Implemented and tested Tukey window

src/Numerics.Tests/WindowTest.cs

@@ -0,0 +1,59 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+using NUnit.Framework;
+
+namespace MathNet.Numerics.Tests
+{
+    [TestFixture, Category("WindowFunctions")]
+    public class WindowTest
+    {
+
+        [Test]
+        public void TukeyWin0()
+        {
+
+            var expected = new[] { 1, 1, 1, 1, 1, 1 };
+            var actual = Window.Tukey(6, 0);
+
+            Assert.That(actual, Is.EqualTo(expected).Within(0.00005));
+
+        }
+
+        [Test]
+        public void TukeyWin1()
+        {
+
+            var expected = new[] { 0, 0.3455, 0.9045, 0.9045, 0.3455, 0 };
+            var actual = Window.Tukey(6, 1);
+
+            Assert.That(actual, Is.EqualTo(expected).Within(0.00005));
+
+        }
+
+        [Test]
+        public void TukeyWin25()
+        {
+
+            var expected = new[] { 0, 0.9698, 1, 1, 1, 1, 1, 1, 0.9698, 0 };
+            var actual = Window.Tukey(10, 0.25);
+
+            Assert.That(actual, Is.EqualTo(expected).Within(0.00005));
+
+        }
+
+        [Test]
+        public void TukeyWin75()
+        {
+
+            var expected = new[] { 0, 0.2014, 0.6434, 0.9698, 1, 1, 0.9698, 0.6434, 0.2014, 0 };
+            var actual = Window.Tukey(10, 0.75F);
+
+            Assert.That(actual, Is.EqualTo(expected).Within(0.00005));
+
+        }
+
+    }
+}

src/Numerics/Window.cs

@@ -382,5 +382,43 @@ namespace MathNet.Numerics
             }
             return w;
         }
+
+        /// <summary>
+        /// Tukey tapering window. A rectangular window bounded
+        /// by half a cosine window on each side.
+        /// </summary>
+        /// <param name="width">Width of the window</param>
+        /// <param name="r">Fraction of the window occupied by the cosine parts</param>
+        public static double[] Tukey(int width, double r = 0.5)
+        {
+
+            if (r <= 0)
+            {
+                return Generate.Repeat(width, 1.0);
+            }
+            else if (r >= 1)
+            {
+                return Hann(width);
+            }
+
+            var w = new double[width];
+            var period = (width - 1) * r;
+            var step =  2* Math.PI / period;
+            var b1 = (int)Math.Floor((width - 1) * r * 0.5 + 1);
+            var b2 = width - b1;
+            for (var i = 0; i < b1; i++)
+            {
+                w[i] = (1 - Math.Cos(i * step)) * 0.5;
+            }
+            for (var i = b1; i < b2; i++)
+            {
+                w[i] = 1;
+            }
+            for (var i = b2; i < width; i++)
+            {
+                w[i] = w[width-i-1];
+            }
+            return w;
+        }
     }
 }