
"Understanding Digital Signal Processing, 3/e is simply the best practitioner's resource for mastering DSP technology. Richard Lyons has thoroughly updated and expanded his best-selling second edition, building on the exceptionally readable coverage that has made it a favorite of both professionals and students worldwide. Lyons achieves the perfect balance between practice and math, making DSP accessible to beginners without ever oversimplifying it, and offering systematic practical guidance for day-to-day problem-solving. Down-to-earth, intuitive, and example-rich, this book helps readers thoroughly grasp the basics and quickly move on to more sophisticated DSP techniques. Coverage includes: discrete sequences/systems, DFT, FFT, finite/infinite impulse response filters, quadrature (I/Q) processing, discrete Hilbert transforms, sample rate conversion, signal averaging, and much more. This edition adds extensive new coverage of FIR and IIR filter analysis techniques. The previous multirate processing, and binary number format, material has been significantly updated and expanded. It also provides new coverage of digital differentiators, integrators, and matched filters. Lyons has also doubled the number of DSP tips and tricks as in the previous edition including techniques even seasoned DSP professionals may have overlooked. He has also added end-of-chapter homework problems throughout to support college instruction and professional self-study."--Publisher's website.
Those changed my life, in a sense. Not my professional life, but outside of work it led me down a deep rabbit hole into mathematics, digital signal processing, and even analogue electronics and some light RF engineering. (This is not relevant to my professional life, since I started to take great care not to make any more of my hobbies my job.)
I spent endless hours thinking about this stuff on my commute, and hunched over Matlab.
The other book I recommend is Richard G. Lyons "Understanding Digital Signal Processing".
Also [2] is a decent book for overall dsp concepts.
[1] DAFX - Digital Audio Effects (Second Edition) Edited by Udo Zölzer https://dafx.de/DAFX_Book_Page_2nd_edition/index.html
[2] Understanding Digital Signal Processing, Richard Lyons
i think it may even discuss the integer multiple issue you speak of with nice illustrations of the "wrapping" effect.
I think the fundamental problem is that:
1) there isn't a whole lot of comfort with complex numbers generally, so getting rid of them makes the material seem more approachable - at the cost of being significantly more complicated, and
2) a lack of good resources for implementing common DSP algorithms in actual hardware. The jump from Matlab to raw C is mystifying to many people (myself included in many cases).
I actually prefer Lyons's Understanding Digital Signal Processing as an intro text over this one.
I also really benefitted from having a good teacher in this stuff. Dan Boschen with DSPrelated runs some great online classes on DSP that helped me immensely in understanding this material. About $200 for five classes, with tons of great iPython notebooks of examples. (He was the one who helped me get the "all math works the same at baseband" advantage of complex numbers.)
For intellectual ability: it wasn't a particular book, but it was an honors-level Real Analysis class that forced me to re-learn the way I learn mathematics.