mathnet-numerics/src/UnitTests/IntegralTransformsTests/FourierTest.cs

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using System;
using MathNet.Numerics.Distributions;
using MathNet.Numerics.IntegralTransforms;
using MathNet.Numerics.IntegralTransforms.Algorithms;
using MathNet.Numerics.Signals;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.IntegralTransformsTests
{
    using Random = System.Random;

#if NOSYSNUMERICS
    using Complex = Numerics.Complex;
#else
    using Complex = System.Numerics.Complex;
#endif

    /// <summary>
    /// Fourier test.
    /// </summary>
    [TestFixture]
    public class FourierTest
    {
        /// <summary>
        /// Continuous uniform distribution.
        /// </summary>
        IContinuousDistribution GetUniform(int seed)
        {
            return new ContinuousUniform(-1, 1, new Random(seed));
        }

        /// <summary>
        /// Naive transforms real sine correctly.
        /// </summary>
        [Test]
        public void NaiveTransformsRealSineCorrectly()
        {
            var samples = SignalGenerator.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 16);

            // real-odd transforms to imaginary odd
            var dft = new DiscreteFourierTransform();
            var spectrum = dft.NaiveForward(samples, FourierOptions.Matlab);

            // all real components must be zero
            foreach (var c in spectrum)
            {
                Assert.AreEqual(0, c.Real, 1e-12, "real");
            }

            // all imaginary components except second and last musth be zero
            for (var i = 0; i < spectrum.Length; i++)
            {
                if (i == 1)
                {
                    Assert.AreEqual(-8, spectrum[i].Imaginary, 1e-12, "imag second");
                }
                else if (i == spectrum.Length - 1)
                {
                    Assert.AreEqual(8, spectrum[i].Imaginary, 1e-12, "imag last");
                }
                else
                {
                    Assert.AreEqual(0, spectrum[i].Imaginary, 1e-12, "imag");
                }
            }
        }

        /// <summary>
        /// Radix2XXX when not power of two throws <c>ArgumentException</c>.
        /// </summary>
        [Test]
        public void Radix2ThrowsWhenNotPowerOfTwo()
        {
            var samples = SignalGenerator.Random((u, v) => new Complex(u, v), GetUniform(1), 0x7F);

            var dft = new DiscreteFourierTransform();

            Assert.Throws(typeof (ArgumentException), () => dft.Radix2Forward(samples, FourierOptions.Default));
            Assert.Throws(typeof (ArgumentException), () => dft.Radix2Inverse(samples, FourierOptions.Default));
            Assert.Throws(typeof (ArgumentException), () => DiscreteFourierTransform.Radix2(samples, -1));
            Assert.Throws(typeof (ArgumentException), () => DiscreteFourierTransform.Radix2Parallel(samples, -1));
        }
    }
}