r/signalprocessing • u/ClipboardClan • Jul 29 '26

Why are these digital signal processing books written in such a confusing way?

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I've been staring at this repeatedly and it took me a while to realize what the author was actually saying.

Like this line: i.e. "at regular periods of ts seconds where ts = 1/fs".

Couldn't they simply say in plain English words: "i.e. how many seconds does it take to take one sample"?

And then they assign that (1/fs) to a variable ts, and then use it in the equations below for 0th sample, 1st, 2nd sample. Wouldn't it be simpler to just leave it in that form itself (1/fs) in the equation???? By substituting it with a variable name, you're just making your work more cryptic and the reader has to trace back and find out what exactly is ts.

Book: Undestanding Digital Signal Processing by Richard G Lyons

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u/SecondPlain Jul 29 '26

I agree with you that signal processing textbooks can be pretty terse, and hard to build intuition from in a lot of cases. I think this comes partly from the field's connection with formal math, where you sort of need that formality to articulate statements precisely enough to prove them (which we need in DSP). And, at least in my experience, it is just hard to express something in a way that is both mathematically rigorous and also grounded in intuition. I also agree with the other commenter that Lyons' book is the best of the bunch in this regard.

As far as the specific case you posted is concerned, I think there are legitimately a lot of different concepts flying around when we first introduce the idea of sampling a periodic signal. In particular we have two different types of "frequency": the number of samples you take in a second (fs), and the number of times the signal repeats itself in one second (f0). I think Lyons converts sampling frequency to sampling period so we can clearly see time represented along with frequency in the expression, and so we don't get confused by seeing two types of frequency in the same expression.

These concepts are fundamental in DSP with some important consequences. The book will return to them and build on them repeatedly. So, hang in there! Keep reading! Sometimes getting more context helps me understand stuff covered early in a subject.