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]\! $
