| Line 1: | Line 1: | ||
| − | Given the following LTI system | + | Given the following LTI DT system |
| − | <math>\,s[t]= | + | <math>\,s[t]=x[t]+x[t-1]\,</math> |
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The unit impulse response is simply (plug a <math>\,\delta[n]\,</math> into the system) | The unit impulse response is simply (plug a <math>\,\delta[n]\,</math> into the system) | ||
| − | <math>\,h[n]= | + | <math>\,h[n]=\delta[n]+\delta[n-1]\,</math> |
| + | |||
| + | |||
| + | The system function can be found using the following formula (for LTI systems) | ||
| + | |||
| + | <math>\,H(z)=\sum_{m=-\infty}^{\infty}h[m]z^{-m}\,</math> | ||
== Part B == | == Part B == | ||
Revision as of 18:13, 25 September 2008
Given the following LTI DT system
$ \,s[t]=x[t]+x[t-1]\, $
Part A
Find the system's unit impulse response $ \,h[n]\, $ and system function $ \,H(z)\, $.
The unit impulse response is simply (plug a $ \,\delta[n]\, $ into the system)
$ \,h[n]=\delta[n]+\delta[n-1]\, $
The system function can be found using the following formula (for LTI systems)
$ \,H(z)=\sum_{m=-\infty}^{\infty}h[m]z^{-m}\, $
