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.
View course sampler
Tuition:
Instructor:
Instructor:
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)
What you will learn:
Course Outline:
- 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.
Comments from participants:
"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.
