Worked Problem Assignment 6#

Due 10 Nov 23

We have shown that we can use a Fourier Transform to decompose a function into its frequency components. We’ve graphed the solutions, and we’ve seen how we can construct signals with certain properties. In this assignment, you are asked to use these tools to solve a problem of your choosing. Consider a scenario where a signal of some sort is being generated and you want to understand the frequency content of the signal. You can use the tools we have developed to do this.

Updated Rubric

Remember that a worked problem means the scale of a detailed (e.g., parts a-h) homework problem.

Starting your Analysis#

You will need to orient us to your problem as there are many potential signals. You will need to develop an analytical tractable situation that can also be explored using the numerical methods we have developed. You will need to do the following:

  1. Write a paragraph or two describing the system you are investigating. Make sure to explain the parameters and variables.

  2. Explain what you are going to do and why. If you can point us to where things are being done, that’s helpful.

  3. You need to clearly set up your analytical problem. This means write down and explain the equations you are constructing.

Investigating the System#

After you set things up, please conduct an investigation using the tools we have developed in class. The order in which it proceeds is up to you, but make sure the flow is logical and clear. We want to understand how your investigations are going to help you be successful with your projects.

Assignment#

  1. Choose a signal or set of signals to investigate (these should be continuous functions of time)

  2. Write a paragraph or two describing the system you are investigating. Explain what you are going to do and why. If you can point us to where things are being done, that’s helpful.

  3. Conduct your analysis of the signal (you may do so analytical and/or numerically). If you are using numerical approaches, don’t yet use the fft function. You should be able to do this with the tools we have developed in class.

  4. Graph the results of your analysis and explain what you have found.

Looking ahead (earn extra credit)#

If you are looking into these systems and finding them interesting here’s two things you can do to earn extra credit.

  1. Compare your analysis of several signals and compare their frequency content. What do you notice?

  2. (challenging) Develop a way to filter out certain frequencies. And then reconstruct the signal. What do you notice? Have you kept the proper phase information?

Submitting your work#

You will upload your work to D2L. It should be a single PDF of your work. If you also write code, please submit the associated files as well. If you do all of this in a Jupyter notebook, please export the notebook as a PDF and submit the notebook and PDF file. If you have any questions, please ask. We want you to enjoy working on these problems.