Some background about myself, I am an electrical and computer engineering in my junior year. I am interested in mathematical analysis in various fields $($real, complex, functional$)$ and have self studied them. I am currently being introduced to Fourier analysis in continuous-time and discrete-time domain in my signal processing course.
Therefore, I was wondering if someone can recommend me some excellent books/notes that maintain a rigorous introduction on Fourier Analysis with theorems and proofs and its applications dedicated to only signals and systems.
The purpose for this request is that I have seen many books (even famous ones like Stein's book) but they kind of diverge their focus and interest on PDEs mainly and other physical systems.
Edit : I have accepted Manlio's answer since it satisfies the requirements for my question. However, Any other recommendations are still welcomed and I would be also grateful. I also hope this question is beneficial to anyone who shares my question.
Best Answer
A possibility:
Gasquet, Claude; Witomski, Patrick, Fourier analysis and applications. Filtration, numerical calculus, wavelets, Enseignement des Mathématiques. Paris: Masson. xi, 355 p. (1995). ZBL0914.94001.
It explores several aspects of the theory, but has a lot of focus on applications and algorithms.