Enum WaveletType

Namespace

AiDotNet.Enums

Assembly

AiDotNet.dll

Defines the different types of biorthogonal wavelets that can be used for signal processing and analysis.

public enum WaveletType

Fields

ReverseBior11 = 0

Reverse Biorthogonal 1.1 wavelet - the simplest biorthogonal wavelet with one vanishing moment in both decomposition and reconstruction.

For Beginners: This is the simplest biorthogonal wavelet.

The "1.1" means it has one vanishing moment in both decomposition and reconstruction. A vanishing moment determines how well the wavelet can represent polynomial behavior.

This wavelet is good for:

• Simple signals with minimal complexity
• Cases where computational efficiency is important
• Situations where you need a symmetric wavelet with minimal filter length

ReverseBior13 = 1

Reverse Biorthogonal 1.3 wavelet - has one vanishing moment for decomposition and three for reconstruction.

For Beginners: This wavelet has one vanishing moment for decomposition and three for reconstruction.

The increased reconstruction moments (3) means it can better represent complex patterns during the reconstruction phase while keeping the decomposition simple.

This wavelet provides a good balance between:

• Computational efficiency (from the simple decomposition)
• Reconstruction quality (from the more complex reconstruction)

ReverseBior22 = 2

Reverse Biorthogonal 2.2 wavelet - has two vanishing moments in both decomposition and reconstruction.

For Beginners: This wavelet has two vanishing moments in both decomposition and reconstruction.

With two vanishing moments, this wavelet can accurately represent linear trends in your data.

This wavelet is useful for:

• Signals with linear components
• Applications where symmetry is important
• Cases where you need a balance between simplicity and representation power

ReverseBior24 = 3

Reverse Biorthogonal 2.4 wavelet - has two vanishing moments for decomposition and four for reconstruction.

For Beginners: This wavelet has two vanishing moments for decomposition and four for reconstruction.

The higher number of reconstruction moments (4) allows it to better capture complex patterns during reconstruction while maintaining a relatively simple decomposition.

This wavelet is good for:

• Applications where reconstruction quality is more important than decomposition
• Signals with both linear trends and more complex components

ReverseBior26 = 4

Reverse Biorthogonal 2.6 wavelet - has two vanishing moments for decomposition and six for reconstruction.

For Beginners: This wavelet has two vanishing moments for decomposition and six for reconstruction.

With six vanishing moments in reconstruction, this wavelet can represent more complex patterns during the reconstruction phase while keeping decomposition relatively simple.

This wavelet is suitable for:

• Applications requiring high-quality reconstruction
• Signals with complex patterns that need to be preserved during processing

ReverseBior28 = 5

Reverse Biorthogonal 2.8 wavelet - has two vanishing moments for decomposition and eight for reconstruction.

For Beginners: This wavelet has two vanishing moments for decomposition and eight for reconstruction.

The high number of reconstruction moments (8) makes this wavelet excellent at preserving complex details during reconstruction while maintaining a simpler decomposition.

This wavelet is particularly useful for:

• Applications where detail preservation is critical
• Complex signals with many frequency components
• Cases where reconstruction quality is significantly more important than decomposition

ReverseBior31 = 6

Reverse Biorthogonal 3.1 wavelet - has three vanishing moments for decomposition and one for reconstruction.

For Beginners: This wavelet has three vanishing moments for decomposition and one for reconstruction.

Unlike previous wavelets, this one has more complexity in decomposition than reconstruction. This makes it good at analyzing complex patterns but with simpler reconstruction.

This wavelet is useful for:

• Applications where analysis (decomposition) is more important than synthesis (reconstruction)
• Detecting quadratic trends in data
• Feature extraction where simple reconstruction is sufficient

ReverseBior33 = 7

Reverse Biorthogonal 3.3 wavelet - has three vanishing moments in both decomposition and reconstruction.

For Beginners: This wavelet has three vanishing moments in both decomposition and reconstruction.

With three vanishing moments on both sides, this wavelet can accurately represent quadratic trends in your data during both analysis and synthesis.

This wavelet provides:

• Balanced performance between decomposition and reconstruction
• Good representation of quadratic patterns
• Symmetry properties that are useful in image processing

ReverseBior35 = 8

Reverse Biorthogonal 3.5 wavelet - has three vanishing moments for decomposition and five for reconstruction.

For Beginners: This wavelet has three vanishing moments for decomposition and five for reconstruction.

This combination provides good analysis of complex patterns with even better reconstruction quality.

This wavelet is suitable for:

• Applications requiring both good analysis and high-quality reconstruction
• Signals with quadratic trends and additional complexity
• Image processing tasks where detail preservation is important

ReverseBior37 = 9

Reverse Biorthogonal 3.7 wavelet - has three vanishing moments for decomposition and seven for reconstruction.

For Beginners: This wavelet has three vanishing moments for decomposition and seven for reconstruction.

The high number of reconstruction moments (7) combined with good decomposition properties makes this wavelet excellent for detailed analysis with high-quality reconstruction.

This wavelet is good for:

• Applications requiring detailed analysis and high-fidelity reconstruction
• Complex signals with multiple frequency components
• Image processing where preserving fine details is critical

ReverseBior39 = 10

Reverse Biorthogonal 3.9 wavelet - has three vanishing moments for decomposition and nine for reconstruction.

For Beginners: This wavelet has three vanishing moments for decomposition and nine for reconstruction.

With nine vanishing moments in reconstruction, this wavelet excels at preserving very complex patterns during reconstruction while maintaining good analysis capabilities.

This wavelet is particularly useful for:

• Applications where extremely high-quality reconstruction is needed
• Signals with very fine details that must be preserved
• Advanced image processing tasks requiring maximum detail preservation

ReverseBior44 = 11

Reverse Biorthogonal 4.4 wavelet - has four vanishing moments in both decomposition and reconstruction.

For Beginners: This wavelet has four vanishing moments in both decomposition and reconstruction.

With four vanishing moments on both sides, this wavelet can accurately represent cubic trends in your data during both analysis and synthesis.

This wavelet provides:

• Balanced performance for complex signals
• Good representation of cubic patterns
• Symmetry properties beneficial for image processing
• Higher computational complexity but better accuracy for complex signals

ReverseBior46 = 12

Reverse Biorthogonal 4.6 wavelet - has four vanishing moments for decomposition and six for reconstruction.

For Beginners: This wavelet has four vanishing moments for decomposition and six for reconstruction.

This combination provides excellent analysis of complex patterns with even better reconstruction quality.

This wavelet is suitable for:

• Applications requiring both detailed analysis and high-quality reconstruction
• Signals with cubic trends and additional complexity
• Advanced signal processing where both decomposition and reconstruction quality matter

ReverseBior48 = 13

Reverse Biorthogonal 4.8 wavelet - has four vanishing moments for decomposition and eight for reconstruction.

For Beginners: This wavelet has four vanishing moments for decomposition and eight for reconstruction.

The high number of moments on both sides makes this a very powerful wavelet for complex signals.

This wavelet is excellent for:

• Applications requiring detailed analysis and very high-quality reconstruction
• Complex signals with multiple frequency components and cubic trends
• Advanced image processing where preserving fine details is critical

ReverseBior55 = 14

Reverse Biorthogonal 5.5 wavelet - has five vanishing moments in both decomposition and reconstruction.

For Beginners: This wavelet has five vanishing moments in both decomposition and reconstruction.

With five vanishing moments on both sides, this wavelet can accurately represent quartic (4th degree polynomial) trends in your data during both analysis and synthesis.

This wavelet provides:

• High-performance balanced analysis and synthesis
• Excellent representation of complex polynomial patterns
• Symmetry properties beneficial for advanced signal processing
• Higher computational complexity but superior accuracy for complex signals

ReverseBior68 = 15

Reverse Biorthogonal 6.8 wavelet - has six vanishing moments for decomposition and eight for reconstruction.

For Beginners: This wavelet has six vanishing moments for decomposition and eight for reconstruction.

This is one of the most complex biorthogonal wavelets, capable of representing very sophisticated patterns in both decomposition and reconstruction.

This wavelet is ideal for:

• The most demanding signal processing applications
• Signals with very complex polynomial trends (up to 5th degree)
• Applications where maximum accuracy in both analysis and synthesis is required
• Advanced scientific and engineering applications requiring highest precision

Remarks

For Beginners: Wavelets are mathematical functions that cut up data into different frequency components.

Think of wavelets like special lenses that let you look at your data in different ways:

• They can zoom in to see fine details (high frequencies)
• They can zoom out to see the big picture (low frequencies)

Biorthogonal wavelets (Bior) are a special family of wavelets that have useful properties for signal processing. The "Reverse" prefix indicates these are the reconstruction filters.

The numbers in each wavelet name (like "11" in ReverseBior11) represent:

• First number: Decomposition filter length
• Second number: Reconstruction filter length

Different wavelets are better suited for different types of data and applications.