Summary and Info
I'm an electrical engineer, with a focus in signal processing. This is the book I learned Fourier analysis from, and once I did, the classes that EEs usually dread were relatively easy for me. This is the only textbook I actually read every chapter of (and we only covered the first half in the Fourier analysis course). Kammeler writes in a conversational style, which I like in a text, and goes through many practical examples in math, physics, and engineering. I appreciated the rigor devoted to generalized functions (Dirac deltas are almost always glossed over in engineering texts, and thus remain mysterious and sometimes non-sensical), yet Kammeler always keeps intuition close by so it's relatively easy to follow if you're not a mathematician. The parts I didn't like were when Kammeler fell back on more elementary yet more complicated presentations to avoid introducing too many new concepts. For example, I think the FFT is most easily understood with Z-transforms and multirate systems, and that Fourier analysis in general is more easily understood in terms of Hilbert spaces. It's hard to fault him for it though, because it's primarily a math book and needs to be mostly self-contained. It's also typeset in LaTeX, and looks beautiful.