Редактор цифровых фильтров
В данном примере мы разберём принципы использования приложения «Редактор цифровых фильтров» на основе заранее описанного зашумлённого сигнала и применения к нему с фильтрации с конечной импульсной характеристикой.
Объявим вспомогательные функции, которые нам понадобятся в данной работе:
- функция для парсинга коэффициентов, сгенерированных «Редактором цифровых фильтров»;
- вспомогательная функия для расчёта спектра сигнала.
Resolving package versions...
No Changes to `~/.project/Project.toml`
No Changes to `~/.project/Manifest.toml`
Out[0]:
compute_spectrum (generic function with 1 method)
Теперь перейдём к определению входного сигнала и его анализу при условии, что частота дискретизации равна 1МГц.
Анализируя спектр сигнала, мы видим один пик в 0 Гц. Наличие амплитудного пика на спектре сегмента указывает на наличие сильной гармонической составляющей.
Чтобы отфильтровать все частоты, кроме пиковой, амплитудно-частотная характеристика (АЧХ) фильтра должна быть плоской до частоты среза и затем резко снижаться до бесконечно малых значений для всех остальных частот.
Это может быть реализовано с помощью низкочастотного фильтра (lowpass filter). В данном случае используем оконный КИХ-фильтр. И здесь нам необходимо расчитать коэффициенты этого фильтра при помощи приложения «Редактор цифровых фильтров».
Ниже приведён пример генерации коэффициентов.
После генерации мы выполняем скачивание файлов и следом парсинг файла с коэффициентами. Помимо этого стоит обратить внимание на то, что знаменатель фильтра задан коэффициентами, равными единице, что позволяет их отбросить.


Выгрузим коэффициенты из сгенерированных TXT-файлов.
Out[0]:
11-element Vector{Float64}:
0.08670710125932124
0.08919851935658485
0.0911692583414991
0.0925947918347827
0.09345731482134326
0.09374602877293467
0.09345731482134309
0.09259479183478204
0.09116925834149865
0.08919851935658467
0.0867071012593207
Теперь объявим оконный КИХ-фильтр с ранее рассчитанными коэффициентами.
Out[0]:
FIRWindow{Float64}([0.08670710125932124, 0.08919851935658485, 0.0911692583414991, 0.0925947918347827, 0.09345731482134326, 0.09374602877293467, 0.09345731482134309, 0.09259479183478204, 0.09116925834149865, 0.08919851935658467, 0.0867071012593207], true)
Выполним фильтрацию сигнала и сравним входные и выходные значения как самого сигнала, так и спектра.
После фильтрации сигнал стал сглаженным, подавляя шумовые компоненты. Форма сигнала теперь лучше отражает общую тенденцию поведения сигнала.
Пиковые выбросы шума практически исчезли, что подтверждает успешную фильтрацию высокочастотных компонентов.
Частоты выше 65 Гц полностью подавлены. Основные амплитуды спектра сосредоточены на частотах 0 Гц. Это говорит о том, что фильтр эффективно подавил шум выше частоты среза и позволил выделить полезный исходный сигнал.
Вывод
В данном примере были продемонстрированы возможности фильтрации сигналов в интерактивных скриптах Engee и способы применения дополнительного приложения среды – «Редактора цифровых фильтров». Мы убедились в том, что поставленные задачи выполняются корректно с помощью данных инструментов.
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