/// <summary>
/// Returns a matrix whose columns consist of the bottom row of the WPD tree for each WPD window of length 2^L where L= levelNumber.
/// The WPD windows do not overlap.
/// </summary>
/// <param name="signal"></param>
/// <param name="levelNumber"></param>
/// <returns></returns>
public static double[,] GetWPDSpectralSequence(double[] signal, int levelNumber)
{
int windowWidth = (int)Math.Pow(2, levelNumber);
int halfWindow = windowWidth / 2;
int sampleCount = signal.Length / windowWidth;
//int minLag,
//int maxLag
double[,] wpdByTime = new double[halfWindow, sampleCount];
for (int s = 0; s < sampleCount; s++)
{
int start = s * windowWidth;
double[] subArray = DataTools.Subarray(signal, start, windowWidth);
//double[] autocor = AutoCorrelation.MyAutoCorrelation(subArray);
//autocor = DataTools.filterMovingAverage(autocor, 5);
//autocor = DataTools.Subarray(autocor, autocor.Length / 4, windowWidth);
//DataTools.writeBarGraph(autocor);
// only interested in autocorrelation peaks > half max. An oscillation spreads autocor energy.
//double threshold = autocor.Max() / 2;
//int[] histo = DataTools.GetHistogramOfDistancesBetweenEveryPairOfPeaks(autocor, threshold);
var wpd = new WaveletPacketDecomposition(subArray);
double[] energySpectrumWithoutDC = wpd.GetWPDEnergySpectrumWithoutDC();
// there should only be one dominant oscilation in any one freq band at one time.
// keep only the maximum value but divide by the total energy in the spectrum.
// Energy dispersed through the spectrum is indicative of a single impulse, not an oscilation.
int index = DataTools.GetMaxIndex(energySpectrumWithoutDC);
double[] spectrum = new double[halfWindow];
spectrum[index] = energySpectrumWithoutDC[index] / energySpectrumWithoutDC.Sum();
MatrixTools.SetColumn(wpdByTime, s, spectrum);
}
// calculate statistics for values in matrix
//string imagePath = @"C:\SensorNetworks\Output\Sonograms\wpdHistogram.png";
//Histogram.DrawDistributionsAndSaveImage(wpdByTime, imagePath);
string path = @"C:\SensorNetworks\Output\Sonograms\testwavelet.png";
ImageTools.DrawReversedMatrix(wpdByTime, path);
// MatrixTools.writeMatrix(wpdByTime);
return(wpdByTime);
}
/// <summary>
///
/// </summary>
/// <param name="signal"></param>
/// <param name="fftWindowWidth"></param>
/// <param name="wpdLevelNumber"></param>
/// <returns></returns>
public static double[,] GetFrequencyByOscillationsMatrix(double[] signal, int fftWindowWidth, int wpdLevelNumber)
{
// produce spectrogram
int wpdWindowWidth = (int)Math.Pow(2, wpdLevelNumber);
int sampleCount = signal.Length / wpdWindowWidth;
double[,] wpdByTime = new double[wpdWindowWidth, sampleCount];
double[,] freqByOscillationsMatrix = new double[fftWindowWidth, wpdWindowWidth];
// do a WPD over each frequency bin
// accumulate the WPD spectra into a frequency bin by oscillations per second matrix.
//double[,] matrix = Wavelets.GetWPDSpectralSequence(signal, wpdLevelNumber);
double[,] matrix = WaveletPacketDecomposition.GetWPDEnergySequence(signal, wpdLevelNumber);
double[] V = MatrixTools.GetRowAverages(matrix);
return(freqByOscillationsMatrix);
}
/// <summary>
/// Returns a matrix whose columns consist of the energy vector derived from the WPD tree for each WPD window of length 2^L where L= levelNumber.
/// The WPD windows do not overlap.
/// </summary>
/// <param name="signal"></param>
/// <param name="levelNumber"></param>
/// <returns></returns>
public static double[,] GetWPDEnergySequence(double[] signal, int levelNumber)
{
int windowWidth = (int)Math.Pow(2, levelNumber);
int sampleCount = signal.Length / windowWidth;
int lengthOfEnergyVector = (int)Math.Pow(2, levelNumber + 1) - 1;
double[,] wpdByTime = new double[lengthOfEnergyVector, sampleCount];
for (int s = 0; s < sampleCount; s++)
{
int start = s * windowWidth;
double[] subArray = DataTools.Subarray(signal, start, windowWidth);
var wpd = new WaveletPacketDecomposition(subArray);
double[] energyVector = wpd.GetWPDEnergyVector();
// reverse the energy vector so that low resolution coefficients are at the bottom.
energyVector = DataTools.reverseArray(energyVector);
MatrixTools.SetColumn(wpdByTime, s, energyVector);
}
return(wpdByTime);
}
/// <summary>
/// These examples are used to do Wavelet Packet Decomposition on test signals to which noise can be added.
/// </summary>
public static void ExampleOfWavelets_1()
{
//this signal contains one block impulse in centre
//double[] signal = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
// 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
//double[] signal = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
// 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
double[] signal =
{
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
};
//double[] signal = {1,0,0,0,0,0,0,0};
//double[] signal = { 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 };
//double[] signal = { 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 };
//this signal contains four cycles
//double[] signal = { 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0 };
//this signal contains eight cycles
//double[] signal = { 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
// 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0 };
//this signal contains 16 cycles
//double[] signal = { 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
// 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0 };
//this signal contains four step cycles
//double[] signal = { 1, 1, 0.5, 0, -0.5, -1.0, -1.0, -0.5, 0, 0.5, 1.0, 1.0, 0.5, 0.0, -0.5, -1, -1, -0.5, 0, 0.5, 1.0, 1.0, 0.5, 0.0, -0.5, -1.0, -1.0, -0.5, 0, 0.5, 1.0, 1.0,
// 1, 1, 0.5, 0, -0.5, -1.0, -1.0, -0.5, 0, 0.5, 1.0, 1.0, 0.5, 0.0, -0.5, -1, -1, -0.5, 0, 0.5, 1.0, 1.0, 0.5, 0.0, -0.5, -1.0, -1.0, -0.5, 0, 0.5, 1.0, 1.0 };
//this 128 sample signal contains 32 cycles
//double[] signal = { 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
// 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
// 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
// 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0 };
//this 128 sample signal contains 64 cycles
//The output bin vector tree and image will show strong energy at level level 8, bin zero and bin 64.
//i.e. bin 64 implies 64 cycles within the length of the WPD window of 128.
//double[] signal = { 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
// 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
// 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
// 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0};
// add noise to signal
//RandomNumber rn = new RandomNumber();
//double[] rv = RandomNumber.GetRandomVector(128, rn);
// note that even when noise is twice amplitude of signal the first column of UMatrix is excellent reproduction of
// first column when signal has no added noise.
// relative noise amplitude
//double noiseAmplitude = 2.0;
//DataTools.Normalise(rv, 0.0, noiseAmplitude);
//// signal plus noise
//signal = DataTools.AddVectors(signal, rv);
//// normalising seems to make little difference to the result
//signal = DataTools.NormaliseMatrixValues(signal);
//int levelNumber = 7;
WaveletPacketDecomposition wpd = new WaveletPacketDecomposition(signal);
double[,] M = wpd.GetWPDSignalTree();
string path = @"C:\SensorNetworks\Output\Test\testwavelet.png";
ImageTools.DrawReversedMatrix(M, path);
//MatrixTools.writeMatrix(M);
MatrixTools.WriteLocationOfMaximumValues(M);
double[] energySpectrumWithoutDC = wpd.GetWPDEnergySpectrumWithoutDC();
}
