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1-D Continuous Wavelet Analysis

The Wavelet Toolbox™ software enables you to perform a continuous wavelet analysis of your univariate or bivariate 1-D input signals. You can perform continuous wavelet analyses at the command line or with the app which you access by typing waveletAnalyzer at the command line.

Key features include:

  • Continuous wavelet transform (CWT) of a 1-D input signal using real-valued and complex-valued wavelets. The Wavelet Toolbox software features a CWT algorithm, cwt, which is based on the correlation of the signal with an analyzing analytic wavelet, .

  • Inverse CWT of 1–D input signal. For select analyzing wavelets, you can invert the CWT to reconstruct a time and scale-localized approximation to your input signal. See icwt for details.

  • Wavelet cross spectrum and coherence. You can use wcoherence to compute the wavelet cross spectrum and coherence between two time series. The wavelet cross spectrum and coherence can reveal localized similarities between two time series in time and scale. See Wavelet Coherence for examples.

  • Pattern-adapted wavelets for signal analysis. A strength of wavelet analysis is the ability to design wavelets that mimic the structures you wish to detect. Using pat2cwav and wavemngr you can add custom wavelets optimized to detect specified patterns in your data. See Pattern Adapted Wavelets for Signal Detection for examples.

In this section, you'll learn how to

  • Load a signal

  • Perform a continuous wavelet transform of a signal

  • Produce a plot of the coefficients

  • Produce a plot of coefficients at a given scale

  • Produce a plot of local maxima of coefficients across scales

  • Select the displayed plots

  • Switch from scale to pseudo-frequency information

  • Zoom in on detail

  • Display coefficients in normal or absolute mode

  • Choose the scales at which analysis is performed

Since you can perform analyses either from the command line or using the Wavelet Analyzer app, this section has subsections covering each method.

The final subsection discusses how to exchange signal and coefficient information between the disk and the graphical tools.

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