What do you understand by aliasing?

Aliasing is the process distortion that takes place when the signal is reconstructed from the provided sample and is different from the original continuous signal.

Aliasing is an effect that results in the signals that make the signals to be indifferentiable (or aliases of one another) when sampled.

In specially sampled signals aliasing can occur, let us consider an example of the Moire patterns in digital images. This process can occur in different samples in time, for this let us consider an example of digital audio. In the case of specially sampled signals, it is known as the special aliasing, and in time of the sample signals, it is referred to as temporal aliasing.

In any field that captures analog data digitally, aliasing is a pervasive problem. These fields follow the widely accepted principles and practices to avoid or minimize the issues.

One key principle is the Nyquist–Shannon sampling theorem.

Nyquist–Shannon theorem

For the domain of digital signal processing, there is a theorem named the sampling theorem that acts as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.

This leads us to arguably the most important concept, the Nyquist Rate: the minimum rate at which a signal can be sampled without introducing errors, which is twice the highest frequency present in the signal.

The simple summary of all of that is that if you want to accurately capture an event that occurs (for example) every 10 seconds, you need to sample at least every 5 seconds. Sampling more coarsely can introduce errors and distortions in the resulting signal, called aliasing.

Examples of aliasing

Photography

The most common issue in digital photography are subjects with fine repeating patterns, for example, consider this photo of a striped shirt:

Now, when this photo is resized to 25%, a psychedelic pattern emerges:

This kind of aliasing is known as moiré and is usually the same as the earlier example we have discussed of a 60-second sine wave sampled every 59 seconds and resulted in an incorrect pattern.

To get this Moire thing reduced while scaling the images anti-aliasing is done, but this process can result in lost of the details of the images.

Video

A wagon-wheel effect is a common form of aliasing in video recordings where rotating objects may appear stationary or rotate slower, or even in a reverse direction.

Audio

Audio is one of the mediums where aliasing is the most noticeable. When audio is downsampled improperly, high frequencies turn into lower ones, and the audio sounds are highly distorted. It is an excellent proxy for what happens to performance data when improperly sampled.

How to detect aliasing

Aliasing can be seen when a signal is not sampled by an oscilloscope fast enough to construct an accurate record of the waveform. The waveforms that are displayed on the oscilloscope become indifferent when the frequency of the signal is misidentified.

When a horizontal test is run on the oscilloscope, and if the shape of the waveform is changed drastically, the aliasing can be detected. A peak detect test can also be performed and if in this test as well the pattern of the waveform changes then the issue must be due to aliasing.

Aliasing vs. sampling rate

To show the effects of aliasing, let us consider 60 seconds sine wave sampled at various rates. The Nyquist Rate for this signal mandates a minimum sampling rate of 30 seconds to prevent aliasing. The source signal (gray) accurately reflects in the 30-second sampled result (black):

When the sampling rate is lowered to 45 seconds, the sampled result (red) starts to differ from the source:

At 59 seconds, the result is significantly different:

At 60 seconds, the sampled result would lead you to believe there’s no signal at all:

At 90 seconds, the sampled result completely misrepresents the source, suggesting the frequency is 1/4 what it is:

Here’s a side-by-side comparison of the same source data when sampled at 16 different rates:

Take a moment to reflect on the previous image. The same signal is related 16 different ways, and 15 of them are wrong. They’re not “less accurate”—they’re entirely incorrect.

If the data that is monitoring the performance suffered from aliasing, the the issue may be hidden due to the issue of aliasing, rule out a true root cause, or lead you to chase a false root cause. This result in the wasted efforts and a negative effect on the job.

Angular aliasing

When a continuous signal is captured or produced by a discrete element the frequency ambiguity is caused due to which aliasing occurs. For angular frequency there is a special aliasing can occur during the production of the light or the sound field with the help of the discrete elements.

This type of the aliasing can be seen in the images or the posters

This kind of aliasing is visible in images such as posters with lenticular printing. If they have a low angular resolution, then as one moves past them, say from left to right, the 2D image does not initially change (so it appears to move left). Then as one moves to the next angular image, the image suddenly changes (so it jumps right), and the frequency and amplitude of this side-to-side movement correspond to the angular resolution of the image (and, for frequency, the speed of the viewer's lateral movement), which is the angular aliasing of the 4D light field. The lack of parallax on viewer movement in 2D images and in a 3-D film produced by stereoscopic glasses (in 3D films the effect is called "yawing", as the image appears to rotate on its axis) can similarly be seen as the loss of angular resolution, all angular frequencies being aliased to 0 (constant).

Common Mistakes

Students often get confuse aliasing with imaging. Always remember that Aliasing is when a higher frequency mirrors DOWN about 1/2 the Nyquist frequency, but Imaging is when a lower frequency mirrors UP about the Nyquist frequency.

Context and Applications

This topic is significant in the professional exams for both graduate and postgraduate courses, especially for:

• Bachelor of Technology in Mechanical Engineering
• Bachelor of Technology in Computer Sciences
• Master of Technology in Computer Sciences

Related Concepts

• Supersampling
• Sinusoid waveform
• Analog-to-digital conversions

Practice Problems

Q1. Aliasing refers to

1. a sampling of signals less than at Nyquist rate
2. a sampling of signals greater than at Nyquist rate
3. a sampling of signals at Nyquist rate
4. none of the above

Correct option: (1)

Explanation: Aliasing can be explained as the existence of undesired particles in a certain reconstructed signal. Also, aliasing relates to the sampling of signals less than at the Nyquist rate.

Q2. The sampling of object characteristics at a high resolution and displaying the result at a lower resolution is called

1. super-sampling
2. post-filtering
3. anti-aliasing
4. a or b

Correct option: (4)

Explanation: Super-sampling is the term that relates to the selection of component features at a greater resolution and portrays the output at a low resolution. It is also known as post-filtering.

Q3. To avoid losing information from periodic objects we need

1. sampling frequency twice
2. Nyquist sampling frequency
3. both a or b
4. neither a nor b

Correct option: (3)

Explanation: The Nyquist sampling frequency is one of the essential factors in order to avoid failing information from periodic objects. Nyquist sampling frequency also refers to sampling frequency twice.

Q4. Anti-aliasing by computing overlap areas is referred to as

1. area sampling
2. supersampling
3. pixel phasing
4. Only b

Correct option: (1)

Explanation: Anti-aliasing is represented as the method to evaluate the intensity of a pixel. In this method, the area of overlap of pixels is also used. So, area sampling is related to anti-aliasing.

Q5. Area sampling is also known as

1. pre-filtering
2. pixel phasing
3. post-filtering
4. anti-aliasing

Correct Option: (1)

Explanation: Area sampling is