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Консультация № 194161
12.12.2018, 18:21
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Здравствуйте! У меня возникли сложности: мне необходимо прорешать тест по ТФКП, он у меня в программе, т.к. я студент)
Застрял на следующих заданиях, к слову, я в конкретно в них вообще не имею понятия что делать.
Фото задачек прикрепляю к сообщению. Прошу помочь с решением, и, пожалуйста, прошу подробно объяснить решение каждого из заданий. Буду очень всем благодарен за помощь, для меня это очень важно, т.к. скоро сессия)
Спасибо за внимание!
Застрял на следующих заданиях, к слову, я в конкретно в них вообще не имею понятия что делать.
Фото задачек прикрепляю к сообщению. Прошу помочь с решением, и, пожалуйста, прошу подробно объяснить решение каждого из заданий. Буду очень всем благодарен за помощь, для меня это очень важно, т.к. скоро сессия)
Спасибо за внимание!
Обсуждение
17.12.2018, 03:07
общий
это ответ
Здравствуйте, Alexis!
1. Преобразование Фурье функции f(x) определяется выражением
или в тригонометрической форме
В данном случае f(x) = e[sup]-|x|[/sup]sin x и
Так как функция e[sup]-|x|[/sup]sin x cos [$969$]x - нечётная, то первый интеграл равен нулю. Функция e[sup]-|x|[/sup]sin x sin [$969$]x - чётная, поэтому
Остаётся найти несобственный интеграл вида
Дважды проинтегрировав по частям, получаем
откуда
и
Соответствующий несобственный интеграл равен
Тогда
и искомое преобразование Фурье будет иметь вид
1. Преобразование Фурье функции f(x) определяется выражением
или в тригонометрической форме
В данном случае f(x) = e[sup]-|x|[/sup]sin x и
Так как функция e[sup]-|x|[/sup]sin x cos [$969$]x - нечётная, то первый интеграл равен нулю. Функция e[sup]-|x|[/sup]sin x sin [$969$]x - чётная, поэтому
Остаётся найти несобственный интеграл вида
Дважды проинтегрировав по частям, получаем
откуда
и
Соответствующий несобственный интеграл равен
Тогда
и искомое преобразование Фурье будет иметь вид
5
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