Anti-Aliasing.com
Sampling Functions
Aliasing effects can be analyzed using the Nyquist frequency and the Nyquist–Shannon sampling theorem.
Sampling Functions
Nyquist Frequency: When displaying a repetitive pattern, the Nyquist frequency defines the
maximum allowable frequency before aliasing occurs.
Definitions from Wikipedia
Nyquist frequency: https://en.wikipedia.org/wiki/Nyquist_frequency
Nyquist Rate: https://en.wikipedia.org/wiki/Nyquist_rate
Nyquist–Shannon sampling theorem:
https://en.wikipedia.org/wiki/Nyquist%e2%80%93Shannon_sampling_theorem
Book References
There is a great book reference about analysis of signal aliasing and jaggies by:
Blinn, James F.: Jim Blinn’s Corner: Dirty Pixels,
Morgan Kaufmann Publishers, Inc., 1998, ISBN 1-55860-455-3
Chapter 2: ‘What We Need Around Here is More Aliasing’
Chapter 8: ‘The Wonderful World of Video’
Chapter 3: ‘Return of the Jaggy’
Chapter 13: ‘ NTSC: Nice Technology, Super Color’
Spatial Domain and Frequency Domain
When taking samples within a pixel and all samples have the same weight, the sampling
window in Spatial Domain is a Square Window, or Box Filter.
In the frequency domain, the frequency response for a Box Filter is a sinc() function.
Refer to Wikipedia and Figure 1:
Sampling Function sinc(): https://en.wikipedia.org/wiki/Sinc_function
Aliasing when Signal Frequency Greater than Nyquist Frequency
When the signal frequency is greater than the Nyquist Frequency, this results in signal frequency aliasing. In the frequency domain, the frequency response for a Box Filter is a sinc() function. The Refer to Figures 2 & 3.
