Wavelets: A Conceptual, Practical Approach
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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
Wavelets: A Conceptual, Practical Approach
- 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.
- 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.
- The Continuous Wavelet Transform (CWT). Stretching and shifting the Wavelet for optimal correlation. Predefined vs. Constructed Wavelets.
- 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.
- 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.
- “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.
- 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.
- 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.
- 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.
- Further Resources. The very best of Wavelet references.
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.”
our 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.
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