Questions and Comments for Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f

Please post your review, comments and questions below.

- Xiaozhe's review:

It's a great slecture, examples developed are in detail and the logic between the steps is quite clear. Also,it is very useful way to use properties of FT in solving practical problem. This slecture greatly helps me to understand the transformation from a function with variable ω (in rad/s) into another with variable f(in hertz).

- Review by John S.

The explanation of the first method for solving the first example problem is very concise. Unfortunately, you seem to skip over the work for the second method. I think it would be better if you showed more of the steps in the direct calculation including converting the cosine into exponentials and solution of the integral. In the second example, you should mention of use of the translation property used to quickly solve the integral. Overall, this slecture is cleanly organized. Good job!

- Review by Yerkebulan Y.

I think after you found FT of cos(w_{0}t) by changing variables you were supposed prove it by using ICTFT and get cos(w_{0}t) from its FT. Because you cannot directly use CTFT formula for cosine function, because of exponential integration.

- Review by Fabian Faes

I really enjoyed the fact that both the ECE301 and ECE438 usage of the CTFT and ICTFT were listed together enabling the comparison of the two, allowing a student to see the progression. Also very convenient in this Slecture is that there is a link to the table of further CTFT pairs. However I do agree with John S. that I wish that the second example had a few more steps shown since it was so easy to follow the first but it would be beneficial to have more steps for the second. In conlusion I would still say that this is a great Slecture.

- Review by Talha Takleh Omar Takleh:

I like how you approach this topic by comparing the difference in the formula between omega and frequency. The examples are good although, need more clarification on how you got your answer on the second example. Overall great slecture and it did provide me with a good understanding on the topic.

- Review by Soonho Kwon

The explanation of the content was very clear. Also, I like the orientation of the overall page. However, it would be better if there exists specific explanations in the example part. For an example, it would be better why 'w' is between 0 to 2pi.

- Review by Sahil Sanghani

I like how you review the differences between the formulas from 301 and 438. Your first example flows very well. However, I think that the second method could use a few more steps with an explanation. There are a couple intuitive jumps that could be elucidated.

- Review by Michel Olvera

I liked the fact that you included the comparison between the formulas used in ECE 301 and ECE 438. It is easy to follow the step by step solutions for the examples provided inspite of having skipped some details in the second one. Clarifying the solutions for the last example could be a nice improvement of your Slecture. Great job!

- Review by Randall Cochran

I liked that you compared the formulas for the Fourier Transforms in both the w and f forms. Showing a few more steps in the second example would help make it clearer.

- Review by Michael Hayashi

The examples you chose illustrated the Fourier transform well. A right arrow would help with the CTFT pair (in $ \omega $) in the first example, and the example seems to flow the wrong direction:

$ X(f) = \mathcal{X}(\frac{\omega}{2\pi}) $

would more clearly establish that we want to obtain answers in terms of frequcny in Hertz. Ending the second example with a statement about the bidirectional nature of Fourier transform pairs would give even greater power to your examples.

- Review by Ryan Johnson

I really like the example. It clearly illustrates the point that you are trying to make in your conclusion. Good job overall.

- Review by Robert Stein

Nice job. It's easy to follow. I might change the grammar in the conclusion section ("used change of variables" sounds strange). Also there is a missing period on the last sentence.

- Review by Ben Capano

Good work. I like how you included formulas learned in 301 and 438 and tied them together. You're missing a few arrows in terms of formatting but it's easy to follow the steps.