Question

Task 1) For this task, you will be apply, the concepts of sampling theory to understand how aliasing impacts measured data Assume you need to check the drive belt on a lawn mower that is rotating at 2000 rpm. What is the necessary camera frames per second (fps) to correctly measure the rotational frequency of this belt system? What is the Nyquist frequency? tsampling Hz (or equivalently frames per second) Hz (or equivalently frames per second) Calculate the frequency of the reconstructed signal if a lower sampling frequency of 30 fps is used rpm Note: Please pay attention to units throughout this assignment. When talking about aliasing of signals, we often use units such as: "samples", "cycles", "Hz", etc. When talking about videos, the following are equivalent - samples/second (Hz) - d rev/sec cycles/secon cycles/sample rev/frame

Answer 1

The rotational speed of the lawn mower is 2000rpm = 33.33 rotations/sec

According to samping theorm, the sampling frequency should be atleast twice the maximum frequency of the signal that is being sampled.

In this case the frequency of the signal is 33.33 Hz. Therefore, f_sampling = 2*33.33 = 66.66Hz. In other words, the camera should have atleast 66.66 fps.

Nyquist frequency is half the sampling frequency. Therefore, f_NYQ = 66.66/2 = 33.33 Hz

If a lower fps of 30 is used, the sampling frequency is 30Hz. Since, the frequency of the signal is greater than sampling rate. the frequency of the new signal can be found out using the following formula:

n Jsampling

where n is the maximum value of integer such that f is greater than or equal to zero.

> f 33.3-1 * 30 3.33Hz