Why does the wheel on the screen look upside down?

When watching the wheels turn in movies and TV, you must not see the spokes continuously, but only at regular intervals. Because movies and TV pictures are discontinuous. Physiologically, as long as the frame rate of the picture we see is higher than 10~ 12 frames per second, our eyes can't distinguish between still pictures and dynamic pictures, and they will think that this is a coherent action. Movies are 24 frames per second, which means that they flash 24 frames per second, while TV is 25 frames per second. In other words, every few tenths of a second, your vision will be cut off because of the picture switching.

This illusion exists in this period of separation. There are three possible situations, let's study them one by one:

The first possibility is that in the time when the line of sight is cut off, the wheel has just had time to turn an integer circle. At this point, the position of the spokes of the wheel in the picture is exactly the same as that in the previous picture. Assuming that the speed of the car is constant and the wheel will turn an integer circle in the next same time interval, the position of the spokes is still the same as before. The spokes we see are always in the same position, so there will be the illusion that the wheels don't turn.

The second possibility is that in each time interval, the wheel not only has time to complete an integer circle, but also can turn a smaller half circle on this basis. When we see this changing picture, our eyes don't think there is an integer rotation here, but only see a small part of the wheel that turns too much, so it seems to us that the wheel turns very slowly, only a small part at a time, which looks very slow.

The third possibility is that in the time interval between two photos, the wheel has no time to turn a whole circle, and it is only a small part short of a whole circle; Or turn too fast, and you can turn more than half a turn after turning an integer circle. At this point, it seems to us that any spoke is turning in the opposite direction. This illusion will last until the wheel changes speed.

In information theory, this phenomenon is actually a manifestation of "aliasing". When we sample continuous signals at equal intervals, if the sampling theorem cannot be satisfied, the frequencies of the sampled signals will overlap, that is, the frequency components higher than half of the sampling frequency will be reconstructed into signals lower than half of the sampling frequency. Distortion caused by overlapping spectrum is called aliasing, and the reconstructed signal is called aliasing doubling of the original signal because the two signals have the same sample value. The wonderful phenomenon that the wheel does not rotate or even rotates backward is the aliasing caused by the overlapping of two signals sampled by the wheel and the camera.

In order to avoid this aliasing phenomenon, Nyquist, an American telecom engineer, put forward the sampling theorem in 1928, also known as Nyquist theorem. Nyquist theorem explains the relationship between sampling frequency and signal spectrum, which is the basic basis for discretization of continuous signals. It is pointed out that when the sampling frequency fs.max is more than 2 times of the highest frequency fmax in the signal, the sampled digital signal will completely retain the information in the original signal, and the sampling frequency is guaranteed to be between 2.56 and 4 times of the highest frequency of the signal in general practical application.

In other words, if we use a high-speed camera with higher frequency and sample and play at the same high frame rate, the phenomenon of wheel inversion will be eliminated. Of course, due to economic reasons, we rarely shoot or play an ordinary movie with such top-class equipment, but the theory derived from this theorem put forward by Nyquist has been applied to other aspects of our lives, such as noise reduction of music signals and anti-aliasing processing of video signals. This still makes our life better.