Пример. Пары преобразований Фурье

Символьные операции > Работа с символьными операциями > дифференциальные и интегральные; > Пример. Пары преобразований Фурье

Задайте период, частоту выборки и количество элементов выборки для сигнала.

Синусоидальный сигнал

1. Используйте аналитические преобразования, чтобы найти преобразование Фурье синусоидального сигнала.

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Перестановка членов в результате дает следующее:

В результате отображаются два компонента, включающих дельта-функцию Дирака (единичную импульсную функцию) Δ.

2. Используйте функцию sin, чтобы определить синусоидальный сигнал.

3. Постройте график первых нескольких элементов функции f1.

Щелкните для копирования этого выражения

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4. Используйте функцию dft, чтобы найти дискретное преобразование Фурье сигнала.

5. Постройте график двух компонентов преобразования Фурье функции. Используйте вертикальные маркеры, чтобы показать их появление относительно частоты выборки.

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Прямоугольный импульсный сигнал

1. Используйте функцию Хевисайда Φ, чтобы определить прямоугольный импульсный сигнал.

2. Постройте график первых нескольких элементов функции f2.

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3. Используйте функцию dft, чтобы найти дискретное преобразование Фурье прямоугольного импульсного сигнала.

4. Постройте график преобразования Фурье прямоугольного импульсного сигнала. Используйте вертикальные маркеры, чтобы показать их появление относительно частоты выборки.

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Гауссов сигнал

1. Определите следующий гауссов сигнал.

2. Постройте график первых нескольких элементов функции f3.

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3. Используйте функцию dft, чтобы найти дискретное преобразование Фурье гауссова сигнала.

4. Постройте график преобразования Фурье гауссова сигнала. Используйте вертикальные маркеры, чтобы показать их появление относительно частоты выборки.

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