System Analysis - LTI Systems

LTI Systems

As mentioned above, there are many methods of analysis developed specifically for LTI systems. This is due to their simplicity of specification. An LTI system is completely specified by its transfer function (which is a rational function for digital and lumped analog LTI systems). Alternatively, we can think of an LTI system being completely specified by its frequency response. A third way to specify an LTI system is by its characteristic linear differential equation (for analog systems) or linear difference equation (for digital systems). Which description is most useful depends on the application.

The distinction between lumped and distributed LTI systems is important. A lumped LTI system is specified by a finite number of parameters, be it the zeros and poles of its transfer function, or the coefficients of its differential equation, whereas specification of a distributed LTI system requires a complete function

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LTI System Theory - Overview
... The defining properties of any LTI system are linearity and time invariance ... that the relationship between the input and the output of the system is a linear map If input produces response and input produces response then the scaled and summed input produces the scaled and summed response where ... Time invariance means that whether we apply an input to the system now or T seconds from now, the output will be identical except for a time delay of the T seconds ...

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