Aliasing

Aliasing is a phenomenon that occurs in digital signal processing, particularly in images and video.

It refers to the effect of undersampling, where a signal that is sampled at a rate lower than the Nyquist rate (the minimum sampling rate required to accurately represent a signal) can create artifacts and distorted images.

Aliasing can be considered an illusion in the sense that it creates an image or signal that is different from the way it actually is.

When aliasing occurs, the signal is undersampled, meaning that it is not sampled at a high enough rate to accurately represent it. This results in the creation of artifacts and distorted images that appear different from the original signal.

In the image below, the picture is actually a star with 1024 points but the sheer number of points makes the image appear to be a circle with intricate designs around the edges.

Table of Contents

• How does Aliasing work?
• Versions of Aliasing
• Illusions like Aliasing
• Discovery of Aliasing
• References and Resources
• Sign up for emails from Mental Bomb

How does Aliasing work?

Aliasing works by undersampling a signal, meaning that it is sampled at a rate lower than the Nyquist rate, which is the minimum sampling rate required to accurately represent a signal.

In digital signal processing, a signal is sampled by taking snapshots of its value at regular intervals. The sample rate determines how often the signal is sampled, and this directly affects the accuracy of the signal representation. The Nyquist rate is the minimum sample rate that must be used to accurately represent a signal, and it is based on the highest frequency present in the signal.

If the sample rate is lower than the Nyquist rate, the signal will not be accurately represented, and the highest frequency components will be aliased, meaning that they will appear as lower frequency components in the sampled signal. This can cause the signal to appear jagged and stair-stepped, rather than smooth and curved, creating the appearance of artifacts and distorted images.

For example, in images and video, aliasing can occur when the spatial frequency of an image is higher than the sampling rate, causing the image to appear jagged and stair-stepped, rather than smooth and curved. This can result in the creation of “moiré” patterns, which are wavy, repetitive patterns that appear as an artifact in the image.

In audio signals, aliasing can create a metallic or “phased” sound that can be heard as an artifact in the audio.

To reduce aliasing, techniques such as anti-aliasing and oversampling can be used to sample the signal at a higher rate, ensuring that it is accurately represented and reducing the occurrence of distorted or jagged images.

Versions of Aliasing

The following is another example of the same image with and without aliasing.

The following is another examples of Aliasing, the Wagon Wheel Illusion

Illusions like Aliasing

Aliasing can be considered a type of sensory illusion because it creates an image or signal that is different from the way it actually is. When aliasing occurs, the signal is undersampled, meaning that it is not sampled at a high enough rate to accurately represent it. This results in the creation of artifacts and distorted images that appear different from the original signal.

The phenomenon of aliasing can be considered an illusion because it tricks the observer into perceiving the image or signal differently from the way it actually is, just like other optical illusions. By creating distorted images and artifacts, aliasing can cause the brain to perceive a signal differently from the way it actually is, creating an illusion of a different image or sound.

In this sense, aliasing can be considered a type of sensory illusion, as it tricks the brain into perceiving information in a way that is different from reality. The specific type of sensory illusion created by aliasing depends on the context in which it occurs, as it can affect both visual and auditory signals.

The following are some illusions that are related Aliasing:

The wagon wheel illusion is a visual illusion in which a rotating wheel appears to be rotating in the opposite direction or at a different speed than its actual rotation.

The illusion is most commonly observed when viewing a wheel that is lit with strobe lights or a series of still images, such as a filmstrip or video.

Troxler’s fading, also known as Troxler’s effect, is a phenomenon in which a stationary visual stimulus, such as a dot or a shape, disappears from perception after a certain period of time.

The Phi phenomenon is the illusion of movement created by the rapid succession of static images or light sources.

The Rotating Snakes is a peripheral drift illusion that consists of a grid of shapes, with some of them appearing to be rotating or undulating. The illusion is created by the interaction of the shapes with the neural processing of the visual system.

The Moiré pattern illusion: This illusion is created by superimposing two similar patterns on top of each other, such as a grid of lines or circles. The resulting pattern appears to be moving or changing.

The Scintillating Grid Illusion, in which a grid of black and white squares appears to pulsate or “breathe” when viewed from the periphery of the image.

The Hermann Grid Illusion, in which the intersections of a white grid on a black background appear to be gray, even though they are actually the same color as the background.

The Zöllner Illusion, in which parallel lines appear to be tilted or bent when intersected by diagonal lines.

The Fraser Spiral Illusion, in which a pattern of short, curved lines appears to form a spiral.

The Café Wall Illusion is a visual illusion that is created by a grid of alternating light and dark horizontal and vertical lines. The lines appear to be bent or tilted, even though they are actually straight.

These illusions are usually caused by the way our eyes process visual information and the way the brain interprets it. They can also be caused by the interaction of different visual elements, such as lines and angles, in the image. They are often used in research on visual perception and the neural basis of perception.

Discovery of Aliasing

The concept of aliasing has been known since the early days of digital signal processing, and its existence has been widely recognized by researchers and engineers working in the field. The term “aliasing” was first introduced by Harry Nyquist in 1928, and it is based on the Nyquist Sampling Theorem, which states that a signal must be sampled at a rate greater than twice the highest frequency present in the signal in order to accurately represent it.

It’s important to note that the concept of aliasing and the Nyquist Sampling Theorem are based on mathematical principles that were known long before they were formally defined by Harry Nyquist. The Nyquist Sampling Theorem and the concept of aliasing are widely recognized and studied in the field of digital signal processing, and are considered fundamental concepts in the field.

In this sense, the discovery of aliasing is not attributed to a single individual, but rather is a result of the collective efforts of many researchers and engineers who have worked in the field of digital signal processing over the years.

Harry Nyquist was an American electrical engineer and mathematician who made significant contributions to the field of communication theory and digital signal processing. He was born in 1889 in Sweden and immigrated to the United States as a young man.

Nyquist is best known for his work on the sampling theorem, which is now known as the Nyquist Sampling Theorem. This theorem states that a signal must be sampled at a rate greater than twice the highest frequency present in the signal in order to accurately represent it. The theorem is widely used in digital signal processing and has been fundamental in the development of modern digital communication systems.

Nyquist’s work laid the foundation for the development of modern digital communication systems, and he is widely recognized as one of the pioneers of the field. His contributions to the field of digital signal processing have had a lasting impact on the field, and his work continues to be widely studied and applied today.

References and Resources

Check out our complete list of illusions.

Sign Up to Have Your Mind Blown