Wavelets: A Conceptual, Practical Approach

Summary:

This three-day (four-day live instructor lead virtual online) course is vastly different from traditional math-oriented Wavelet courses or books in that we use examples, figures, and computer demonstrations to show how to understand and work with Wavelets

Fast Fourier Transforms (FFT) are in wide use and work very well if your signal stays at a constant frequency (“stationary”). But if the signal could vary, have pulses, “blips” or any other kind of interesting behavior then you need Wavelets. Wavelets are remarkable tools that can stretch and move like an amoeba to find the hidden “events” and then simultaneously give you their location, frequency, and shape. Wavelet Transforms allow this and many other capabilities not possible with conventional methods like the FFT.

This course is vastly different from traditional math-oriented Wavelet courses or books in that we use examples, figures, and computer demonstrations to show how to understand and work with Wavelets. This is a comprehensive, in-depth. up-to-date treatment of the subject, but from an intuitive, conceptual point of view. We do look at a few key equations from the traditional literature but only AFTER the concepts are demonstrated and understood. If desired, further study from scholarly texts and papers is then made much easier and more palatable when you already understand the fundamental equations and how they relate to the real world. Each student will receive extensive course slides, a CD with MATLAB demonstrations, and a copy of the instructor’s new book, Conceptual Wavelets.

If convenient for you we recommend that you bring a laptop to this class. A disc with the course materials will be provided and the laptop will allow you to utilize the materials in class. Note: the laptop is NOT a requirement.

What you will learn:

  • How to use Wavelets as a “microscope” to analyze data that changes over time or has hidden “events” that would not show up on an FFT.
  • How to understand and efficiently use the 3 types of Wavelet Transforms to better analyze and process your data. State-of-the-art methods and applications.
  • How to compress and de-noise data using advanced Wavelet techniques. How to avoid potential pitfalls by understanding the concepts. A “safe” method if in doubt.
  • How to increase productivity and reduce cost by choosing (or building) a Wavelet that best matches your particular application.“This course uses very little math, yet provides an in-depth understanding of the concepts and real-world applications of these powerful tools.”

Course Outline:

  1. What is a Wavelet? Examples and Uses. “Waves” that can start, stop, move and stretch. Real-world applications in many fields: Signal and Image Processing, Internet Traffic, Airport Security, Medicine, JPEG, Finance, Pulse and Target Recognition, Radar, Sonar, etc.
  2. Comparison with traditional methods. The concept of the FFT, the STFT, and Wavelets as all being various types of comparisons with the data. Strengths, weaknesses, optimal choices.
  3. The Continuous Wavelet Transform (CWT). Stretching and shifting the Wavelet for optimal correlation. Predefined vs. Constructed Wavelets.
  4. The Discrete Wavelet Transform (DWT). Shrinking the signal by factors of 2 through downsampling. Understanding the DWT in terms of correlations with the data. Relating the DWT to the CWT. Demonstrations and uses.
  5. The Redundant Discrete Wavelet Transform (RDWT). Stretching the Wavelet by factors of 2 without downsampling. Tradeoffs between the alias-free processing and the extra storage and computational burdens. A hybrid process using both the DWT and the RDWT. Demonstrations and uses.
  6. “Perfect Reconstruction Filters”. How to cancel the effects of aliasing. How to recognize and avoid any traps. A breakthrough method to see the filters as basic Wavelets. The “magic” of alias cancellation demonstrated in both the time and frequency domains.
  7. Highly useful properties of popular Wavelets. How to choose the best Wavelet for your application. When to create your own and when to stay with proven favorites.
  8. Compression and De-Noising using Wavelets. How to remove unwanted or non-critical data without throwing away the alias cancellation capability. A new, powerful method to extract signals from large amounts of noise. Demonstrations.
  9. Additional Methods and Applications. Image Processing. Detecting Discontinuities, Self-Similarities and Transitory Events. Speech Processing. Human Vision. Audio and Video. BPSK/QPSK Signals. Wavelet Packet Analysis. Matched Filtering. How to read and use the various Wavelet Displays. Demonstrations.
  10. Further Resources. The very best of Wavelet references.

Testimonial:

  • Your Wavelets course was very helpful in our Radar studies. We often use wavelets now instead of the Fourier Transform for precision denoising.

    Long To, NAWC WD, Point Wugu, CA

  • I was looking forward to this course and it was very rewarding--Your clear explanations starting with the big picture immediately contextualized the material allowing us to drill a little deeper with a fuller understanding

    Steve Van Albert, Walter Reed Army Institute of Research

  • Good overview of key wavelet concepts and literature. The course provided a good physical understanding of wavelet transforms and applications.

    Stanley Radzevicius, ENSCO, Inc.

Scheduling:

If this course is not on the current schedule of open enrollment courses and you are interested in attending this or another course as an open enrollment, please contact us at (410)956-8805 or ati@aticourses.com. Please indicate the course name, number of students who wish to participate. and a preferred time frame. ATI typically schedules open enrollment courses with a 3-5 month lead time. For on-site pricing, you can use the request an on-site quote form, call us at (410)956-8805, or email us at ati@aticourses.com.

Instructors:

  • D. Lee Fugal is the Founder and President of an independent consulting firm. He has over 30 years of industry experience in Digital Signal Processing (including Wavelets) and Satellite Communications. He has been a full-time consultant on numerous assignments since 1991. Recent projects include Excision of Chirp Jammer Signals using Wavelets, design of Space-Based Geolocation Systems (GPS & Non-GPS), and Advanced Pulse Detection using Wavelet Technology. He has taught upper-division University courses in DSP and in Satellites as well as Wavelet short courses and seminars for Practicing Engineers and Management. He holds a Masters in Applied Physics (DSP) from the University of Utah, is a Senior Member of IEEE, and a recipient of the IEEE Third Millennium Medal.

    Contact this instructor (please mention course name in the subject line)

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