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# Lecture 2: Transfer Functions

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Schedule :: Intro :: Inverse :: Properties :: Solution :: Transfer Functions :: System Realization :: Bilateral :: Frequency Response :: Rubber Sheet Geometry :: FIR Filters

Under the assumption of zero initial conditions (the zero-state response) the general LTI difference equation

may be transformed to
Solving for the output,
We define

as the transfer function . Note that

and the output is obtained by
The poles of the transfer function are the roots of the characteristic equation, and we can determine the stability of the system by examination of the transfer function.

If the input is , then the output is

So

The transfer function is the Z-transform of the impulse response.

Nomenclature . A discrete-time filter which has only a numerator part (only zeros, except for possible poles at the origin which correspond to delays) is said to be a finite impulse response (FIR) filter.

A filter with poles is said to be an infinite impulse response (IIR) filter.

Note that there is no practical way of making an FIR filter for continuous time systems: this is available only for digital filters.

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 17). Lecture 2: Transfer Functions. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/node5.html. This work is licensed under a Creative Commons License