public static Wave operator +(Wave wave1, Wave wave2)
{
if (wave1.frequency != wave2.frequency)
{
throw new ArgumentException("The frequencies of 'wave1' and 'wave2' don't match.");
}
double basePhase = wave1.phase;
double phaseDifference = wave2.phase - wave1.phase;
double frequency = Items.Equal(wave1.frequency, wave2.frequency);
double amplitude = Scalars.SquareRoot
(
wave1.amplitude.Square() +
2 * wave1.amplitude * wave2.amplitude * Scalars.PSine(phaseDifference + 0.25) +
wave2.amplitude.Square()
);
double phase =
basePhase +
Scalars.ArcTangent
(
wave2.amplitude * Scalars.PSine(phaseDifference),
wave1.amplitude + wave2.amplitude * Scalars.PSine(phaseDifference + 0.25)
)
/ (2 * Math.PI);
return(new Wave(frequency, amplitude, phase));
}
public static IEnumerable <Wave> SignalToSpectrum(IEnumerable <double> signal, double length)
{
if (signal == null)
{
throw new ArgumentNullException("signal");
}
if (length <= 0)
{
throw new ArgumentOutOfRangeException("length");
}
Complex[] spectrum = DiscreteFourierTransform.TransformForward(signal.Select(sample => (Complex)sample)).ToArray();
for (int spectrumIndex = 0; spectrumIndex < spectrum.Length; spectrumIndex++)
{
double frequencyIndex = spectrumIndex > spectrum.Length / 2 ? spectrumIndex - spectrum.Length : spectrumIndex;
double frequency = frequencyIndex / length;
double cosineAmplitude = spectrum[spectrumIndex].Real;
double sineAmplitude = spectrum[spectrumIndex].Imaginary;
double mixedAmplitude = Scalars.SquareRoot(cosineAmplitude.Square() + sineAmplitude.Square());
double amplitude = mixedAmplitude / Scalars.SquareRoot(spectrum.Length);
double phase = Scalars.ArcTangent(sineAmplitude, cosineAmplitude);
yield return(new Wave(frequency, amplitude, -phase / (2 * Math.PI) + 0.25));
}
}
// Intended for synthesis
// Input \ Output | Real | Imaginary
// ---------------|------|----------
// Real | + | -
// Imaginary | + | +
static MatrixComplex GetReverseTransformation(int size)
{
MatrixComplex transformation = new MatrixComplex(size, size);
Complex factor = (2 * Math.PI / size) * Complex.ImaginaryOne;
for (int row = 0; row < transformation.RowCount; row++)
{
for (int column = 0; column < transformation.ColumnCount; column++)
{
transformation[row, column] = Scalars.Exponentiate(-factor * row * column);
}
}
return((1 / Scalars.SquareRoot(size)) * transformation);
}