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System analysis

System analysis is the branch of electrical engineering that characterizes electrical systems and their properties. Although many of the methods of system analysis can be applied to non-electrical systems, it is a subject often studied by electrical engineers because it has direct relevance to many other areas of their discipline, most notably signal processing.

A system is characterized by how it responds to input signals. In general, a system has one or more input signals and one or more output signals. Therefore, one natural characterization of systems is by how many inputs and outputs they have:

It is often useful to break up a system into smaller pieces for analysis. Therefore, we can regard a SIMO system as multiple SISO systems (one for each output), and similarly for a MIMO system. By far, the greatest amount of work in system analysis has been with SISO systems, although many parts inside SISO systems have multiple inputs (such as adders).
Signals can be continuous or discrete in time, as well as continuous or discrete in the values they take at any given time: A system can be characterized as to which type of signals it deals with: Another way to characterize systems is by whether their output at any given time depends only on the input at that time or perhaps on the input at some time in the past (or in the future!). Yet another way to characterize systems is by certain properties which facilitate their analysis: There are many methods of analysis developed specifically for linear, time-invariant, deterministic systems. Unfortunately, in the case of analog systems, none of these properties are ever perfectly achieved. Linearity implies that operation of a system can be scaled to arbitrarily large magnitudes. Time-invariance is violated by aging effects that can change the outputs of analog systems over time (usually years or even decades). Thermal noise and other random phenomena ensure that the operation of any analog system will have some degree of stochastic behavior. Despite these limitations, however, it is usually reasonable to assume that deviations from these ideals will be small.

Some important concepts in system analysis are the transfer function, feedback and stability, frequency response, steady-state and transient behavior, filters, and noise.