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");
}
}
}
public void FourierBluesteinMatchesNaiveOnRandomNonPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), _uniform, 0x7F);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRealSine(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Sample.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 16);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierBluesteinMatchesNaiveOnRandomNonPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Sample.Random((u, v) => new Complex(u, v), _uniform, 0x7F);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}
public void FourierBluesteinMatchesNaiveOnRealSineNonPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Sample.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 14);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}
public void FourierBluesteinMatchesNaiveOnRandomPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), GetUniform(1), 0x80);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRealSine([Values(FourierOptions.Default, FourierOptions.Matlab, FourierOptions.NumericalRecipes)] FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 16);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRandom([Values(FourierOptions.Default, FourierOptions.Matlab, FourierOptions.NumericalRecipes)] FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), _uniform, 0x80);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRandom(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Sample.Random((u, v) => new Complex(u, v), _uniform, 0x80);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRealSine([Values(FourierOptions.Default, FourierOptions.Matlab, FourierOptions.NumericalRecipes)] FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 16);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRandom(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), GetUniform(1), 0x80);
VerifyMatchesNaiveComplex(
samples,
10,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
10,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
/// <summary>
/// Initiate the Series
/// </summary>
/// <param name="Control">Control Options for the FourierLevSet</param>
protected FourierLevSetBase(FourierLevSetControl Control)
{
this.control = Control;
this.FourierP = Control.FourierP;
this.current_samplP = Control.samplP;
this.numFp = FourierP.Length;
this.DomainSize = Control.DomainSize;
this.h_min = Control.h_min;
this.mode = Control.mode;
this.FourierEvolve = Control.FourierEvolve;
// set up DFT
invDFT_coeff = new Complex[numFp];
for (int sp = 0; sp < numFp; sp++)
{
invDFT_coeff[sp] = (Complex)current_samplP[sp];
}
DFT = new DiscreteFourierTransform();
DFT_coeff = DFT.NaiveForward(invDFT_coeff, FourierOptions.Matlab);
}
public void FourierNaiveIsReversible([Values(FourierOptions.Default, FourierOptions.Matlab)] FourierOptions options)
{
var dft = new DiscreteFourierTransform();
VerifyIsReversibleComplex(
0x80,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.NaiveInverse(s, options));
}
public void FourierBluesteinMatchesNaiveOnRealSineNonPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 14);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRandom(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), GetUniform(1), 0x80);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRealSine(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Sample.EquidistantPeriodic(w => new Complex(Math.Sin(w), 0), Constants.Pi2, 0, 16);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierBluesteinMatchesNaiveOnRandomPowerOfTwo([Values(FourierOptions.Default, FourierOptions.Matlab, FourierOptions.NumericalRecipes)] FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), _uniform, 0x80);
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
1e-12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}