MathFunctions.cs

// <copyright file="MathFunctions.cs" company="Math.NET">
// Math.NET Filtering, part of the Math.NET Project
// http://filtering.mathdotnet.com
// http://github.com/mathnet/mathnet-filtering
//
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using System;
using System.Numerics;
using MathNet.Numerics;

namespace MathNet.Filtering.Helpers
{
    /// <summary>
    /// Collection of mathematical functions used across the project.
    /// </summary>
    internal static class MathFunctions
    {
        /// <summary>
        /// Computes the warped frequency.
        /// </summary>
        /// <param name="cutoffFrequency">Digital cutoff frequency.</param>
        /// <param name="samplingTime">Sampling time (computed as the reverse of the sampling frequency).</param>
        /// <returns>Warped frequency.</returns>
        internal static double WarpFrequency(double cutoffFrequency, double samplingTime)
        {
            return Math.Tan(Math.PI * cutoffFrequency / samplingTime);
        }

        /// <summary>
        /// Computes the coefficients of the polynomial whose solutions are roots are given as input parameter.
        /// </summary>
        /// <param name="roots">Roots of the polynomial.</param>
        /// <returns>Polynomial coefficients.</returns>
        internal static Complex[] PolynomialCoefficients(Complex[] roots)
        {
            Complex[] y = Generate.Repeat(roots.Length + 1, Complex.Zero);
            y[0] = Complex.One;

            for (int i = 0; i < roots.Length; i++)
            {
                for (int j = i; j >= 0; j--)
                {
                    y[j + 1] -= roots[i] * y[j];
                }
            }

            return y;
        }
    }
}