Tutorials

• Visualizing Wavelets, Wavelet Packets, and Wavelet Filters
  

  Obtain the filters, wavelet, or wavelet packets corresponding to a particular wavelet family.

• Time-Frequency Analysis and Continuous Wavelet Transform
  

  Learn how the CWT can help you obtain a sharp time-frequency representation.

• Discrete Wavelet Analysis
  

  Analyze and denoise signals and images using discrete wavelet transform techniques.

• Critically Sampled Wavelet Packet Analysis
  

  Obtain the wavelet packet transform of a 1-D signal and a 2-D image.

• Matching Pursuit
  

  Create matching pursuit dictionaries and perform matching pursuit on 1-D signals.

• Lifting
  

  Use lifting to design wavelet filters while performing the discrete wavelet transform.

About Wavelets

• What is a Wavelet?
  

  Learn general information about wavelets and how to detect a signal discontinuity.

• Continuous and Discrete Wavelet Transforms
  

  Decide whether to use a discrete or continuous wavelet transform.

• Choose a Wavelet
  

  Learn criteria for choosing the right wavelet for your application.

Featured Examples

Practical Introduction to Continuous Wavelet Analysis

Perform and interpret continuous wavelet analysis. The example helps you answer common questions such as: What is the difference between continuous and discrete wavelet analysis? Why are the frequencies, or scales in continuous wavelet analysis logarithmically spaced? In what types of signal analysis problems are continuous wavelet techniques particularly useful?

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Practical Introduction to Multiresolution Analysis

Perform and interpret basic signal multiresolution analysis (MRA). The example uses both simulated and real data to answer questions such as: What does multiresolution analysis mean? What insights about my signal can I gain performing a multiresolution analysis? What are some of the advantages and disadvantages of different MRA techniques? Many of the analyses presented here can be replicated using the Signal Multiresolution Analyzer app.

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Continuous Wavelet Analysis of Modulated Signals

Use the continuous wavelet transform (CWT) to analyze modulated signals.

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Denoise a Signal with the Wavelet Signal Denoiser

Use the Wavelet Signal Denoiser app to denoise a real-valued 1-D signal. You can create and compare multiple versions of a denoised signal with the app and export the desired denoised signal to your MATLAB® workspace. To reproduce the denoised signal in your workspace, or to apply the same denoising parameters to other data, you can generate and edit a MATLAB script. This example illustrates one possible workflow.

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Classify Time Series Using Wavelet Analysis and Deep Learning

Classify heartbeat electrocardiogram data using deep learning and the continuous wavelet transform.

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Music Genre Classification Using Wavelet Time Scattering

Classify the genre of a musical excerpt using wavelet time scattering and the audio datastore. In wavelet scattering, data is propagated through a series of wavelet transforms, nonlinearities, and averaging to produce low-variance representations of the data. These low-variance representations are then used as inputs to a classifier.

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Scale-Localized Volatility and Correlation

There are a number of different variations of the wavelet transform. This example focuses on the maximal overlap discrete wavelet transform (MODWT). The MODWT is an undecimated wavelet transform over dyadic (powers of two) scales, which is frequently used with financial data. One nice feature of the MODWT for time series analysis is that it partitions the data variance by scale. To illustrate this, consider the quarterly chain-weighted U.S. real GDP data for 1974Q1 to 2012Q4. The data were transformed by first taking the natural logarithm and then calculating the year-over-year difference. Obtain the MODWT of the real GDP data down to level six with the 'db2' wavelet. Examine the variance of the data and compare that to the variances by scale obtained with the MODWT.

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Videos

Understanding Wavelets, Part 1: What Are Wavelets
Explore the fundamental concepts of wavelet transforms in this introductory MATLAB Tech Talk. This video covers what wavelets are and how you can use them to explore your data in MATLAB. The video focuses on two important wavelet transform concepts: scaling and shifting. The concepts can be applied to 2-D data such as images.

Understanding Wavelets, Part 2: Types of Wavelet Transforms
Explore the workings of wavelet transforms in detail. You will learn more about the continuous wavelet transforms and the discrete wavelet transform. You will also learn important applications of using wavelet transforms with MATLAB.

Understand Wavelets, Part 3: An Example Application of the Discrete Wavelet Transform
Learn how to use to wavelets to denoise a signal while preserving its sharp features in this MATLAB Tech Talk. This video outlines the steps involved in denoising a signal with the discrete wavelet transform using MATLAB. Learn how this denoising technique compares with other denoising techniques.

Understanding Wavelets, Part 4: An Example Application of the Continuous Wavelet Transform
Explore a practical application of using continuous wavelet transforms in this MATLAB Tech Talk. Get an overview of how to use MATLAB to obtain a sharper time-frequency analysis of a signal with the continuous wavelet transform. This video uses an example seismic signal to highlight the frequency localization capabilities of the continuous wavelet transform.