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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, communication systems and control 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. Switched capacitor systems, for instance, are often used in integrated circuits. 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 or PWM amplifiers, 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.

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Covers the analysis and properties of Linear Time-Invariant (LTI) systems.

Explores the implications of the Z-transform for Linear Time-Invariant (LTI) systems.

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Time-invariant system

In control theory, a time-invariant (TI) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is a function of the time-dependent input function. If this function depends only indirectly on the time-domain (via the input function, for example), then that is a system that would be considered time-invariant.

Time-variant system

A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior. Time variant systems respond differently to the same input at different times. The opposite is true for time invariant systems (TIV). There are many well developed techniques for dealing with the response of linear time invariant systems, such as Laplace and Fourier transforms.

Linear time-invariant system

In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).