Everything about Aliasing totally explained
» This article applies to signal processing, including computer graphics. For uses in computer programming, please refer to aliasing (computing).
In
statistics,
signal processing,
computer graphics and related disciplines,
aliasing refers to an effect that causes different continuous signals to become indistinguishable (or
aliases of one another) when
sampled. It also refers to the
distortion or
artifact that results when a signal is sampled and reconstructed as an alias of the original signal.
When we view a digital photograph, the reconstruction (interpolation) is performed by a display or printer device, and by our eyes and our brain. If the reconstructed image differs from the original image, we're seeing an alias. An example of
spatial aliasing is the
Moiré pattern one can observe in a poorly pixelized image of a brick wall. Techniques that avoid such poor pixelizations are called
anti-aliasing.
Temporal aliasing is a major concern in the sampling of
video and
audio signals. Music, for instance, may contain high-frequency components that are inaudible to us. If we sample it with a frequency that's too low and reconstruct the music with a
digital to analog converter, we may hear the low-frequency aliases of the undersampled high frequencies. Therefore, it's common practice to remove the high frequencies with a filter before the sampling is done.
Situations also exist where the low frequencies are removed (if necessary), and the high frequency components are intentionally undersampled and reconstructed as lower ones. Some digital channelizers
exploit aliasing in this way for computational efficiency; see
IR/RF sampling. Signals that contain no low frequencies are often referred to as
bandpass or non-
baseband.
In video or cinematography, temporal aliasing results from the limited frame rate, and causes the
wagon-wheel effect, whereby a spoked wheel appears to rotate too slowly or even backwards. Aliasing has changed its frequency of rotation. A reversal of direction can be described as a
negative frequency.
Like the video camera, most sampling schemes are periodic; that's they've a characteristic
sampling frequency in time or in space. Digital cameras provide a certain number of samples (
pixels) per degree or per radian, or samples per mm in the focal plane of the camera. Audio signals are sampled (
digitized) with an
analog-to-digital converter, which produces a constant number of samples per second. Some of the most dramatic and subtle examples of aliasing occur when the signal being sampled also has periodic content.
Sampling sinusoidal functions
Sinusoids are an important type of periodic function, because realistic signals are often modeled as the summation of many sinusoids of different frequencies and different amplitudes. Understanding what aliasing does to the individual sinusoids is a big help in understanding what happens to their sum.
Here a plot depicts a set of samples whose sample-interval is 1.0 and two (of many) different sinusoids that could have produced the samples. The sample-rate in this case is
= 1.0. For instance, if the interval is 1 second, the rate is 1 sample per second. 9 cycles of the red sinusoid and 1 cycle of the blue sinusoid span an interval of 10. The respective sinusoid frequencies are
