(New page: ==Memoryless System== A system is memoryless if for any <math> t \in \mathbb{R} </math> the output at <math> t_0 \, </math> depends only on the input at <math> t_0 \, </math>) |
m (Grammar corrections) |
||
| (6 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| + | =Basic System Properties ([[ECE301]])= | ||
| + | ---- | ||
==Memoryless System== | ==Memoryless System== | ||
A system is memoryless if for any <math> t \in \mathbb{R} </math> the output at <math> t_0 \, </math> depends only on the input at <math> t_0 \, </math> | A system is memoryless if for any <math> t \in \mathbb{R} </math> the output at <math> t_0 \, </math> depends only on the input at <math> t_0 \, </math> | ||
| + | |||
| + | In other words it doesn't depend on past or future events or information. | ||
| + | |||
| + | ==System With Memory== | ||
| + | |||
| + | A system has memory its output at any given time depends somehow on either a past and/or future event or piece of information. | ||
| + | |||
| + | ==Causal System== | ||
| + | |||
| + | A system is causal if its output at any time doesn't depend on a future event/piece of information. In other words its output at any given time only depends on past or present events/information. | ||
| + | |||
| + | ==Non-Causal System== | ||
| + | |||
| + | Any system whose output at any given time depends on a future event or piece of information isn't a causal system. | ||
| + | |||
| + | |||
| + | ==Linear System== | ||
| + | |||
| + | A system is linear if it upholds both additivity and multiplicity. | ||
| + | |||
| + | In mathematical terms the following must be satisfied: | ||
| + | |||
| + | |||
| + | |||
| + | <math>y[a+b]=y[a]+y[b] \,</math> | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | <math>y[ka]=ky[a] \,</math> | ||
| + | |||
| + | |||
| + | ==Non-Linear System == | ||
| + | |||
| + | A system is called non-linear if it doesn't uphold BOTH the additive and multiplicity properties. | ||
| + | |||
| + | ==Time-Invariant System== | ||
| + | |||
| + | A system is called time-invariant if for any input <math>x(t)\,</math> at time <math> t \in \mathbb{R} </math> the shifted input <math>x(t-t_0)\,</math> yields response <math>y(t-t_0) \,</math> | ||
| + | |||
| + | |||
| + | ==Time-Variant System== | ||
| + | |||
| + | |||
| + | A system is called time-variant if for any input <math>x(t)\,</math> at time <math> t \in \mathbb{R} </math> the shifted input <math>x(t-t_0)\,</math> response ISN'T equal to <math>y(t-t_0) \,</math> | ||
| + | |||
| + | ==Stable System== | ||
| + | |||
| + | A system is stable if in CT its impulse is absolutely integrable. That is: | ||
| + | |||
| + | <math>\int_{-\infty}^{\infty} \begin{vmatrix} h(\tau)\end{vmatrix}\, d\tau \ll \infty</math> | ||
| + | ---- | ||
| + | ---- | ||
| + | [[Homework_3_ECE301Fall2008mboutin|Back to HW3]] | ||
| + | |||
| + | [[Main_Page_ECE301Fall2008mboutin|Back to ECE301 Fall 2008]] | ||
Latest revision as of 08:07, 6 October 2011
Contents
Basic System Properties (ECE301)
Memoryless System
A system is memoryless if for any $ t \in \mathbb{R} $ the output at $ t_0 \, $ depends only on the input at $ t_0 \, $
In other words it doesn't depend on past or future events or information.
System With Memory
A system has memory its output at any given time depends somehow on either a past and/or future event or piece of information.
Causal System
A system is causal if its output at any time doesn't depend on a future event/piece of information. In other words its output at any given time only depends on past or present events/information.
Non-Causal System
Any system whose output at any given time depends on a future event or piece of information isn't a causal system.
Linear System
A system is linear if it upholds both additivity and multiplicity.
In mathematical terms the following must be satisfied:
$ y[a+b]=y[a]+y[b] \, $
$ y[ka]=ky[a] \, $
Non-Linear System
A system is called non-linear if it doesn't uphold BOTH the additive and multiplicity properties.
Time-Invariant System
A system is called time-invariant if for any input $ x(t)\, $ at time $ t \in \mathbb{R} $ the shifted input $ x(t-t_0)\, $ yields response $ y(t-t_0) \, $
Time-Variant System
A system is called time-variant if for any input $ x(t)\, $ at time $ t \in \mathbb{R} $ the shifted input $ x(t-t_0)\, $ response ISN'T equal to $ y(t-t_0) \, $
Stable System
A system is stable if in CT its impulse is absolutely integrable. That is:
$ \int_{-\infty}^{\infty} \begin{vmatrix} h(\tau)\end{vmatrix}\, d\tau \ll \infty $
