Aliasing Effect Near Sampling Frequency

Yumin Zhang

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Conference: 2021 ASEE Virtual Annual Conference Content Access
Location: Virtual Conference
Publication Date: July 26, 2021
Start Date: July 26, 2021
End Date: July 19, 2022
Conference Session: Engineering Physics and Physics Division Technical Session 2
Tagged Division: Engineering Physics and Physics
Page Count: 9
DOI: 10.18260/1-2--36659
Permanent URL: https://peer.asee.org/36659
Download Count: 655

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Yumin Zhang Southeast Missouri State University

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Yumin Zhang is a professor in the Department of Engineering and Technology, Southeast Missouri State University. His research interests include semiconductor devices, electronic circuits, neural networks, and engineering education.

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Abstract

Aliasing Effect Near Sampling Frequency

Natural signals picked up by various sensors are analog signals, which often need to be digitized for processing, storage, and transmission. Compared with the very high sampling rate of the electronic circuits, most of these analog signals change rather slowly. Therefore, the criterion of the sampling theorem are met, and the original signals can be reconstructed from the digitized signals. However, if the bandwidth of the original signal is beyond the Nyquist frequency, aliasing happens, and then the reconstructed signal will be distorted.

In many movies, people see that the wheels of a car seemingly rotate backward while the car is moving forward. As we know, the motions in movies are illusions of our eyes, which need at least 50 ms to perceive a picture. Based on this phenomenon, movies are shot and played at 24 frames per second. In other words, each frame takes less than 50 ms so that we are not able to see the still pictures. From the point of view of signal processing, the process of shooting a movie is like digitizing a signal at the sampling rate of 24 Hz. With our eyes serving as a lowpass filter, the original motion is perceived in the same way as the reconstructed signal.

When we watch a rotating wheel, our attention is on the spokes. For example, with a six-spoke wheel rotating at the speed of 4 revolution per second, the pictures of the wheel will be identical if shot at the rate of 24 frames per second. Therefore, the wheels rotating at this speed will look like still in the movie. If the rotating speed is a little lower, then it seems like that the wheel is rotating backward.

A lab was designed in the course of Signals and Systems to demonstrate this phenomenon, and Simulink was used for simulation. The original signal is a sine wave, and it is sampled by multiplying with a square wave with very low duty cycle, which is just like a pulse train. The sampled signal goes through a low pass filter, and the original signal could be recovered if it meets the Nyquist criterion. However, if the frequency of the signal is close to the sampling frequency, a low frequency sine wave will be reconstructed, and the frequency is equal to the difference of the two.

In this lab on aliasing effect, the sampling frequency is 20 Hz, and three original signals are tested with frequencies of 19 Hz, 20 Hz, and 21 Hz, respectively. First, the signal with 20 Hz is tested, and the result is a flat line, which is equivalent to the still car wheel. Second, the signals with 19 Hz and 21 Hz are tested, and the results are sine waves with frequency of 1 Hz, but there is a 180 degree phase shift between these two signals. This result explains the phenomena of forward and reverse rotating car wheels in the movies.

Citation
Format

Zhang, Y. (2021, July), Aliasing Effect Near Sampling Frequency Paper presented at 2021 ASEE Virtual Annual Conference Content Access, Virtual Conference. 10.18260/1-2--36659

TY - CPAPER
AB - Aliasing Effect Near Sampling Frequency

Natural signals picked up by various sensors are analog signals, which often need to be digitized for processing, storage, and transmission. Compared with the very high sampling rate of the electronic circuits, most of these analog signals change rather slowly. Therefore, the criterion of the sampling theorem are met, and the original signals can be reconstructed from the digitized signals. However, if the bandwidth of the original signal is beyond the Nyquist frequency, aliasing happens, and then the reconstructed signal will be distorted.

In many movies, people see that the wheels of a car seemingly rotate backward while the car is moving forward. As we know, the motions in movies are illusions of our eyes, which need at least 50 ms to perceive a picture. Based on this phenomenon, movies are shot and played at 24 frames per second. In other words, each frame takes less than 50 ms so that we are not able to see the still pictures. From the point of view of signal processing, the process of shooting a movie is like digitizing a signal at the sampling rate of 24 Hz. With our eyes serving as a lowpass filter, the original motion is perceived in the same way as the reconstructed signal.

When we watch a rotating wheel, our attention is on the spokes. For example, with a six-spoke wheel rotating at the speed of 4 revolution per second, the pictures of the wheel will be identical if shot at the rate of 24 frames per second. Therefore, the wheels rotating at this speed will look like still in the movie. If the rotating speed is a little lower, then it seems like that the wheel is rotating backward.

A lab was designed in the course of Signals and Systems to demonstrate this phenomenon, and Simulink was used for simulation. The original signal is a sine wave, and it is sampled by multiplying with a square wave with very low duty cycle, which is just like a pulse train. The sampled signal goes through a low pass filter, and the original signal could be recovered if it meets the Nyquist criterion. However, if the frequency of the signal is close to the sampling frequency, a low frequency sine wave will be reconstructed, and the frequency is equal to the difference of the two.

In this lab on aliasing effect, the sampling frequency is 20 Hz, and three original signals are tested with frequencies of 19 Hz, 20 Hz, and 21 Hz, respectively. First, the signal with 20 Hz is tested, and the result is a flat line, which is equivalent to the still car wheel. Second, the signals with 19 Hz and 21 Hz are tested, and the results are sine waves with frequency of 1 Hz, but there is a 180 degree phase shift between these two signals. This result explains the phenomena of forward and reverse rotating car wheels in the movies.

AU - Yumin Zhang
CY - Virtual Conference
DA - 2021/07/26
PB - ASEE Conferences
TI - Aliasing Effect Near Sampling Frequency
UR - https://peer.asee.org/36659
DO - 10.18260/1-2--36659
ER -