Aliasing

Aliasing Fundamentals:
– Description of aliasing in signal processing and computer graphics
– Spatial aliasing, moiré patterns, and temporal aliasing in video and audio signals
– Sampling schemes in digital cameras and audio signals
– Bandlimited functions, frequency content, and Fourier transform
– Nyquist–Shannon sampling theorem and sampling rate for perfect reconstruction

Aliasing Techniques and Filters:
– Anti-aliasing filters and techniques
– Folding and amplitude vs frequency graphs for sinusoids and aliases
– Symmetry in graphs up to Nyquist frequency and Nyquist criterion
– Use of anti-aliasing filters to attenuate high frequencies
– Reconstruction of filtered signals using interpolation algorithms

Aliasing in Signal Processing:
– Bandpass signals and intentional aliasing for computational efficiency
– Undersampling for low-frequency aliases and frequency-shifting signals
– Relation to Nyquist rate, filter banks, and computational efficiency in digital channelizers
– Applications in moiré patterns, spatial aliasing, and temporal aliasing in video
– Bandlimited functions, reconstruction, and undersampling efficiency

Historical Context and Evolution:
– Evolution of the term ‘aliasing’ from radio engineering to signal processing
– Introduction of aliasing concept by Tukey and first written use in 1949
– Published use in 1958 and credit to Tukey for introducing aliasing in this context
– Angular aliasing in capturing continuous signals with discrete elements
– Loss of angular resolution in 2D images, 3D films, and 4D light fields

Practical Examples and Applications:
– Audio examples demonstrating sawtooth aliasing and audible effects of aliasing distortion
– Spatial aliasing in antenna arrays and importance of sampling density
– Various examples of aliasing in different applications
– Use of aliasing in digital images, audio signals, and computational efficiency
– Importance of multirate signal processing in communication systems

Aliasing (Wikipedia)

This article is about aliasing in signal processing, including computer graphics. For accessing the same data using different names in computer programming, see Aliasing (computing).

In signal processing and related disciplines, aliasing is the overlapping of frequency components resulting from a sample rate below the Nyquist rate. This overlap results in distortion or artifacts when the signal is reconstructed from samples which causes the reconstructed signal to differ from the original continuous signal. Aliasing that occurs in signals sampled in time, for instance in digital audio or the stroboscopic effect, is referred to as temporal aliasing. Aliasing in spatially sampled signals (e.g., moiré patterns in digital images) is referred to as spatial aliasing.

An example of aliasing

This full-sized image shows what a properly sampled image of a brick wall should look like with a screen of sufficient resolution.

When the resolution is reduced, aliasing appears in the form of a moiré pattern.

The motion of the 'camera' at a constant shutter speed creates temporal aliasing known as the wagon wheel effect. The speed of the "camera", moving towards the right, constantly increases at the same rate with the objects sliding to the left. Halfway through the 24-second loop, the objects appear to suddenly shift and head in the reverse direction, towards the right.

Aliasing is generally avoided by applying low-pass filters or anti-aliasing filters (AAF) to the input signal before sampling and when converting a signal from a higher to a lower sampling rate. Suitable reconstruction filtering should then be used when restoring the sampled signal to the continuous domain or converting a signal from a lower to a higher sampling rate. For spatial anti-aliasing, the types of anti-aliasing include fast approximate anti-aliasing (FXAA), multisample anti-aliasing, and supersampling.