Mathematical treatment of signals and systems

In summary, the person is looking for books on signals and systems that approach the subject from a mathematical perspective, specifically using linear algebra and functional analysis. They have searched through Amazon, book reviews, and course webpages, but have only found a few potential options that do not fully cover the desired material. They are seeking suggestions and comments on the books they have found.
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Hi there,

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.

Thanks!
 
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Related to Mathematical treatment of signals and systems

1. What is the purpose of mathematical treatment of signals and systems?

The purpose of mathematical treatment of signals and systems is to analyze, manipulate, and understand the behavior and characteristics of signals and systems using mathematical tools and techniques. This allows for the prediction, control, and optimization of signals and systems in various applications such as communications, control systems, and signal processing.

2. What are some common mathematical methods used in signal and system analysis?

Some common mathematical methods used in signal and system analysis include Fourier transforms, Laplace transforms, differential equations, and linear algebra. These methods allow for the representation, manipulation, and analysis of signals and systems in the time and frequency domains.

3. What is the difference between continuous-time and discrete-time signals and systems?

Continuous-time signals and systems are defined and operate over a continuous range of time, while discrete-time signals and systems are defined and operate over a discrete set of time values. This distinction is important in the mathematical treatment of signals and systems as it affects the types of mathematical tools and techniques that can be used.

4. How are signals and systems represented mathematically?

Signals can be represented mathematically as functions of time or space, while systems can be represented as mathematical operators that transform signals. These representations allow for the use of mathematical tools and techniques to analyze and manipulate signals and systems.

5. What are some applications of mathematical treatment of signals and systems?

Some common applications of mathematical treatment of signals and systems include signal processing, communication systems, control systems, and image and audio processing. These applications rely on the analysis, manipulation, and optimization of signals and systems for efficient and effective functioning.

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