System analysis

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System analysis in the field of electrical engineering characterizes electrical systems and their properties. System Analysis can be used to represent almost anything from population growth to audio speakers, electrical engineers often use it because of its direct relevance to many areas of their discipline, most notably signal processing and communication systems.


Characterization of systems

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:

  • SISO (Single Input, Single Output)
  • SIMO (Single Input, Multiple Outputs)
  • MISO (Multiple Inputs, Single Output)
  • MIMO (Multiple Inputs, Multiple Outputs)

It is often useful (or necessary) 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:

  • Signals that are continuous in time and continuous in value are known as analog signals.
  • Signals that are discrete in time and discrete in value are known as digital signals.
  • Signals that are discrete in time and continuous in value are called discrete-time signals. While important mathematically, systems that process discrete time signals are difficult to physically realize. The methods developed for analyzing discrete time signals and systems are usually applied to digital and analog signals and systems.
  • Signals that are continuous in time and discrete in value are sometimes seen in the timing analysis of logic circuits, but have little to no use in system analysis.

With this categorization of signals, a system can then be characterized as to which type of signals it deals with:

  • A system that has analog input and analog output is known as an analog system.
  • A system that has digital input and digital output is known as a digital system.
  • Systems with analog input and digital output or digital input and analog output are possible. However, it is usually easiest to break these systems up for analysis into their analog and digital parts, as well as the necessary analog to digital or digital to analog converter.

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!).

  • Memoryless systems do not depend on any past input.
  • Systems with memory do depend on past input.
  • Causal systems do not depend on any future input.
  • Non-causal or anticipatory systems do depend on future input.
    Note: It is not possible to physically realize a non-causal system operating in "real time". However, from the standpoint of analysis, they are important for two reasons. First, the ideal system for a given application is often a noncausal system, which although not physically possible can give insight into the design of a derivated causal system to accomplish a similar purpose. Second, there are instances when a system does not operate in "real time" but is rather simulated "off-line" by a computer, such as post-processing an audio or video recording.
    Further, some non-causal systems can operate in pseudo-real time by introducing lag: if a system depends on input for 1 second in future, it can process in real time with 1 second lag.

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