Class WaveletPacketDecomposition

An implementation of wavelet pack decomposition (WPD) using the Haar wavelet. For details on the Haar wavelet, and the source for the details in this code, read "WAVELETS FOR KIDS, A Tutorial Introduction", by Brani Vidakovic and Peter Mueller, Duke University. WARNING: This article on the Haar wavelet is NOT for kids!.

Inheritance
Object
WaveletPacketDecomposition
Inherited Members
Namespace: TowseyLibrary
Assembly: TowseyLibrary.dll
Syntax
public class WaveletPacketDecomposition

Constructors

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WaveletPacketDecomposition(Double[])

Initializes a new instance of the WaveletPacketDecomposition class. Assume the signal is power of 2 in length.

Declaration
public WaveletPacketDecomposition(double[] signal)
Parameters
Type Name Description
Double[] signal

Fields

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SQRT2

Declaration
public const double SQRT2 = 1.4142135623730951
Field Value
Type Description
Double

Properties

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NumberOfLevels

Declaration
public int NumberOfLevels { get; }
Property Value
Type Description
Int32

Methods

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CalculateUniversalThreshold(Int32, Double)

Declaration
public static double CalculateUniversalThreshold(int n, double sdOfCoefficients)
Parameters
Type Name Description
Int32 n
Double sdOfCoefficients
Returns
Type Description
Double
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CalculateUniversalThreshold(Int32, Double[])

Returns a universal threshold which is used to zero small or insignificant wavelet coefficients. See pages 15 & 16 of "Wavelets for kids"!! The coefficients should be derived from the bottom row of the WPD tree. I think n = the level number of the coefficients being thresholded. In other words, the standard deviation is calculated from the bottom row of coeficients but is increased for the higher rows. THis is because the coefficients in the lower rows have a lower SNR.

Declaration
public static double CalculateUniversalThreshold(int n, double[] coefficients)
Parameters
Type Name Description
Int32 n

level number.
Double[] coefficients
Returns
Type Description
Double
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ExampleOfWavelets_1()

These examples are used to do Wavelet Packet Decomposition on test signals to which noise can be added.

Declaration
public static void ExampleOfWavelets_1()
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GetFrequencyByOscillationsMatrix(Double[], Int32, Int32)

Declaration
public static double[, ] GetFrequencyByOscillationsMatrix(double[] signal, int fftWindowWidth, int wpdLevelNumber)
Parameters
Type Name Description
Double[] signal
Int32 fftWindowWidth
Int32 wpdLevelNumber
Returns
Type Description
Double[,]
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GetTreeOfBinVectors(List<WaveletPacketDecomposition.BinVector>, WaveletPacketDecomposition.BinVector)

NOTE: THIS METHOD IS RECURSIVE. It performs a depth first calculation of the wavelet coefficients. Depth first search terminates when the bin vector contains only one element.

Declaration
public static List<WaveletPacketDecomposition.BinVector> GetTreeOfBinVectors(List<WaveletPacketDecomposition.BinVector> list, WaveletPacketDecomposition.BinVector bv)
Parameters
Type Name Description
List<WaveletPacketDecomposition.BinVector> list
WaveletPacketDecomposition.BinVector bv
Returns
Type Description
List<WaveletPacketDecomposition.BinVector>
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GetTreeOfBinVectors(Double[])

Declaration
public static List<WaveletPacketDecomposition.BinVector> GetTreeOfBinVectors(double[] signal)
Parameters
Type Name Description
Double[] signal
Returns
Type Description
List<WaveletPacketDecomposition.BinVector>
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GetWPDEnergySequence(Double[], Int32)

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.

Declaration
public static double[, ] GetWPDEnergySequence(double[] signal, int levelNumber)
Parameters
Type Name Description
Double[] signal
Int32 levelNumber
Returns
Type Description
Double[,]
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GetWPDEnergySpectrumWithoutDC()

Declaration
public double[] GetWPDEnergySpectrumWithoutDC()
Returns
Type Description
Double[]
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GetWPDEnergyVector()

assume tree is full decomposed WPD tree. Assume original signal is power of 2 in length.

Declaration
public double[] GetWPDEnergyVector()
Returns
Type Description
Double[]
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GetWPDSignalTree()

assume tree is full decomposed WPD tree. Assume original signal is power of 2 in length.

Declaration
public double[, ] GetWPDSignalTree()
Returns
Type Description
Double[,]
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GetWPDSpectralSequence(Double[], Int32)

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.

Declaration
public static double[, ] GetWPDSpectralSequence(double[] signal, int levelNumber)
Parameters
Type Name Description
Double[] signal
Int32 levelNumber
Returns
Type Description
Double[,]
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HiPassAndDecimate(Double[])

implements the Haar high pass filter.

Declaration
public static double[] HiPassAndDecimate(double[] signal)
Parameters
Type Name Description
Double[] signal
Returns
Type Description
Double[]
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LowPassAndDecimate(Double[])

implements the Haar low pass filter.

Declaration
public static double[] LowPassAndDecimate(double[] signal)
Parameters
Type Name Description
Double[] signal
Returns
Type Description
Double[]

Extension Methods