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 FourierBluesteinIsReversible(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Generate.RandomComplex(0x7FFF, GetUniform(1));
var work = new Complex[samples.Length];
samples.CopyTo(work, 0);
dft.BluesteinForward(work, options);
Assert.IsFalse(work.ListAlmostEqual(samples, 6));
dft.BluesteinInverse(work, options);
AssertHelpers.ListAlmostEqual(samples, work, 10);
}
public void FourierRadix2IsReversible(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), GetUniform(1), 0x8000);
var work = new Complex[samples.Length];
samples.CopyTo(work, 0);
dft.Radix2Forward(work, options);
Assert.IsFalse(work.ListAlmostEqual(samples, 6));
dft.Radix2Inverse(work, options);
AssertHelpers.ListAlmostEqual(samples, work, 12);
}
public void FourierBluesteinMatchesNaiveOnRandomNonPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Generate.RandomComplex(0x7F, GetUniform(1));
VerifyMatchesNaiveComplex(
samples,
10,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
10,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}
public void FourierBluesteinMatchesNaiveOnRandomNonPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = SignalGenerator.Random((u, v) => new Complex(u, v), GetUniform(1), 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 FourierBluesteinIsReversible(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
VerifyIsReversibleComplex(
0x7FFF,
1e-12,
s =>
{
dft.BluesteinForward(s, options);
return s;
},
s =>
{
dft.BluesteinInverse(s, options);
return s;
});
}
public void FourierRadix2MatchesNaiveOnRealSine(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Generate.PeriodicMap(16, w => new Complex(Math.Sin(w), 0), 16, 1.0, Constants.Pi2);
VerifyMatchesNaiveComplex(
samples,
12,
s => dft.NaiveForward(s, options),
s => dft.Radix2Forward(s, options));
VerifyMatchesNaiveComplex(
samples,
12,
s => dft.NaiveInverse(s, options),
s => dft.Radix2Inverse(s, options));
}
public void FourierRadix2MatchesNaiveOnRandom(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Generate.RandomComplex(0x80, GetUniform(1));
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));
}
public void FourierBluesteinMatchesNaiveOnRealSineNonPowerOfTwo(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
var samples = Generate.PeriodicMap(14, w => new Complex(Math.Sin(w), 0), 14, 1.0, Constants.Pi2);
VerifyMatchesNaiveComplex(
samples,
12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}
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));
}
public void FourierRadix2MatchesNaiveOnRealSine(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,
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 FourierRadix2IsReversible(FourierOptions options)
{
var dft = new DiscreteFourierTransform();
VerifyIsReversibleComplex(
0x8000,
1e-12,
s =>
{
dft.Radix2Forward(s, options);
return s;
},
s =>
{
dft.Radix2Inverse(s, options);
return s;
});
}
public void FourierNaiveIsReversible(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,
12,
s => dft.NaiveForward(s, options),
s => dft.BluesteinForward(s, options));
VerifyMatchesNaiveComplex(
samples,
12,
s => dft.NaiveInverse(s, options),
s => dft.BluesteinInverse(s, options));
}