/// <summary>
/// Performs a Discrete Fourier Tranform on the input data.
/// This is a reference algorithm. Please use a Fast Fourier Transform for production.
/// </summary>
/// <param name="inputSignal"></param>
/// <param name="inverseTransform"></param>
/// <returns></returns>
public static Signal1D DFT(Signal1D inputSignal, bool inverseTransform)
{
if (inputSignal.XData.Length != inputSignal.YData.Length)
{
return(null);
}
double direction = 1.0;
if (inverseTransform)
{
direction = -1.0;
}
int length = inputSignal.XData.Length;
Complex[] yout = new Complex[inputSignal.YData.Length];
double[] xout = new double[inputSignal.XData.Length];
// W = e^2i*pi/N
Complex W = new Complex(Math.Cos(direction * 6.283185307179586476925286766559 / (double)length), Math.Sin(direction * 2.0 * Math.PI / (double)length));
for (int k = 0; k < length; k++)
{
for (int n = 0; n < length; n++)
{
yout[k] += (Complex.Pow(W, k * n) * inputSignal.YData[n]);
}
if (inverseTransform)
{
yout[k] /= length;
xout[k] = k / inputSignal.SamplingRate;
}
else
{
xout[k] = k;
}
}
return(new Signal1D(xout, yout, inputSignal.SamplingRate, 0));
}
/// <summary>
/// Transforms a fourier-transformed signal into a frequency magnitude spectrum
/// </summary>
/// <param name="fourierSignal"></param>
/// <returns></returns>
public static Signal1D MagnitudeTransform(Signal1D fourierSignal)
{
if (fourierSignal.SamplingRate <= 0)
{
return(null);
}
int length = fourierSignal.XData.Length;
double[] xout = new double[length / 2]; // Frequency
Complex[] yout = new Complex[length / 2]; // Magnitude
for (int i = 0; i < xout.Length; i++)
{
xout[i] = i * fourierSignal.SamplingRate / (double)fourierSignal.XData.Length;
yout[i] = fourierSignal.YData[i].Magnitude;
}
return(new Signal1D(xout, yout, fourierSignal.SamplingRate, fourierSignal.TimeLength));
}