||
src := make([]float64, test.winLen)
|
||||
src := make([]float64, len(test.want))
|
||||
for i := range src {
|
||||
src[i] = 1
|
||||
}
|
||||
@@ -119,7 +152,7 @@ func TestWindows(t *testing.T) {
|
||||
dst := test.fn(src)
|
||||
|
||||
if !floats.EqualApprox(dst, test.want, tol) {
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%v\nwant:%v", test.name, dst, test.want)
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%#.6v\nwant:%#v", test.name, dst, test.want)
|
||||
}
|
||||
})
|
||||
}
|
||||
@@ -134,15 +167,69 @@ func TestGausWindows(t *testing.T) {
|
||||
}
|
||||
|
||||
for _, test := range gausWindowTests {
|
||||
t.Run(test.name, func(t *testing.T) {
|
||||
// Copy the input since we are mutating it.
|
||||
t.Run(fmt.Sprintf("%s (sigma=%.1f)", test.name, test.sigma), func(t *testing.T) {
|
||||
srcCpy := make([]float64, len(src))
|
||||
copy(srcCpy, src)
|
||||
dst := Gaussian(srcCpy, test.sigma)
|
||||
|
||||
if !floats.EqualApprox(dst, test.want, tol) {
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%v\nwant:%v", test.name, dst, test.want)
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%#.6v\nwant:%#v", test.name, dst, test.want)
|
||||
}
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
func TestWindowsComplex(t *testing.T) {
|
||||
const tol = 1e-6
|
||||
|
||||
for _, test := range windowTests {
|
||||
t.Run(test.name+"Complex", func(t *testing.T) {
|
||||
src := make([]complex128, len(test.want))
|
||||
for i := range src {
|
||||
src[i] = complex(1, 1)
|
||||
}
|
||||
|
||||
dst := test.fnCmplx(src)
|
||||
|
||||
if !equalApprox(dst, test.want, tol) {
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%#.6v\nwant:%#.6v", test.name, dst, test.want)
|
||||
}
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
func TestGausWindowComplex(t *testing.T) {
|
||||
const tol = 1e-6
|
||||
|
||||
src := make([]complex128, 20)
|
||||
for i := range src {
|
||||
src[i] = complex(1, 1)
|
||||
}
|
||||
|
||||
for _, test := range gausWindowTests {
|
||||
t.Run(fmt.Sprintf("%sComplex (sigma=%.1f)", test.name, test.sigma), func(t *testing.T) {
|
||||
srcCpy := make([]complex128, len(src))
|
||||
copy(srcCpy, src)
|
||||
dst := GaussianComplex(srcCpy, test.sigma)
|
||||
|
||||
if !equalApprox(dst, test.want, tol) {
|
||||
t.Errorf("unexpected result for window function %q:\ngot:%#.6v\nwant:%#.6v", test.name, dst, test.want)
|
||||
}
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
func equalApprox(seq1 []complex128, seq2 []float64, tol float64) bool {
|
||||
if len(seq1) != len(seq2) {
|
||||
return false
|
||||
}
|
||||
for i := range seq1 {
|
||||
if !floats.EqualWithinAbsOrRel(real(seq1[i]), seq2[i], tol, tol) {
|
||||
return false
|
||||
}
|
||||
if !floats.EqualWithinAbsOrRel(imag(seq1[i]), seq2[i], tol, tol) {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user