/// <summary>
/// Multilevel 1-D Discreete Wavelet Transform
/// </summary>
/// <param name="signal">The signal. Example: new Signal(5, 6, 7, 8, 1, 2, 3, 4)</param>
/// <param name="motherWavelet">The mother wavelet to be used. Example: CommonMotherWavelets.GetWaveletFromName("DB4")</param>
/// <param name="level">The depth-level to perform the DWT</param>
/// <param name="extensionMode">Signal extension mode</param>
/// <param name="convolutionMode">Defines what convolution function should be used</param>
/// <returns></returns>
public static List <DecompositionLevel> ExecuteDWT(Signal signal, MotherWavelet motherWavelet, int level, SignalExtension.ExtensionMode extensionMode = SignalExtension.ExtensionMode.SymmetricHalfPoint, ConvolutionModeEnum convolutionMode = ConvolutionModeEnum.ManagedFFT)
{
var levels = new List <DecompositionLevel>();
var approximation = (double[])signal.Samples.Clone();
var details = (double[])signal.Samples.Clone();
var realLength = signal.Samples.Length;
for (var i = 1; i <= level; i++)
{
var extensionSize = motherWavelet.Filters.DecompositionLowPassFilter.Length - 1;
approximation = SignalExtension.Extend(approximation, extensionMode, extensionSize);
details = SignalExtension.Extend(details, extensionMode, extensionSize);
approximation = WaveMath.Convolve(convolutionMode, approximation, motherWavelet.Filters.DecompositionLowPassFilter);
approximation = WaveMath.DownSample(approximation);
details = WaveMath.Convolve(convolutionMode, details, motherWavelet.Filters.DecompositionHighPassFilter);
details = WaveMath.DownSample(details);
realLength = realLength / 2;
levels.Add(new DecompositionLevel
{
Signal = signal,
Index = i - 1,
Approximation = approximation,
Details = details
});
details = (double[])approximation.Clone();
}
return(levels);
}
/// <summary>
/// Gets the Mother Wavelet object base on it name. Returns null if the name is not found.
/// </summary>
/// <param name="name">The name of the wavelet. Examples: db4, haar, sym2, dmeyer, coif3</param>
/// <returns></returns>
public static MotherWavelet GetWaveletFromName(string name)
{
name = name.ToLower();
if ((name.StartsWith("d") || name.StartsWith("daub")) && Regex.Match(name, "[?d|^daub][0-9]+").Length > 0)
{
name = name.Replace("d", "db").Replace("dbaub", "db").Replace("dbb", "db");
}
if (!MotherWaveletsCache.ContainsKey(name))
{
if (!Wavelets.ContainsKey(name))
{
return(null);
}
var wavelet = new MotherWavelet(name, (double[])Wavelets[name][1]);
wavelet.CalculateFilters();
MotherWaveletsCache.Add(name, wavelet);
return(wavelet);
}
return(MotherWaveletsCache[name]);
}
/// <summary>
/// Multilevel inverse discrete 1-D wavelet transform
/// </summary>
/// <param name="decompositionLevels">The decomposition levels of the DWT</param>
/// <param name="motherWavelet">The mother wavelet to be used. Example: CommonMotherWavelets.GetWaveletFromName("DB4") </param>
/// <param name="level">The depth-level to perform the DWT</param>
/// <param name="convolutionMode">Defines what convolution function should be used</param>
/// <returns></returns>
public static double[] ExecuteIDWT(List <DecompositionLevel> decompositionLevels, MotherWavelet motherWavelet, int level = 0, ConvolutionModeEnum convolutionMode = ConvolutionModeEnum.ManagedFFT)
{
if (level == 0 || level > decompositionLevels.Count)
{
level = decompositionLevels.Count;
}
if (level <= 0)
{
return(null);
}
var approximation = (double[])decompositionLevels[level - 1].Approximation.Clone();
var details = (double[])decompositionLevels[level - 1].Details.Clone();
for (var i = level - 1; i >= 0; i--)
{
approximation = WaveMath.UpSample(approximation);
approximation = WaveMath.Convolve(convolutionMode, approximation, motherWavelet.Filters.ReconstructionLowPassFilter, true, -1);
details = WaveMath.UpSample(details);
details = WaveMath.Convolve(convolutionMode, details, motherWavelet.Filters.ReconstructionHighPassFilter, true, -1);
//sum approximation with details
approximation = WaveMath.Add(approximation, details);
if (i <= 0)
{
continue;
}
if (approximation.Length > decompositionLevels[i - 1].Details.Length)
{
approximation = SignalExtension.Deextend(approximation, decompositionLevels[i - 1].Details.Length);
}
details = (double[])decompositionLevels[i - 1].Details.Clone();
}
return(approximation);
}