Table of Contents

Interface IWaveletFunction<T>

Namespace
AiDotNet.Interfaces
Assembly
AiDotNet.dll

Defines the functionality for wavelet transforms used in signal processing and data analysis.

public interface IWaveletFunction<T>

Type Parameters

T

The numeric data type used for calculations (e.g., float, double).

Remarks

Wavelets are mathematical functions that split data into different frequency components and analyze each component with a resolution matched to its scale. They are particularly useful for analyzing signals with discontinuities or sharp changes.

For Beginners: Think of wavelets as special tools for breaking down complex signals (like audio, images, or any sequence of measurements) into simpler pieces that are easier to analyze.

Imagine you're trying to understand a song:

  • Regular analysis might tell you which notes are played throughout the entire song
  • Wavelet analysis tells you which notes are played at specific moments in time

This makes wavelets excellent for:

  • Removing noise from signals (like cleaning up a blurry photo)
  • Compressing data (like making image files smaller)
  • Detecting patterns or features at different scales (like finding anomalies in heart rate data)
  • Analyzing signals that change over time (like stock market prices)

Unlike simpler transforms (like Fourier), wavelets can capture both frequency and time information, making them more powerful for many real-world applications.

Methods

Calculate(T)

Calculates the wavelet function value at a specific point.

T Calculate(T x)

Parameters

x T

The input value at which to evaluate the wavelet function.

Returns

T

The value of the wavelet function at the specified point.

Remarks

This method evaluates the wavelet function at a given input value.

For Beginners: This is like asking "what's the value of this wavelet at this specific point?"

Different wavelet functions have different shapes. Some common ones include:

  • Haar wavelets (simple step functions)
  • Daubechies wavelets (more complex, smoother functions)
  • Mexican hat wavelets (shaped like a Mexican sombrero)

This method gives you the y-value when you provide an x-value for the wavelet function.

Decompose(Vector<T>)

Decomposes a signal into approximation and detail components using the wavelet transform.

(Vector<T> approximation, Vector<T> detail) Decompose(Vector<T> input)

Parameters

input Vector<T>

The input signal (vector) to decompose.

Returns

(Vector<T> mean, Vector<T> logVar)

A tuple containing the approximation and detail components of the signal.

Remarks

This method applies the wavelet transform to break down the input signal into two components: an approximation (low-frequency component) and detail (high-frequency component).

For Beginners: This method splits your data into two parts:

  1. Approximation: The "big picture" or smooth trends in your data
  2. Detail: The fine details, rapid changes, or "texture" in your data

For example, if your input is a heart rate signal:

  • The approximation would capture the overall rhythm and major beats
  • The detail would capture the smaller variations between beats

This separation is useful because you can:

  • Focus on just the important trends by using the approximation
  • Look for anomalies or specific features in the detail
  • Remove noise by modifying the detail component
  • Compress data by storing the approximation with less precision

GetScalingCoefficients()

Gets the scaling coefficients associated with the wavelet function.

Vector<T> GetScalingCoefficients()

Returns

Vector<T>

A vector containing the scaling coefficients of the wavelet function.

Remarks

Scaling coefficients define the scaling function (also called father wavelet) that is used to create the approximation component in wavelet decomposition.

For Beginners: These coefficients are like a recipe for creating the "big picture" part of your data during wavelet analysis.

Think of them as weights that determine how neighboring data points should be combined to create a smoothed version of your signal. Different wavelet families have different sets of scaling coefficients, which affect how the smoothing is performed.

For example:

  • The Haar wavelet has very simple scaling coefficients [0.5, 0.5]
  • More complex wavelets like Daubechies have longer sets of coefficients

You typically don't need to work with these directly unless you're implementing custom wavelet transforms or need to understand the mathematical details of the wavelet being used.

GetWaveletCoefficients()

Gets the wavelet coefficients associated with the wavelet function.

Vector<T> GetWaveletCoefficients()

Returns

Vector<T>

A vector containing the wavelet coefficients of the wavelet function.

Remarks

Wavelet coefficients define the wavelet function (also called mother wavelet) that is used to create the detail component in wavelet decomposition.

For Beginners: These coefficients are like a recipe for extracting the "fine details" part of your data during wavelet analysis.

While scaling coefficients help create a smoothed version of your signal, wavelet coefficients help identify changes, edges, or discontinuities in your data. Different wavelet families have different sets of wavelet coefficients, which affect how details are extracted.

For example:

  • The Haar wavelet has very simple wavelet coefficients [0.5, -0.5]
  • More complex wavelets have longer sets of coefficients designed to capture different types of details

As with scaling coefficients, you typically don't need to work with these directly unless you're implementing custom wavelet transforms or need to understand the mathematical details.

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