# ディジタル信号処理 4/21 課題
## T5-23 下山 歩

###### tags: `ディジタル信号処理`

### 課題1
以下の $a(n),\ b(n)$ について $a(n) * b(n)$ を求めよ.

#### **1.** $a(n) = \left\{ 4,3,1 \right\},\ b(n) = \left\{ 1,1,9,2 \right\}$

##### `ans[0]`
| $a(n)$ | 4 | 3 | 1 |
| - | - | - | - |
| $b(n)$ | 1 |

`ans[0] = 4*1 = 4`
`ans = [4]`

##### `ans[1]`
| $a(n)$ | 4 | 3 | 1 |
| - | - | - | - |
| $b(n)$ | 1 | 1 |

`ans[1] = 4*1 + 3*1 = 7`
`ans = [4, 7]`

##### `ans[2]`

| $a(n)$ | 4 | 3 | 1 |
| - | - | - | - |
| $b(n)$ | 9 | 1 | 1 |

`ans[2] = 4*9 + 3*1 + 1*1 = 40`
`ans = [4, 7, 40]`

##### `ans[3]`
| $a(n)$ | 4 | 3 | 1 |
| - | - | - | - |
| $b(n)$ | 2 | 9 | 1 |

`ans[3] = 4*2 + 3*9 + 1*1 = 36`
`ans = [4, 7, 40, 36]`

##### `ans[4]`
| $a(n)$ | 4 | 3 | 1 |
| - | - | - | - |
| $b(n)$ | | 2 | 9 |

`ans[4] = 3*2 + 1*9 = 15`
`ans = [4, 7, 40, 36, 15]`

##### `ans[5]`
| $a(n)$ | 4 | 3 | 1 |
| - | - | - | - |
| $b(n)$ | | | 2 |

`ans[5] = 1*2 = 2`
`ans = [4, 7, 40, 36, 15, 2]`

#### **2.** $a(n) = \left\{ 1,1,9,2 \right\},\ b(n) = \left\{ 4,3,1 \right\}$

##### `ans[0]`
| $a(n)$ | 1 | 1 | 9 | 2 |
| - | - | - | - | - |
| $b(n)$ | 4 |

`ans[0] = 1*4 = 4`
`ans = [4]`

##### `ans[1]`
| $a(n)$ | 1 | 1 | 9 | 2 |
| - | - | - | - | - |
| $b(n)$ | 3 | 4 |

`ans[1] = 1*3 + 1*4 = 7`
`ans = [4, 7]`

##### `ans[2]`
| $a(n)$ | 1 | 1 | 9 | 2 |
| - | - | - | - | - |
| $b(n)$ | 1 | 3 | 4 |

`ans[2] = 1*1 + 1*3 + 9*4 = 40`
`ans = [4, 7, 40]`

##### `ans[3]`
| $a(n)$ | 1 | 1 | 9 | 2 |
| - | - | - | - | - |
| $b(n)$ | | 1 | 3 | 4 |

`ans[3] = 1*1 + 9*3 + 2*4 = 36`
`ans = [4, 7, 40, 36]`

##### `ans[4]`
| $a(n)$ | 1 | 1 | 9 | 2 |
| - | - | - | - | - |
| $b(n)$ | | | 1 | 3 |

`ans[4] = 9*1 + 2*3 = 15`
`ans = [4, 7, 40, 36, 15]`

##### `ans[5]`
| $a(n)$ | 1 | 1 | 9 | 2 |
| - | - | - | - | - |
| $b(n)$ | | | | 1 |

`ans[5] = 2*1 = 2`
`ans = [4, 7, 40, 36, 15, 2]`

#### **3.** $a(n) = \left\{ 8,5,9 \right\},\ b(n) = \left\{ 2 \right\}$

##### `ans[0]`
| $a(n)$ | 8 | 5 | 9 |
| - | - | - | - |
| $b(n)$ | 2 |

`ans[0] = 8*2 = 16`
`ans = [16]`

##### `ans[1]`
| $a(n)$ | 8 | 5 | 9 |
| - | - | - | - |
| $b(n)$ | | 2 |

`ans[1] = 5*2 = 10`
`ans = [16, 10]`

##### `ans[2]`
| $a(n)$ | 8 | 5 | 9 |
| - | - | - | - |
| $b(n)$ | | | 2 |

`ans[2] = 9*2 = 18`
`ans = [16, 10, 18]`