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Questions and Comments for Discrete Time Fourier Transform with Example

A slecture by ECE student Jacob Holtman



Please post your reviews, comments, and questions below.



  • Review by Miguel Castellanos

You are clear about your thought process in both proving the periodicity property and computing a DTFT. This can be helpful because those general concepts can be applied to other similar problems. I also like your use of color to indicate the what term in the expression your are talking about. In your second computation, remeber that the DTFT is a continous function and therefore you must use the continous delta function, which is infinity (not 1) at a single point. Good job overall!


  • Review by Fabian Faes

I enjoy the flow of this Slecture and the use of color to highlight the use of certain variables in equations. I also enjoy that the Slecture is short and sweet which makes it easy read and process. If there was one caveat I comment on it would be that in the last line that the DTFT of the complex exponential is repeated every 2*pi. Other than that is a great lecture, good job!


  • Review by Michel Olvera

What I liked most about your Slecture was the use of color to emphasize the replacements in equations, since it is really helpful to clearly see and understand what you are talking about. Great job!


  • Review by David Klouda

Great use of color for the equations. It made the page feel as if someone were showing it to me in person rather than a computer screen, almost like a tutor. My only recommendation would be to organize your sections a little more to create a good flow through the document as well as outline the main points of each section.


  • Review by Soonho Kwon

Making this slecture with a few different colors to emphasize the exponential and the delta values. The overall slecture felt a little bit short in lengthwise, however, this slecture clearly explained the topic. Nicely done!

Author answer here


  • Review by Botao Chen

I really appreciate the use of different color to show the importance and point to notice in your demonstration. Because it is just something I could potentially miss. Thanks for pointing that out to me. And if you could provide some graphs it will be better for others to understand your examples.

Author answer here


  • Review by Yerkebulan Y.

DTFT and i DTFT equations are given at the beginning. Periodicity property was explained clearly step by step. Showed that DTFT of exponential cannnot be found from directly from DTFT equation, so iDTFT was used. Perfect !


  • Review by Yijun Han

This slecture clearly states the definition and periodic property of Discrete-time Fourier transform. In the exponential example, it's great to make a guess and prove the guess is right. Good job.


  • Review by Xian Zhang

Good job. The slecture clearly stated the definition of the DTFT and an example of complex exponential. I think it might be better and more organized if you add overview section in the front so that the reader will have a basic idea about what you are going to talk about.



  • Review by Chloe Kauffman

I think an important aspect that you did not include in your final answer is that the DTFT of a DT signal must be periodic. Your answer must be "rep-ed" to denote it's periodicity. Otherwise your answer is only correct for o<=w<=2pi.
The DTFT of x[n] is $ rep_{2\pi}( $2πδ(ω − ω0))

Overall color coating was very helpful, and the slecture was concise and clear.


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Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

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