Пример. Многочлен Фурье

Программы > Пример. Многочлен Фурье

1. Введите программу, моделирующую периодическую функцию:

Щелкните для копирования этого выражения

2. Постройте график функции:

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3. Введите положительную конечную точку периода функции:

4. Задайте порядок аппроксимации ряда Фурье:

5. Введите программу для расчета коэффициентов Фурье:

6. Вычислите коэффициенты Фурье:

7. Вычислите N-й многочлен Фурье:

8. Постройте графики многочлена Фурье и исходной функции:

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Аппроксимация P1 функции f вблизи высокочастотных точек (резких переходов) получилась неточная.

9. Вычислите коэффициенты Фурье:

10. Вычислите N-й многочлен Фурье:

11. Постройте графики многочлена Фурье и исходной функции:

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Многочлен P2, в котором используется Nt=20, дает аппроксимацию исходной функции намного лучше, особенно вблизи высокочастотных точек (резких переходов).

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