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Signal Processing I: Introducing Complex Numbers, the Fourier Series and Fourier Transform

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Tags: fourier-seriestaylor-seriescomplex-numberssignal-processingfourier-transformconvolutionseulers-formulak-spacefftshort-time-fftpeer-teachingopen-educationr-code

Introduction into basics of signal processing, beginning with complex numbers, the Fourier series and Fourier transform (1D/2D), and with more topics along the way, such as Taylor/Maclaurin series, convolutions, signal filtering and more. The tutorial script comes with over 2700 lines of R code, reproducing most of the discussed formulas and algorithms with hand-written code representations, entails three example images, including a magnetic-resonance image (MRI, magnitude image), and around 240 R plots. The tutorial is not written for absolute beginners and requires some basics in R (which we provide on our website though), but it can also be read without executing code, since all results are provided in the tutorial as well. It is mostly written for non-mathematician students, interested in or working with some form of applied mathematics and physics, and which are interested in engaging with interdisciplinary open educational peer-teaching projects.

https://doi.org/10.56776/abbd964d.31b0ea29

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5 Overall score*

54 Rank

7 Votes

3 Comments

Comments

6.5

While it is nicely done and I appreciate approach from application, it would be nice if it was either more focused topic or if it was done in multiple parts. I don’t know if it fits here, I feel like the breadth of it is too much to be considered here, but also that making it more concise would obfuscate material for large part of audience.

I think it should go over less content, complex numbers part would probably end up being cut if it was up to me.

I actually liked this article a lot! But, I think an important tenet of teaching is that for someone who is seeing this for the first time it needs to be digestible, and this is really really dense. It’s not easy for someone who’s new to chew through. Only because I’ve seen some of these things before was I able to really understand it. In that sense, it’s a very complete article, but as an explainer/teacher, it falls short in my opinion.

3.7

The application of FFT and IFFT to MRI image processing was very nice. Good examples and imaging. Overall, this entry bit off more than it could chew. By tackling so much, it made it hard to get through and follow to the end. Indeed, the motivation and goals were stated in the beginning but would have benefited from focusing on less. Also, for this entry for SoME, it would make more sense to focus on the paper’s own explanation and not so much referencing to what I agree are excellent tutorials by Welch labs and 2blue1brown for example.