Talk:Signals and Systems/Introduction

LTI
The introduction page starts discussing LTI systems without even expanding saying what 'LTI' stands for.

System ID
This material is duplicated from other material already found in this book. I am storing the text here for now. --Whiteknight (talk) (current) 21:30, 3 May 2006 (UTC)


 * Memory
 * A system with memory is any system where the output depends on more than just the current value of the input. For example, a system that averages the values of the last five seconds of input and gives that as its output demonstrates memory. Confusingly, a system that can predict the future (say, a function that gives the output you are going to give it in 2 seconds) also demonstrates memory.


 * Invertability:
 * An invertible system is any system where the original signal can be reproduced from the systems output.


 * Causality
 * A causal system is a system that depends only on the current and previous inputs. So a system that gets values from the future may have memory, but it is not causual.


 * Stability
 * A stable system will produce a finite output if the input is finite. An unstable system can create an infinitely big answer, for some finite input.


 * Time Invariance
 * A time invariant system is a system where the same input gives the same output, regardless of how long the system's been running for. An example of a time invariant system is an amplifier.


 * Linearity
 * A linear system scales the output in the same way as the input and is additive.

\forall x_1(t) \mapsto y_1(t), x_2(t) \mapsto y_2(t) \Longrightarrow a*x_1(t)+b*x_2(t) \mapsto a*y_1(t)+b*y_2(t) $$
 * Thus a linear systems responds with zero when the input is zero.