// ********************************************************************************
/// <summary>
/// Single Tone Analysis
/// </summary>
/// <param name="timewaveform">Waveform in time space</param>
/// <param name="Fs">Sampling frequency, unit in Hz</param>
/// <param name="initialGuess">Initial guess for the tone frequency, unit in Hz</param>
/// <param name="searchRange">Peak search range near the initialGuess.</param>
/// <returns>Tone information of the signal. Contains amplitude, frequency and phase.</returns>
/// <created>Wei Jin,2019/11/29</created>
/// <changed>Wei Jin,2019/11/29</changed>
// ********************************************************************************
public static ToneInfo SingleToneAnalysis(double[] timewaveform, double Fs = 1.0, double initialGuess = 0, double searchRange = 0.05)
{
ToneInfo toneInfo;
int i;
int fftSize = timewaveform.Length;
Complex[] spectrum = new Complex[fftSize];
Spectrum.AdvanceComplexFFT(timewaveform, WindowType.Hanning, ref spectrum);
// Use the center position as time '0' reference, which makes the spectrum of the window function pure real number
for (i = 0; i < (fftSize + 1) / 4; i++)
{
spectrum[i * 2 + 1] = -spectrum[i * 2 + 1];
}
// Null DC components
for (i = 0; i < 2; i++)
{
spectrum[i] = 0;
}
// Establish tone search range
int searchStart = 2;
int searchEnd = fftSize / 2 - 2;
if (initialGuess > 0 && initialGuess < Fs / 2.0)
{
searchStart = Math.Max(searchStart, (int)((initialGuess / Fs - searchRange / 2) * fftSize));
searchEnd = Math.Min(searchEnd, (int)((initialGuess / Fs + searchRange / 2) * fftSize));
}
// Gross search for the peak tone
double peakVal = 0;
int peakPos = 0;
for (i = searchStart; i < searchEnd; i++)
{
if (peakVal < spectrum[i].Magnitude)
{
peakVal = spectrum[i].Magnitude;
peakPos = i;
}
}
// Refine peak result for the first round
Complex[] threeFingers = new Complex[3];
Array.Copy(spectrum, peakPos - 1, threeFingers, 0, 3);
toneInfo = FFTPeakCorrection(threeFingers);
toneInfo.Frequency += peakPos - 1;
// Remove aliasing around DC and Fs/2
// The Fourier transform of the hanning window has the following form
// h(z) = sinc(z) / (z * z - 1)
// = sin(pi * z) / (pi * z * (z * z - 1))
// Note: the negative frequency component has conjugate phase
// Question(wjin): Why use add instead of sub?
double x_offset;
for (i = 0; i < 3; i++)
{
x_offset = peakPos - 1 + i + toneInfo.Frequency;
threeFingers[i] += Trig.Sinc(x_offset) / (x_offset * x_offset - 1.0)
* Complex.FromPolarCoordinates(toneInfo.Amplitude, -toneInfo.Phase);
x_offset -= fftSize;
threeFingers[i] += Trig.Sinc(x_offset) / (x_offset * x_offset - 1.0)
* Complex.FromPolarCoordinates(toneInfo.Amplitude, -toneInfo.Phase);
}
// Refine peak result for the second round
toneInfo = FFTPeakCorrection(threeFingers);
toneInfo.Frequency += peakPos - 1;
// Correct the results for output.
toneInfo.Amplitude *= 2.0 / fftSize;
toneInfo.Phase = _PhaseSub(toneInfo.Phase, toneInfo.Frequency * Math.PI); // Change the reference position to the begining of the singal
toneInfo.Phase = _PhaseSub(toneInfo.Phase, -0.5 * Math.PI); // Change Cos phase to Sin phase
toneInfo.Frequency *= Fs / fftSize; // Convert frequency unit from 'bins' to engineering units.
return(toneInfo);
}