Class WaveletTransformContinuous

An implementation of Continuous Wavelet Transform (CWT) 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
WaveletTransformContinuous
Inherited Members
Namespace: TowseyLibrary
Assembly: TowseyLibrary.dll
Syntax
public class WaveletTransformContinuous

Constructors

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WaveletTransformContinuous(Double[], Int32)

Initializes a new instance of the WaveletTransformContinuous class. The signal can be any length. Need not be power of 2 in length.

Declaration
public WaveletTransformContinuous(double[] signal, int maxScale)
Parameters
Type Name Description
Double[] signal
Int32 maxScale

Fields

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Daubechies_D10

Declaration
public static double[] Daubechies_D10
Field Value
Type Description
Double[]
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Daubechies_D12

Declaration
public static double[] Daubechies_D12
Field Value
Type Description
Double[]
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Daubechies_D14

Declaration
public static double[] Daubechies_D14
Field Value
Type Description
Double[]
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Daubechies_D16

Declaration
public static double[] Daubechies_D16
Field Value
Type Description
Double[]
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Daubechies_D18

Declaration
public static double[] Daubechies_D18
Field Value
Type Description
Double[]
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Daubechies_D2

Declaration
public static double[] Daubechies_D2
Field Value
Type Description
Double[]
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Daubechies_D20

Declaration
public static double[] Daubechies_D20
Field Value
Type Description
Double[]
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Daubechies_D4

Declaration
public static double[] Daubechies_D4
Field Value
Type Description
Double[]
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Daubechies_D6

Declaration
public static double[] Daubechies_D6
Field Value
Type Description
Double[]
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Daubechies_D8

Declaration
public static double[] Daubechies_D8
Field Value
Type Description
Double[]
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SQRT2

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

Properties

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MaxScale

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

Methods

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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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GetScaleTimeMatrix()

Declaration
public double[, ] GetScaleTimeMatrix()
Returns
Type Description
Double[,]
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GetWaveletCoefficients(Double[])

The wavelet coefficients are derived by reversing the order of the scaling function coefficients and then reversing the sign of every second one, (i.e., D4 wavelet = {-0.1830127, -0.3169873, 1.1830127, -0.6830127}). Mathematically, this looks like b_k = (-1)^{k} a_{N - 1 - k} where k is the coefficient index, b is a coefficient of the wavelet sequence and a a coefficient of the scaling sequence. N is the wavelet index, i.e., 2 for D2.

Declaration
public static double[] GetWaveletCoefficients(double[] Daubechies_DN)
Parameters
Type Name Description
Double[] Daubechies_DN
Returns
Type Description
Double[]
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GetWaveletCoefficients(Double[], Double[])

Declaration
public static double GetWaveletCoefficients(double[] sampleArray, double[] wavelet)
Parameters
Type Name Description
Double[] sampleArray
Double[] wavelet
Returns
Type Description
Double
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HaarDifference(Double[])

Declaration
public static double HaarDifference(double[] sampleArray)
Parameters
Type Name Description
Double[] sampleArray
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[]
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ProcessScaleTimeMatrix(Double[,], Int32)

Declaration
public static double[, ] ProcessScaleTimeMatrix(double[, ] inputM, int minOscilCount)
Parameters
Type Name Description
Double[,] inputM
Int32 minOscilCount
Returns
Type Description
Double[,]
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ReadDaubechiesCoefficients()

Declaration
public static List<double[]> ReadDaubechiesCoefficients()
Returns
Type Description
List<Double[]>

Extension Methods