Continuous Wavelet Transforms

1-D and 2-D CWT, inverse 1-D CWT, 1-D CWT filter bank, wavelet cross-spectrum and coherence

Obtain the continuous wavelet transform (CWT) of a signal or image, construct signal approximations with the inverse CWT, compare time-varying patterns in two signals using wavelet coherence, visualize wavelet bandpass filters, and obtain high resolution time-frequency representations using wavelet synchrosqueezing.

Functions

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1-D Analysis

`cwt`	Continuous 1-D wavelet transform
`icwt`	Inverse continuous 1-D wavelet transform
`cwtfilterbank`	Continuous wavelet transform filter bank
`cwtmag2sig`	Signal reconstruction from CWT magnitude (Since R2023b)
`wt`	Continuous wavelet transform with filter bank
`freqz`	CWT filter bank frequency responses
`timeSpectrum`	Time-averaged wavelet spectrum (Since R2020b)
`scaleSpectrum`	Scale-averaged wavelet spectrum (Since R2020b)
`cwtfreqbounds`	CWT maximum and minimum frequency or period
`wcoherence`	Wavelet coherence and cross-spectrum
`wsst`	Wavelet synchrosqueezed transform
`iwsst`	Inverse wavelet synchrosqueezed transform
`wsstridge`	Time-frequency ridges from wavelet synchrosqueezing
`wtmm`	Wavelet transform modulus maxima

2-D Analysis

`cwtft2`	2-D continuous wavelet transform
`cwtftinfo2`	Supported 2-D CWT wavelets and Fourier transforms

Apps

Wavelet Image Analyzer	Decompose and visualize images (Since R2023a)
Wavelet Time-Frequency Analyzer	Visualize scalogram of signals (Since R2022a)

Topics

Apps

Using Wavelet Image Analyzer App
Visualize discrete and continuous wavelet decompositions of images.
Using Wavelet Time-Frequency Analyzer App
Learn how to use to visualize scalograms of 1-D signals and recreate results in your workspace.
Viewing CWT Decomposition of Image in Wavelet Image Analyzer
Learn how to use Wavelet Image Analyzer to visualize a CWT decomposition of an image and recreate the analysis in your workspace.

1-D CWT Analysis and Synthesis

Continuous Wavelet Analysis
Perform time-frequency analysis with the continuous wavelet transform.
Continuous Wavelet Analysis of Modulated Signals
This example shows how to use the continuous wavelet transform (CWT) to analyze modulated signals.
Continuous Wavelet Analysis of Cusp Signal
Understand the differences between wavelet transform modulus maxima and the CWT of a cusp signal.
Inverse Continuous Wavelet Transform
Understand the mathematics of the inverse continuous wavelet transform.
Boundary Effects and the Cone of Influence
Learn about the cone of influence and how it represents regions of significant boundary effects.
Morse Wavelets
Learn about the generalized Morse family of analytic wavelets.

2-D CWT Analysis

Two-Dimensional CWT of Noisy Pattern
This example shows how to detect a pattern in a noisy image using the 2-D continuous wavelet transform (CWT).
2-D Continuous Wavelet Transform
Learn about the 2-D Continuous Wavelet Transform.

Wavelet Coefficients, Scales, and Synchrosqueezing

Continuous Wavelet Transform and Scale-Based Analysis
Learn about the continuous wavelet transform and the relationship between frequencies and scales.
Continuous Wavelet Transform as a Bandpass Filter
Understand the continuous wavelet transform as bandpass filtering.
Wavelet Synchrosqueezing
Time-frequency reassignment technique for analyzing signals with oscillating modes.

Featured Examples

Relative Velocity Changes in Seismic Waves Using Time-Frequency Analysis

Learn how to use wavelet coherence and the wavelet cross spectrum to characterize frequency-dependent delays in nonstationary signals.

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Time-Frequency Reassignment and Mode Extraction with Synchrosqueezing

Use wavelet synchrosqueezing to obtain a higher resolution time-frequency analysis. The example also shows how to extract and reconstruct oscillatory modes in a signal.

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Frequency- and Time-Localized Reconstruction from the Continuous Wavelet Transform

Reconstruct a frequency-localized approximation of the Kobe earthquake data. The data is sampled at 1 Hz. Extract information from the CWT for frequencies in the range of [0.030, 0.070] Hz.

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Continuous and Discrete Wavelet Analysis of Frequency Break

The difference between the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT).

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Wavelet Analysis of Financial Data

Use wavelets to analyze financial data.

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Wavelet Analysis of Physiologic Signals

Use wavelets to analyze physiologic signals.

Open Live Script