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>
/// Run example
/// </summary>
public void Run()
{
// 1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]
var result = SignalGenerator.EquidistantInterval(Function, -5, 5, 11);
Console.WriteLine(@"1. Get 11 samples of f(x) = (x * x) / 2 equidistant within interval [-5, 5]");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5 and retrieve sample points
double[] samplePoints;
result = SignalGenerator.EquidistantStartingAt(Function, 1, 0.5, 10, out samplePoints);
Console.WriteLine(@"2. Get 10 samples of f(x) = (x * x) / 2 equidistant starting at x=1 with step = 0.5 and retrieve sample points");
Console.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
Console.Write(samplePoints[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5
result = SignalGenerator.EquidistantPeriodic(Function, 10, 5, 10);
Console.WriteLine(@"3. Get 10 samples of f(x) = (x * x) / 2 equidistant within period = 10 and period offset = 5");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Sample f(x) = (x * x) / 2 equidistant to an integer-domain function starting at x = 0 and step = 2
var equidistant = SignalGenerator.EquidistantToFunction(Function, 0, 2);
Console.WriteLine(@" 4. Sample f(x) = (x * x) / 2 equidistant to an integer-domain function starting at x = 0 and step = 2");
for (var i = 0; i < 10; i++)
{
Console.Write(equidistant(i).ToString("N") + @" ");
}
Console.WriteLine();
}
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 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));
}