[digital signal processing] basic sequence (basic sequence lists | unit pulse sequence | unit pulse function | discrete unit pulse function | difference between unit pulse function and discrete unit p

One 、 Basic sequence enumeration

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Basic sequence Yes

• Unit pulse sequence
• Unit step sequence
• Rectangular sequence
• Real exponential sequence
• Sinusoidal sequence
• Complex exponential sequence

Two 、 Unit pulse sequence

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Unit pulse sequence :

$$\delta (n)=\{\begin{array}{l}1n=0\\ \\ 0n=1\end{array}$$

1、 Unit pulse function

Unit pulse function ( Unit impulse function ) Corresponding Function image as follows : The horizontal axis is $n$ , The vertical axis is $\delta (n)$ ;

• $n=0$ when , $\delta (n)=1$
• $n=1$ when , $\delta (n)=0$
  

2、 Discrete unit impulse function

Here pay attention to and " Discrete unit impulse function " Distinguish , I added " discrete " Two words , Its value is no longer fixed $0,1$ ;

Discrete unit impulse function ( Discrete unit impulse function ) Corresponding Function image as follows : The horizontal axis is $t$ , The vertical axis is $\delta (t)$ ;

• $t=0$ when , $\delta (t)$ Is infinite
• $t=1$ when , $\delta (t)=0$
  

3、 Unit pulse function And The difference between discrete unit impulse functions

Unit pulse function And Discrete unit impulse function The difference between :

① The horizontal axis coordinate is 0 The situation of :

stay Unit pulse function $\delta (n)$ in , $n=0$ when , $\delta (n)=1$

stay Discrete unit impulse function $\delta (t)$ in , $t=0$ when , $\delta (t)$ Is infinite ;

② The vertical axis coordinate is 0 The situation of , That is, the function is $0$ The situation of :

stay Unit pulse function $\delta (n)$ in , stay $n=\cdots ,-3,-2,-1,1,2,3,\cdots$ The value at the position of an equal integer is $0$ ;

stay Discrete unit impulse function $\delta (t)$ in , $t$ Divide by $0$ Any value other than , The corresponding function value $\delta (t)$ All for $0$ ;

③ Whether it can be realized :

Unit pulse function $\delta (n)$ It is physically achievable ;

Discrete unit impulse function $\delta (t)$ Physically impossible ;