
If you're looking for deeper explanations, I recommend "Practical Signal Processing": https://www.amazon.com/Practical-Signal-Processing-Mark-Owen...
Many of the chapters are here: https://battle.shawwn.com/sdb/books/PSP/ but buy the book if you can afford to.
In particular, Chapter 4's "untwisting" intuition is the best I've found: https://imgur.com/a/r7KvO60
Another way of phrasing it: You know that effect when a wheel is spinning so fast, it looks like it's going backwards? If it looks like it's standing still, there's a Fourier coefficient at that rotational frequency.
... Or at least, I think there is. It's hard to be precise with analogies.
It's gonna fall near the extreme end of succinctness.
I had since purchased the book but haven't gone more than a couple chapters deep. It definitely looks like it allows you to dive into the meat of DSP. Don't know if it will fit the bill for rigorous.
I also didn't pay anything near what it's currently listing for on Amazon.
I remember two introductory books which were quite good - Kamen/Heck's 'Signals and Systems' - tells you a bit about the tools of the trade, laplace and fourier transforms, transfer functions, filter design &c - the book was accompanied by a number of MatLab scripts which let you visualise how manipulating properties of a filter affected the output; most useful.
Proakis & Manolakis' Digital Signal Processing was also quite good; both books assume you know your way around engineering mathematics - series, integrals mostly - but in particular Kamen/Heck I remember provoking quite a number of insights from the text alone.
Again, the ARRL may be of some assistance - the radio amateur's handbook has a couple of chapters on the basics of filters, leaning very much against the applied end of things.
I hear good things about Owen's Practical Signal Processing, too, but haven't studied it myself yet; as you say, there's only so much time in a day...
Oh, and steer clear of anything with the phrase 'non-linear' anywhere in the title or blurb. Just don't go there.