(New page: == Definition == A system characterized by a difference is given as: <math>\,\ \sum_{k=1}^N k^2 </math>) |
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== Definition == | == Definition == | ||
| − | A system characterized by a difference is given as: | + | A system characterized by a difference equation in DT is given as: |
| − | <math>\,\ | + | |
| + | <math>\, | ||
| + | \sum_{k=0}^N a_k\,y[n-k]=\sum_{k=0}^N b_k\,x[n-k] | ||
| + | </math> | ||
| + | |||
| + | We will likely be asked to solve for the frequency response <math>\,H(e^{j\omega})</math>, the unit impulse response <math>\,h[n]</math>, or the system's response to an input <math>\,x[n]</math>. | ||
| + | |||
| − | + | == Example 1 == | |
| + | Find <math>\,H(e^{j\omega})</math>, and <math>\,h[n]</math> for the following system in DT domain: | ||
| + | <math>\, | ||
| + | \frac{2}{5}y[n-1]+\frac{3}{5}y[n-3]+6y[n]=4x[n] | ||
</math> | </math> | ||
Revision as of 08:59, 24 October 2008
Definition
A system characterized by a difference equation in DT is given as:
$ \, \sum_{k=0}^N a_k\,y[n-k]=\sum_{k=0}^N b_k\,x[n-k] $
We will likely be asked to solve for the frequency response $ \,H(e^{j\omega}) $, the unit impulse response $ \,h[n] $, or the system's response to an input $ \,x[n] $.
Example 1
Find $ \,H(e^{j\omega}) $, and $ \,h[n] $ for the following system in DT domain:
$ \, \frac{2}{5}y[n-1]+\frac{3}{5}y[n-3]+6y[n]=4x[n] $
