Министерство науки, высшей школы и технической политики Российской

Федерации.

Новосибирский Государственный

Технический Университет.

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Контрольная работа по специальным главам математики.

Факультет: АВТ.
Кафедра: АСУ.
Группа: А-513.
Студент: Борзов Андрей Николаевич.
Преподаватель: Хоменко Валентин Михайлович.
Дата: 10 мая 1997 года.

Новосибирск – 1997.
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Исходные данные.

| |0 | 2 |4 |6 |8 |10 |12 |
|X1 |-10 |8.391 |-4.081 |-1.543 |6.669 |-9.65 |9.524 |
|X2 |3.536 |0.365 |-4.012 |4.881 |-2.368 |-1.785 |4.701 |
|X3 |0.721 |0.229 |0.721 |0.114 |6.835 |0.244 |0.252 |
|X4 |2.718 |1.94 |0.885 |0.439 |0.379 |0.631 |1.432 |
|X5 |0 |3.934 |-2.402 |-5.716 |-1.382 |-6.299 |-3.36 |
|X6 |0.667 |-0.099 |-0.465 |0 |0.635 |0.331 |-0.445 |
|X7 |8.999 |6.524 |1.183 |7.583 |1.021 |7.315 |1.011 |
|X8 |-7.568 |-0.484 |4.227 |-5.015 |-0.114 |6.974 |-2.05 |
|X9 |-0.661 |4.998 |-1.017 |1.683 |4.545 |-3.739 |3.496 |
| X10 |0 |-0.497 |-0.8 |0.247 |-0.008 |-0.397 |0.333 |
| X11 |1 |0.336 |0.931 |0 |0.143 |0.314 |0 |
| X12 |-4.741 |2.22 |0.01 |-4.854 |0.02 |0.006 |-4.55 |
| X13 |0 |-2.961 |-3.872 |-1.701 |-2.786 |-0.085 |-5.197 |
|X14 |0 |0.328 |1.339 |2.677 |4.247 |6.001 |7.907 |

1. Построим матрицу mxt(t).

|t |0 |2 |4 |6 |8 |10 |12 |
|mxt |-0.38 |1.8 |-0.525 |-0.086 |1.274 |-0.01 |0.932 |

2. Строим корреляционную матрицу.

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| |0 |2 |4 |6 |8 |10 |12 |
| | | | | | | | |
|t | | | | | | | |
|0 |20.072 |-1.34 |0.655 |11.543 |-3.915 |7.718 |-1.858 |
|2 |-1.34 |9.03 |-1.198 |1.766 |4.212 |-5.479 |5.756 |
|4 |0.655 |-1.198 |5.341 |-0.267 |0.904 |8.101 |-1.556 |
|6 |11.543 |1.766 |-0.267 |12.725 |1.464 |6.552 |7.517 |
|8 |-3.915 |4.212 |0.904 |1.464 |8.862 |-2.406 |7.679 |
|10 |7.718 |-5.479 |8.101 |6.552 |-2.406 |20.64 |-3.602 |
|12 |-1.858 |5.756 |-1.556 |7.517 |7.679 |-3.602 |17.288 |

|t |0 |2 |4 |6 |8 |10 |12 |
|Dx |20.072 |9.03 |5.341 |12.725 |8.862 |20.64 |17.288 |
|(x |4.48 |3.005 |2.311 |3.567 |2.977 |4.543 |4.158 |

3. Строим нормированную корреляционную матрицу.

|t |0 |2 |4 |6 |8 |10 |12 |
|0 |1 |-0.1 |0.063 |0.722 |-0.294 |0.379 |-0.1 |
|2 |-0.1 |1 |-0.173 |0.165 |0.471 |-0.395 |0.461 |
|4 |0.063 |-0.173 |1 |-0.032 |0.131 |0.772 |-0.162 |
|6 |0.722 |0.165 |-0.032 |1 |0.138 |0.404 |0.507 |
|8 |-0.294 |0.471 |0.131 |0.138 |1 |-0.178 |0.62 |
|10 |0.379 |-0.395 |0.772 |0.404 |-0.178 |1 |-0.19 |
|12 |-0.1 |0.461 |-0.162 |0.507 |0.62 |-0.19 |1 |

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4. Строим таблицу ((t).

|t |0 |2 |4 |6 |8 |10 |12 |
|( |1 |-0.089 |0.277 |0.618 |-0.284 |0.42 |-0.1 |

Строим график нормированной корреляционной функции (при необходимости аппроксимируем по методу наименьших квадратов).
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5. Найдем спектральную характеристику Sx(() и построим её график.

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