[digital signal processing] basic sequence (unit step sequence | relationship between unit step sequence and unit pulse sequence | rectangular sequence | relationship between rectangular sequence and

One 、 Unit step sequence

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Unit step sequence :

$$u(n)=\{\begin{array}{l}1n\ge 0\\ \\ 0n<0\end{array}$$

Unit step sequence Function image As shown in the figure below :

1、 The relationship between unit step sequence and unit pulse sequence

Unit step sequence And Unit pulse sequence The relationship between :

$$\delta (n)=u(n)-u(n-1)$$

$u(n)$ from Infinite $\delta (n)$ Linear shift composition :

$$u(n)=\sum _{i=0}^{\infty }\delta (n-i)$$

Review the last blog post 【 Digital signal processing 】 Basic sequence ( Basic sequence enumeration | Unit pulse sequence | Unit pulse function | Discrete unit impulse function | Unit pulse function And The difference between discrete unit impulse functions ) , The unit pulse sequence is :

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

Two 、 Rectangular sequence

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Rectangular sequence :

$$R_N(n)=\{\begin{array}{l}10\le n\le N-1\\ \\ 0other\end{array}$$

Rectangular sequence Function image As shown in the figure below :

1、 Relationship between rectangular sequence and unit step sequence

Rectangular sequence And Unit step sequence The relationship between :

$$R_N(n)=u(n)-u(n-N)$$

2、 Rectangular sequence action

Rectangular sequence action : Continuous periodic signals cannot be processed in a computer , Must be aligned for sampling , Can be processed in the computer , Will be original Continuous signal multiply Rectangular sequence , You can get Discrete time signals ;

Rectangular sequence Of effect Namely sampling ;