Random Processes in Linear Systems

In this chapter, we consider the response of both continuous time and discrete-time linear systems to random processes, such as a signal plus noise. We develop statistical descriptions of the output of linear systems with random inputs by viewing the systems in both the time domain and the frequency domain. An engineering application section at the end of this chapter demonstrates how filters can be optimized for the purpose of enhancing signal-to-noise ratios. It is assumed that the reader is familiar with the study of linear time-invariant (LTI) systems. A brief overview is provided in Appendix C for those needing a refresher.

11.1 Continuous Time Linear Systems

Consider a linear time-invariant ...

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