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== Finding the Frequency Response from a Difference Equation == | == Finding the Frequency Response from a Difference Equation == | ||
| − | If we are given a system defined by a difference equation, it is possible to find the frequency response (actually it is quite simple to find the frequency response). | + | If we are given a system defined by a difference equation, it is possible to find the frequency response (actually it is quite simple to find the frequency response). An example of this is given below. |
=== Example === | === Example === | ||
| + | <math>y[n] + 2y[n-1] - \frac{1}{2}y[n-3] + y[n-4] = x[n]\!</math> | ||
Revision as of 10:20, 23 October 2008
Difference Equations
DT systems described by linear constant-coefficient difference equations are very important to the practice of signals and systems. They are of special importance when implementing filters. These equations are of the form:
Finding the Frequency Response from a Difference Equation
If we are given a system defined by a difference equation, it is possible to find the frequency response (actually it is quite simple to find the frequency response). An example of this is given below.
Example
$ y[n] + 2y[n-1] - \frac{1}{2}y[n-3] + y[n-4] = x[n]\! $
