This commit is contained in:
Ivan I. Ovchinnikov 2023-03-09 13:06:04 +03:00
parent 6573c9605d
commit 9576ffec68
7 changed files with 4087 additions and 5 deletions

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@ -99,6 +99,7 @@ $x(t)$ -- это входной непрерывный сигнал, умнож
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-signal-discretization.svg}
\caption{Дискретизация сигнала}
\label{pic:sig-discr}
\end{figure}
Дискретный сигнал в частотной области -- бесконечное число повторяющихся копий дискретного представления сигнала. В цифровом вычислительном блоке мы всегда работаем с дискретным сигналом. Важно на каком расстоянии стоят частоты дискретного сигнала (виртуальные образы цифрового сигнана). Чтобы они не накладывались друг на друга нужна предварительная фильтрация (производимая ФПО).
@ -160,6 +161,7 @@ $\frac{\sin{X}}{X}$ -- первый замечательный предел
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-sampling-afc.svg}
\caption{Завал из-за усреднения напряжения на УВХ}
\label{pic:sig-discr-uvh}
\end{figure}
В предельном случае -- импульсная характеристика идеального ФНЧ, а в реальности это простая фильтрация. то есть сам АЦП выступает в роли фильтра.
@ -240,11 +242,16 @@ $\frac{\sin{X}}{X}$ -- первый замечательный предел
$\frac{sin 2\pi f_a(t-t_k)}{2\pi f_a(t-t_k)}$ -- импульсная характеристика идеального фильтра низких частот с прямоугольной АЧХ. То есть это указание о том, как именно восстанавливать сигнал -- пропустить через идеальный ФНЧ. Важно в теореме -- ширина спектра сигнала. а не максимальная частота.
(1)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-adc-out.svg}
\caption{На выходе АЦП}
\end{figure}
Вводить для 8-битной системы мощные средства передискретизации -- избыточно.
Классический случай дискретизации -- когда исходный сигнал находится в первой зоне (рис2, рис4). Другие сигналы называются полосовые сигналы. Для полосового сигнала спектр окажется такой же
Классический случай дискретизации -- когда исходный сигнал находится в первой зоне (рис. \hrf{pic:sig-discr}, \hrf{pic:sig-discr-uvh}). Другие сигналы называются полосовые сигналы. Для полосового сигнала спектр окажется такой же
Субдискретизация -- (англ. under-sampling) дискретизация полезного сигнала, располагающегося вне основной полосы, т.е. лежащего в зоне с номером больше, чем 1 (полосовая дискретизация).
@ -258,16 +265,49 @@ $\frac{sin 2\pi f_a(t-t_k)}{2\pi f_a(t-t_k)}$ -- импульсная харак
Котельников в лоб -- дискретизация должна быть на 400+ МГЦ.
(2)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-freq-move.svg}
\caption{Перенос частоты}
\end{figure}
Применяя методику субдискретизации можно существенно уменьшить требования к параметрам приёмника. Но требования к АЦП остаются такими же.
(3)
\begin{figure}[H]
\centering
\begin{subfigure}[b]{0.9\textwidth}
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-freq-z1.svg}
\caption{ }
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\begin{subfigure}[b]{0.9\textwidth}
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-freq-z2.svg}
\caption{ }
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\begin{subfigure}[b]{0.9\textwidth}
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-freq-z3.svg}
\caption{ }
\end{subfigure}
\end{figure}
Когда сигнал лежит в зоне нечётным номером -- это полный образ, если с чётным -- инверсия. В любом случае в интересующей полосе образ.
Фильтр для классической дискретизации -- это ФНЧ. для субдискретизации -- полосовой фильтр.
(4)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-freq-z-dd.svg}
\caption{ }
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полосовой фильтру
полоса пропускания f1-f2

546
pics/04-cedd-00-adc-out.svg Normal file
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After

Width:  |  Height:  |  Size: 22 KiB