
"Master the basic concepts and methodologies of digital signal processing with this systematic introduction, without the need for an extensive mathematical background. The authors lead the reader through the fundamental mathematical principles underlying the operation of key signal processing techniques, providing simple arguments and cases rather than detailed general proofs. Coverage of practical implementation, discussion of the limitations of particular methods and plentiful MATLAB illustrations allow readers to better connect theory and practice. A focus on algorithms that are of theoretical importance or useful in real-world applications ensures that students cover material relevant to engineering practice, and equips students and practitioners alike with the basic principles necessary to apply DSP techniques to a variety of applications. Chapters include worked examples, problems and computer experiments, helping students to absorb the material they have just read. Lecture slides for all figures and solutions to the numerous problems are available to instructors"
Applied Digital Signal Processing by Manolakis & Ingle is the book I always turn to for reference and the code examples don't suck. Oppenheim & Schafer is a classic but frankly only useful as a reference, that tome is a bit dated otherwise. The Scientists and Engineer's guide to DSP is also not bad as a practical text.
- Oppenheim & Schafer Discrete Time Signal Processing (the Bible of DSP)
- Manolakis & Ingle, Applied Digital Signal Processing (good discussion of orthogonal transforms).
A lot of what I know about transform analysis comes from self study of linear algebra/vector spaces with some reading here and there in commonly cited papers. Might want to pick up a text on that subject, it's the same idea but more rigor than an engineer would use.
There's also a book I haven't worked all the way through yet and is dated, heavily based in EE concepts (non negligible amount of circuit theory) and extremely rigorous called Theory of Linear Physical Systems by Ernst Guilleman. I picked it up last week actually and quite like it.
It has a lot of information and approaches with Fourier/Laplace methods, which is interesting since it predates the FFT and has so much information on concepts that engineers 50 years ago would need to build their intuition with instead of through tooling. I picked it up for the network theory/dynamical systems angle (which relates to some stuff I'm working on) but the rigor is definitely higher than what you'd see in those more digestible books.