Table of Contents

Enum WaveletAlgorithmType

Namespace
AiDotNet.Enums.AlgorithmTypes
Assembly
AiDotNet.dll

Represents different types of wavelet transform algorithms for signal processing.

public enum WaveletAlgorithmType

Fields

DWT = 0

Discrete Wavelet Transform - the standard wavelet transform algorithm.

For Beginners: The Discrete Wavelet Transform (DWT) is the most common wavelet transform method.

Imagine having a set of different-sized magnifying glasses to examine your data:

  1. DWT first looks at your data with a "low-power" lens to capture the overall shape (low frequencies)
  2. Then it uses progressively "higher-power" lenses to capture finer details (high frequencies)
  3. At each step, it downsamples the data (keeps only every other point)

Key characteristics:

  • Very efficient computation (fast and uses little memory)
  • Provides a compact representation (good for compression)
  • The result has the same number of points as the original signal
  • Works best with signals whose length is a power of 2 (like 128, 256, 512)
  • Not shift-invariant (results change if you shift your input signal)

DWT is widely used in image compression, noise reduction, and feature extraction.

MODWT = 1

Maximal Overlap Discrete Wavelet Transform - a redundant wavelet transform that preserves time invariance.

For Beginners: The Maximal Overlap Discrete Wavelet Transform (MODWT) is a modified version of DWT that overcomes some of its limitations.

Unlike DWT, MODWT:

  1. Doesn't downsample the data at each step (keeps all points)
  2. Produces the same number of coefficients at each scale (level of detail)
  3. Is shift-invariant (shifting your input signal doesn't change the pattern of results)

Think of it like taking multiple overlapping photos of the same scene to ensure you don't miss anything:

Key characteristics:

  • More computationally intensive than DWT (needs more memory and processing)
  • Produces redundant information (more coefficients than the original signal)
  • Works with any signal length (not just powers of 2)
  • Better for analysis purposes where preserving time information is critical
  • Excellent for detecting patterns regardless of their position in time

MODWT is particularly useful in financial time series analysis, biomedical signal processing, and other applications where the exact timing of events matters.

SWT = 2

Stationary Wavelet Transform - another non-decimated wavelet transform similar to MODWT.

For Beginners: The Stationary Wavelet Transform (SWT) is very similar to MODWT and is sometimes called the "undecimated wavelet transform" or "algorithme à trous" (algorithm with holes).

Like MODWT, SWT:

  1. Doesn't downsample the data
  2. Is shift-invariant (results don't change if you shift your input)
  3. Produces redundant information

The main difference is in the implementation details and how the filters are applied:

  • SWT upsamples the filters at each level (inserts zeros between filter coefficients)
  • MODWT modifies the filters differently

Key characteristics:

  • Computationally intensive but can be implemented efficiently
  • Excellent for denoising applications
  • Particularly good for image processing tasks
  • Preserves the time information at all scales
  • Often used in applications where detecting transient signals is important

SWT is widely used in image denoising, edge detection, and feature extraction where shift-invariance is critical.

Remarks

For Beginners: Wavelet transforms are mathematical techniques that break down signals (like audio, images, or any data that changes over time) into different frequency components, similar to how a prism breaks light into different colors.

Unlike traditional Fourier transforms that only give frequency information, wavelets show both:

  • What frequencies are present (like bass or treble in music)
  • When these frequencies occur in time (like knowing exactly when a drum hit happens)

This makes wavelets extremely useful for:

  • Analyzing signals that change over time
  • Compressing images and audio (like JPEG2000)
  • Removing noise from signals
  • Detecting patterns or features in data
  • Many scientific and engineering applications

Think of wavelets as special measuring tools that can zoom in on both short-lived and long-lasting patterns in your data, giving you a more complete picture than traditional methods.

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