本文仅供学习使用
本文参考:
B站:DR_CAN
线性时不变系统 : LIT System
冲激响应:Impluse Response
卷积:Convolution
运算operator : O { ⋅ } O\left\{ \cdot \right\} O{
⋅}
I n p u t O { f ( t ) } = o u t p u t x ( t ) \begin{array}{c} Input\\ O\left\{ f\left( t \right) \right\}\\ \end{array}=\begin{array}{c} output\\ x\left( t \right)\\ \end{array} InputO{
f(t)}=outputx(t)
线性——叠加原理superpositin principle
:
{ O { f 1 ( t ) + f 2 ( t ) } = x 1 ( t ) + x 2 ( t ) O { a f 1 ( t ) } = a x 1 ( t ) O { a 1 f 1 ( t ) + a 2 f 2 ( t ) } = a 1 x 1 ( t ) + a 2 x 2 ( t ) \begin{cases} O\left\{ f_1\left( t \right) +f_2\left( t \right) \right\} =x_1\left( t \right) +x_2\left( t \right)\\ O\left\{ af_1\left( t \right) \right\} =ax_1\left( t \right)\\ O\left\{ a_1f_1\left( t \right) +a_2f_2\left( t \right) \right\} =a_1x_1\left( t \right) +a_2x_2\left( t \right)\\ \end{cases} ⎩
⎨
⎧O{
f1(t)+f2(t)}=x1(t)+x2(t)O{
af1(t)}=ax1(t)O{
a1f1(t)+a2f2(t)}=a1x1(t)+a2x2(t)
时不变Time Invariant:
O { f ( t ) } = x ( t ) ⇒ O { f ( t − τ ) } = x ( t − τ ) O\left\{ f\left( t \right) \right\} =x\left( t \right) \Rightarrow O\left\{ f\left( t-\tau \right) \right\} =x\left( t-\tau \right) O{
f(t)}=x(t)⇒O{
f(t−τ)}=x(t−τ)
LIT系统,h(t)可以完全定义系统
更多【算法-[足式机器人]Part2 Dr. CAN学习笔记-数学基础Ch0-4线性时不变系统中的冲激响应与卷积】相关视频教程:www.yxfzedu.com