网站主机方式,便民服务,给银行做网站,简约式网站模板本文仅供学习使用 本文参考#xff1a; B站#xff1a;DR_CAN 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 1. LIT System#xff1a;Linear Time Invariant2. 卷积 Convolution3. 单位冲激 Unit Impulse——Dirac Delta 线性时不变系统 #xff1a; L… 本文仅供学习使用 本文参考 B站DR_CAN 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 1. LIT SystemLinear Time Invariant2. 卷积 Convolution3. 单位冲激 Unit Impulse——Dirac Delta 线性时不变系统 LIT System 冲激响应Impluse Response 卷积Convolution
1. LIT SystemLinear Time Invariant 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)
2. 卷积 Convolution 3. 单位冲激 Unit Impulse——Dirac Delta
LIT系统h(t)可以完全定义系统
