我一直在尝试学习麻省理工学院的生物医学信号处理课程，我认为最好的学习方法是解决一些问题。尽管它们可能超出了我的理解范围，但我并不是在寻找快速的答案，而是要了解问题以及如何弥补我在该领域的知识空白。具体来说，我想解决这个问题：

If you have ever seen a Western, you must have noticed that, as the stagecoach changes
speed, the wheel appears to reverse direction even though the coach moves forward. This
is an example of aliasing. The sampling mechanism is the movie camera capturing images
at a frequency of 24 frames/second. The eye acts as a lowpass filter, in the sense that
successive images reaching the eye at a rate exceeding 10 images/second appear as if they
are superimposed. This is called the critical fusion frequency.
Answer the following questions assuming that the wagon wheel is 1.6 m in diameter and has
12 spokes.

(a) Express the true angular velocity of the wheel (in radians/second) as a function of the
coach velocity.

(b) At what set of coach velocities does the wheel appear to reverse direction?

(c) Determine an expression for the apparent angular velocity of the wheel as a function of
the coach velocity.

(d) How many spokes does the wheel appear to have the first time it appears to reverse
direction? The second time? Explain the difference between these two cases.

我想我理解混叠，由于采样率的低频，它导致输出信号的频率低于实际频率，为了解决这个问题，需要一个低通滤波器。然而，我正在努力开始解决这个问题，因为我被困在第一个问题上，即将车轮的真实角速度表示为教练速度的函数。

因此，如果有人可以就我应该如何解决这些问题向我提供一些提示或某种指南，我将非常感激。

编辑：我想我想多了（a），它看起来很简单。所以这意味着车轮的角速度只是教练的速度除以车轮的半径，在这种情况下为 0.8 m。