Some thoughts on teaching signals and systems

I’m teaching Linear Systems and Signals[*] (ECE 345) this semester at Rutgers. The course overall has 260+ students, split between two sections: I am teaching one section. This is my second time teaching it: last year I co-taught with Vishal Patel (who has decamped to Hopkins), and this semester I am co-teaching with Sophocles Orfanidis. I inherited a bit of a weird course: this is a 3-unit junior-level class with an associated 1-unit lab (ECE 347). Previous editions of the course had no recitations, which boggled my mind, since the recitation was where I really learned the material when I took the course (6.003 at MIT, with Greg Wornell as my recitation instructor). How are you supposed to understand how to do all these transforms without seeing some examples?

So this year we have turned ECE 347 into a recitation and moved the coding/simulation part of the course into the homework assignments. Due to the vagaries of university bureaucracy, however, we still have to assign a separate grade for the recitation (née lab). Moreover, there are some students who took the class without the lab and now just need to take 347! It’s a real mess. Hopefully it’s just one year of transition but this is also the year ABET [**] is showing up so we’ll see how things go.

After surveying a wide variety of textbook options for the course, we decided to go with the brand-new and free book by Ulaby and Yagle, Signals and Systems: Theory and Applications [***]. I really have to commend them on doing a fantastic job and making the book free, which is significantly better than \$247 for the same book I used literally 20 years ago when I took this course. Actually, we mainly used another book, whose title/author eludes me now, but it had a green slipcover and was more analog control-focused (perhaps since Munther Dahleh was teaching).

One major difference I noticed between textbooks was the order of topics. Assuming you want to do convolution, Laplace (L), Z, Fourier Series (FS), and Fourier Transforms (FT), you can do a sort of back and forth between continuous time (CT) and discrete time (DT):

CT convolution, DT convolution, CTFS, DTFS, CTFT, DTFT, Laplace, Z
CT convolution, DT convolution, Laplace, Z, CTFS, DTFS, CTFT, DTFT

or do all one and then the other

CT convolution, Laplace, CTFS, CTFT, DT convolution, Z, DTFS, DTFT
DT convolution, Z, DTFS, DTFT, CT convolution, Laplace, CTFS, CTFT

I like the alternating version because it emphasizes the parallels between CT and DT, so if you cover sampling at the end you can kind of tie things together. This tends to give students a bit of whiplash, so we are going for:

CT convolution, DT convolution, Laplace, Z, CTFS, CTFT, DTFS, DTFT

It’s all a bit of an experiment, but the thing I find with all textbooks is that they are never as modular as one might like. That’s good for a book but maybe not as good for a collection of curricular units, which in the end is what a S & S [****] class is. CNX is one type of alternative, or maybe something like the interactive book that my colleague Roy Yates dreams of.

I find myself questioning my own choices of ordering and how to present things in the midst of teaching — it’s tempting to experiment mid-stream but I have to tamp down the urges so that I don’t lose the class entirely.

[*] You can tell by the word ordering that it was a control theorist who must have named the course.

[**] Accreditation seems increasingly like a scam these days.

[***] You can tell by the word ordering where the sympathies of the authors lie.

[****] Hedging my bets here.

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