I am looking for books that treat signals and systems from a mathematical perspective. When I say "signals and systems", I am referring to the typical second/third year material taught in EE programs: system characteristics (causality, memory, stability), LTI systems, linearization, feedback, state-space models, continuous- and discrete-time signals, Laplace and Fourier transforms, Z- and discrete-time Fourier transforms, spectral densities, sampling and so on. The books I am in search of should ideally treat the aforementioned subjects from a linear algebra/functional analysis point-of-view.
Browsing through Amazon, book reviews and countless course webpages has turned up the following:
- Signal Analysis (Allen and Mills) - looks at signals in vector spaces and even discusses some wavelets, but doesn't cover systems/basic controls
- Modern Signals and Systems (Kwakernaak and Sivan) - reviews tell me that this is what I need, but I haven't been able to get hold of a preview or a library copy
- Signal Theory (Franks) - once again, only looks at signals, and I can't come across a preview/copy
Does anyone have any other suggestions? Any comments on the books I listed above are also appreciated.