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DataPRO/FftSharp/Windows/Kaiser.cs

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+using System;
+
+namespace FftSharp.Windows
+{
+    public class Kaiser : Window, IWindow
+    {
+        public readonly double Beta;
+        public override string Name => $"Kaiser-Bessel";
+        public override string Description =>
+            "A Kaiser-Bessel window strikes a balance among the various conflicting goals of amplitude " +
+            "accuracy, side lobe distance, and side lobe height. It compares roughly to the BlackmanHarris window functions, " +
+            "but for the same main lobe width, the near side lobes tend to be higher, but the further out side lobes are lower. " +
+            "Choosing this window often reveals signals close to the noise floor";
+
+        public Kaiser()
+        {
+            Beta = 15;
+        }
+
+        public Kaiser(double beta)
+        {
+            Beta = beta;
+        }
+
+        public static double I0(double x)
+        {
+            // Derived from code workby oygx210/navguide:
+            // https://github.com/oygx210/navguide/blob/master/src/common/bessel.c
+
+            double ax = Math.Abs(x);
+            if (ax < 3.75)
+            {
+                double y = Math.Pow(x / 3.75, 2);
+                double[] m = { 3.5156229, 3.0899424, 1.2067492, 0.2659732, 0.360768e-1, 0.45813e-2 };
+                return 1.0 + y * (m[0] + y * (m[1] + y * (m[2] + y * (m[3] + y * (m[4] + y * m[5])))));
+            }
+            else
+            {
+                double y = 3.75 / ax;
+                double[] m = { 0.39894228, 0.1328592e-1, 0.225319e-2, -0.157565e-2, 0.916281e-2, -0.2057706e-1, 0.2635537e-1, -0.1647633e-1, 0.392377e-2 };
+                return (Math.Exp(ax) / Math.Sqrt(ax)) * (m[0] + y * (m[1] + y * (m[2] + y * (m[3] + y * (m[4] + y * (m[5] + y * (m[6] + y * (m[7] + y * m[8]))))))));
+            }
+        }
+
+        protected override double windowValue(int index, int size)
+        {
+            int M = size;
+            double alpha = (M - 1) / 2.0;
+
+
+            return I0(Beta * Math.Sqrt(1 - Math.Pow((index - alpha) / alpha, 2))) / I0(Beta);
+        }
+    }
+}