public void ReferenceDftTransformsRealSineCorrectly64()
{
var samples = Generate.PeriodicMap(16, w => new Complex(Math.Sin(w), 0), 16, 1.0, Constants.Pi2);
// real-odd transforms to imaginary odd
ReferenceDiscreteFourierTransform.Forward(samples, FourierOptions.Matlab);
// all real components must be zero
foreach (var c in samples)
{
Assert.AreEqual(0, c.Real, 1e-12, "real");
}
// all imaginary components except second and last musth be zero
for (var i = 0; i < samples.Length; i++)
{
if (i == 1)
{
Assert.AreEqual(-8, samples[i].Imaginary, 1e-12, "imag second");
}
else if (i == samples.Length - 1)
{
Assert.AreEqual(8, samples[i].Imaginary, 1e-12, "imag last");
}
else
{
Assert.AreEqual(0, samples[i].Imaginary, 1e-12, "imag");
}
}
}
public void ReferenceDftSatisfiesParsevalsTheorem64(int count)
{
var samples = Generate.RandomComplex(count, GetUniform(1));
var timeSpaceEnergy = (from s in samples select s.MagnitudeSquared()).Mean();
var spectrum = new Complex[samples.Length];
samples.CopyTo(spectrum, 0);
ReferenceDiscreteFourierTransform.Forward(spectrum);
var frequencySpaceEnergy = (from s in spectrum select s.MagnitudeSquared()).Mean();
Assert.AreEqual(timeSpaceEnergy, frequencySpaceEnergy, 1e-12);
}
public void ReferenceDftIsReversible64(FourierOptions options)
{
var samples = Generate.RandomComplex(0x80, GetUniform(1));
var work = new Complex[samples.Length];
samples.CopyTo(work, 0);
ReferenceDiscreteFourierTransform.Forward(work, options);
Assert.IsFalse(work.ListAlmostEqual(samples, 6));
ReferenceDiscreteFourierTransform.Inverse(work, options);
AssertHelpers.AlmostEqual(samples, work, 12);
}