dsp/window/window_test.go

// 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"
	"gonum.org/v1/gonum/floats/scalar"
)

var windowTests = []struct {
	name    string
	fn      func([]float64) []float64
	fnCmplx func([]complex128) []complex128
	want    []float64
}{
	{
		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, fnCmplx: SineComplex,
		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: "Lanczos", fn: Lanczos, fnCmplx: LanczosComplex,
		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: "LanczosOdd", fn: Lanczos, fnCmplx: LanczosComplex,
		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: "Triangular", fn: Triangular, fnCmplx: TriangularComplex,
		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: "Hann", fn: Hann, fnCmplx: HannComplex,
		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: "BartlettHann", fn: BartlettHann, fnCmplx: BartlettHannComplex,
		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: "Hamming", fn: Hamming, fnCmplx: HammingComplex,
		want: []float64{
			0.08, 0.104924, 0.176995, 0.288404, 0.427077, 0.577986, 0.72478, 0.85155, 0.944558, 0.993726,
			0.993726, 0.944558, 0.85155, 0.72478, 0.577986, 0.427077, 0.288404, 0.176995, 0.104924, 0.08,
		},
	},
	{
		name: "Blackman", fn: Blackman, fnCmplx: BlackmanComplex,
		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: "BlackmanHarris", fn: BlackmanHarris, fnCmplx: BlackmanHarrisComplex,
		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: "Nuttall", fn: Nuttall, fnCmplx: NuttallComplex,
		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: "BlackmanNuttall", fn: BlackmanNuttall, fnCmplx: BlackmanNuttallComplex,
		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: "FlatTop", fn: FlatTop, fnCmplx: FlatTopComplex,
		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: "Gaussian{0.3}.Transform", fn: Gaussian{0.3}.Transform, fnCmplx: Gaussian{0.3}.TransformComplex,
		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{0.5}.Transform", fn: Gaussian{0.5}.Transform, fnCmplx: Gaussian{0.5}.TransformComplex,
		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{1.2}.Transform", fn: Gaussian{1.2}.Transform, fnCmplx: Gaussian{1.2}.TransformComplex,
		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: "Tukey{1}.Transform", fn: Tukey{1}.Transform, fnCmplx: Tukey{1}.TransformComplex,
		want: []float64{ // Hann window case.
			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: "Tukey{0}.Transform", fn: Tukey{0}.Transform, fnCmplx: Tukey{0}.TransformComplex,
		want: []float64{ // Rectangular window case.
			1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
			1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
		},
	},
	{
		name: "Tukey{0.5}.Transform", fn: Tukey{0.5}.Transform, fnCmplx: Tukey{0.5}.TransformComplex,
		want: []float64{
			0.000000, 0.105430, 0.377257, 0.700847, 0.939737, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000,
			1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 0.939737, 0.700847, 0.377257, 0.105429, 0.000000,
		},
	},
}

func TestWindows(t *testing.T) {
	t.Parallel()
	const tol = 1e-6

	for _, test := range windowTests {
		t.Run(test.name, func(t *testing.T) {
			src := make([]float64, len(test.want))
			for i := range src {
				src[i] = 1
			}

			dst := test.fn(src)
			if !floats.EqualApprox(dst, test.want, tol) {
				t.Errorf("unexpected result for window function %q:\ngot:%#.6v\nwant:%#v", test.name, dst, test.want)
			}

			for i := range src {
				src[i] = 1
			}

			vals := NewValues(test.fn, len(src))
			dst = vals.Transform(src)
			if !floats.EqualApprox(dst, test.want, tol) {
				t.Errorf("unexpected result for lookup window function %q:\ngot:%#.6v\nwant:%#.6v", test.name, dst, test.want)
			}

			for i := range src {
				src[i] = 1
			}

			dst = make([]float64, len(src))
			vals.TransformTo(dst, src)
			if !floats.EqualApprox(dst, test.want, tol) {
				t.Errorf("unexpected result for lookup window function %q:\ngot:%#.6v\nwant:%#.6v", test.name, dst, test.want)
			}
		})
	}
}

func TestWindowsComplex(t *testing.T) {
	t.Parallel()
	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)
			}

			for i := range src {
				src[i] = complex(1, 1)
			}

			vals := NewValues(test.fn, len(src))
			dst = vals.TransformComplex(src)
			if !equalApprox(dst, test.want, tol) {
				t.Errorf("unexpected result for lookup window function %q:\ngot:%#.6v\nwant:%#.6v", test.name, dst, test.want)
			}

			for i := range src {
				src[i] = complex(1, 1)
			}

			dst = make([]complex128, len(src))
			vals.TransformComplexTo(dst, src)
			if !equalApprox(dst, test.want, tol) {
				t.Errorf("unexpected result for lookup 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 !scalar.EqualWithinAbsOrRel(real(seq1[i]), seq2[i], tol, tol) {
			return false
		}
		if !scalar.EqualWithinAbsOrRel(imag(seq1[i]), seq2[i], tol, tol) {
			return false
		}
	}
	return true
}