“Introduction to the Fourier Transform” by Glassner
Conference:
Type(s):
Title:
- Introduction to the Fourier Transform
Organizer(s):
Presenter(s)/Author(s):
Abstract:
The Fourier Transform is a fundamental conceptual and practical tool in computer graphics. Among its many features, it explains where aliasing comes from, and why noise can be a good thing. It tells us how to filter textures, spend rendering resources wisely, and scale images up and down without introducing artifacts. The Fourier transform is the basis of the JPEG image compression method, and reveals to us why wagons wheels seem to rotate backwards as they spin faster. The Fourier Transform not only describes the source of these (and other) problems in graphics, it often enables us to avoid or suppress them in the first place. Unfortunately, this terrific, everyday tool is unfamiliar to many people, and opaque to many others. This is often because people are put off by its technical language and complicated looking mathematics. For many people, this level of detail is unnecessary. What’s important and useful for them is knowing what the Fourier Transform is all about, and how to use it. High-quality library routines can be relied upon to actually perform the mechanics. In this course, I show the key concepts of the Fourier transform and its applications to computer graphics, with special emphasis on aliasing. There’s almost no math, because I convey the ideas with words, pictures, and animations. Attendees will leave knowing what the Fourier Transform is about, what it does, and how to use it in their own projects to make great computer graphics.
Additional Information:
- 00 – 05: Audio demo
- 05 – 10: Overview
- 10 – 20: Using sine waves
- 20 – 28: Convergence and separability
- 28 – 38: Signals and spectra
- 38 – 46: Multiplication and convolution
- 46 – 56: Useful Fourier pairs
- 56 – 62: 1D sampling and reconstruction
- 62 – 67: 2D sampling and reconstruction
- 67 – 79: 1D aliasing and the Nyquist rate
- 79 – 84: 2D aliasing and the Nyquist rate
- 84 – 90: What’s next
Beginner
Prerequisite: There are no prerequisites. We only require an interest in how this beautiful tool illuminates our world and helps us write great programs for computer graphics.
Topics: Education
List of topics and approximate times:
Additional Info: The Fourier Transform is fundamental to computer graphics, explaining topics from aliasing and sampling to image compression and filtering. This friendly course explains the principles in words, pictures, and animation, rather than math. The concepts are the important thing. We show that they are comprehensible, useful, and beautiful.
