Wavelets Analysis: A Concise Guide Training
|Commitment||2 days, 7-8 hours a day.|
|How To Pass||Pass all graded assignments to complete the course.|
|User Ratings||Average User Rating 4.8 See what learners said|
|Delivery Options||Instructor-Led Onsite, Online, and Classroom Live|
Wavelets Analysis: A Concise Guide Training Course – Hands-on
Wavelets Analysis: A Concise Guide Training Course – Customize it
- We can adapt this training course to your group’s background and work requirements at little to no added cost.
- If you are familiar with some aspects of this training course, we can omit or shorten their discussion.
- We can adjust the emphasis placed on the various topics or build the training around the mix of technologies of interest to you (including technologies other than those included in this outline).
- If your background is nontechnical, we can exclude the more technical topics, include the topics that may be of special interest to you (e.g., as a manager or policy-maker), and present the training course in manner understandable to lay audiences.
Wavelets Analysis: A Concise Guide Training Course – Audience/Target Group
The target audience for this training course:
Wavelets Analysis: A Concise Guide Training Course – Objectives:
Upon completing this training course, learners will be able to meet these objectives:
- Important mathematical structures of signal spaces: orthonormal bases and frames.
- Time, frequency, and scale localizing transforms: the windowed Fourier transform and the continuous wavelet transform, and their implementation.
- Multi-resolution analysis spaces, Haar and Shannon wavelet transforms. Orthogonal and biorthogonal wavelet transforms of compact support: implementation and applications.
- Orthogonal wavelet packets, their implementation, and the best basis algorithm.
- Wavelet transform implementation for 2D images and compression properties.
Wavelets Analysis: A Concise Guide Training – Course Content
Mathematical structures of signal spaces. Review of important structures in function (signal) spaces required for analysis of signals, leading to orthogonal basis and frame representations and their inversion.
Linear time invariant systems. Review linear time invariant systems, convolutions and correlations, spectral factorization for finite length sequences, and perfect reconstruction quadrature mirror filters.
Time, frequency and scale localizing transforms. The windowed Fourier transform and the continuous wavelet transform (CWT). Implementation of the CWT.
The Harr and Shannon wavelets: two extreme examples of orthogonal wavelet transforms, and corresponding scaling and wavelet equations, and their description in terms of FIR and IIR interscale coefficients.
General properties of scaling and wavelet functions. The Haar and Shannon wavelets are seen to be special cases of a more general set of relations defining multi-resolution analysis subspaces that lead to orthogonal and biorthogonal wavelet representations of signals. These relations are examined in both time and frequency domains.
The Discrete Wavelet Transform (DWT). The orthogonal discrete wavelet transform applied to finite length sequences, implementation, denoising and thresholding. Implementation of the biorthogonal discrete wavelet transform to finite length sequences.
Wavelet Regularity and Solutions. Response of the orthogonal DWT to data discontinuities and wavelet regularity. The Daubechies orthogonal wavelets of compact support. Biorthogonal wavelets of compact support and algebraic methods to solve for them. The lifting scheme to construct biorthogonal wavelets of compact support.
Wavelets Analysis: A Concise Guide Training – Orthogonal Wavelet Packets and the Best Basis Algorithm. Orthogonal wavelet packets and their properties in the time and frequency domains. The minimum entropy best basis algorithm and its implementation.
The 2D Wavelet Transform. The DWT applied to 2D (image) data using the product representation, and implementation of the algorithm. Application of the 2D DWT to image compression and comparison with the DCT.