dsp/window: refactor Gaussian and Tukey windows to be each a single type

dsp/window/window_complex.go

@@ -293,111 +293,3 @@ func FlatTopComplex(seq []complex128) []complex128 {
 	}
 	return seq
 }
-
-// GaussianComplex can modify a sequence by the Gaussian window and return the result.
-// See https://en.wikipedia.org/wiki/Window_function#Gaussian_window
-// and https://www.recordingblogs.com/wiki/gaussian-window for details.
-//
-// 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,
-// 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).
-// It can be used as high or low resolution window, depending of the σ value.
-//
-// Spectral leakage parameters are summarized in the table:
-//         |  σ=0.3  |  σ=0.5 |  σ=1.2 |
-//  -------|---------------------------|
-//  ΔF_0   |   8     |   3.4  |   2.2  |
-//  ΔF_0.5 |   1.82  |   1.2  |   0.94 |
-//  K      |   4     |   1.7  |   1.1  |
-//  ɣ_max  | -65     | -31.5  | -15.5  |
-//  β      |  -8.52  |  -4.48 |  -0.96 |
-type GaussianComplex struct {
-	Sigma float64
-}
-
-// Transform applies the Gaussian transformation to seq in place, using the value
-// of the receiver as the sigma parameter, and returning the result.
-func (g GaussianComplex) Transform(seq []complex128) []complex128 {
-	a := float64(len(seq)-1) / 2
-	for i := range seq {
-		x := -0.5 * math.Pow((float64(i)-a)/(g.Sigma*a), 2)
-		seq[i] *= complex(math.Exp(x), 0)
-	}
-	return seq
-}
-
-// TukeyComplex can modify a sequence using the Tukey window and return the result.
-// See https://en.wikipedia.org/wiki/Window_function#Tukey_window
-// and https://www.recordingblogs.com/wiki/tukey-window for details.
-//
-// The Tukey window is an adjustable window.
-//
-// The sequence weights are
-//  w[k] = 0.5 * (1 + cos(π*(|k - M| - αM)/((1-α) * M))), |k - M| ≥ αM
-//       = 1, |k - M| < αM
-// with M = (N - 1)/2 for k=0,1,...,N-1 where N is the length of the window.
-//
-// Spectral leakage parameters are summarized in the table:
-//         |  α=0.3 |  α=0.5 |  α=0.7 |
-//  -------|--------------------------|
-//  ΔF_0   |   1.33 |   1.22 |   1.13 |
-//  ΔF_0.5 |   1.28 |   1.16 |   1.04 |
-//  K      |   0.67 |   0.61 |   0.57 |
-//  ɣ_max  | -18.2  | -15.1  | -13.8  |
-//  β      |  -1.41 |  -2.50 |  -3.74 |
-type TukeyComplex struct {
-	Alpha float64
-}
-
-// Transform applies the Tukey transformation to seq in place, using the value
-// of the receiver as the Alpha parameter, and returning the result
-func (t TukeyComplex) Transform(seq []complex128) []complex128 {
-	switch {
-	case t.Alpha <= 0:
-		return RectangularComplex(seq)
-	case t.Alpha >= 1:
-		return HannComplex(seq)
-	default:
-		alphaL := t.Alpha * float64(len(seq)-1)
-		width := int(0.5*alphaL) + 1
-		for i := range seq[:width] {
-			w := complex(0.5*(1-math.Cos(2*math.Pi*float64(i)/alphaL)), 0)
-			seq[i] *= w
-			seq[len(seq)-1-i] *= w
-		}
-		return seq
-	}
-}
-
-// ValuesComplex is an arbitrary complex window function.
-type ValuesComplex []complex128
-
-// NewValuesComplex returns a ValuesComplex of length n with weights corresponding
-// to the provided window function.
-func NewValuesComplex(window func([]complex128) []complex128, n int) ValuesComplex {
-	v := make(ValuesComplex, n)
-	for i := range v {
-		v[i] = 1
-	}
-	return window(v)
-}
-
-// Transform applies the weights in the receiver to seq in place, returning the
-// result. If v is nil, Transform is a no-op, otherwise the length of v must
-// match the length of seq.
-func (v ValuesComplex) Transform(seq []complex128) []complex128 {
-	if v == nil {
-		return seq
-	}
-	if len(v) != len(seq) {
-		panic("window: length mismatch")
-	}
-	for i, w := range v {
-		seq[i] *= w
-	}
-	return seq
-}