cedd, vopra pics

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Ivan I. Ovchinnikov 2023-03-23 19:01:15 +03:00
parent bbf3344ca7
commit 88295b8345
16 changed files with 5953 additions and 18 deletions

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@ -496,17 +496,37 @@ $N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (пе
ДПФ (есть оптимизации -- БПФ) $N = 1024$ отсчётов
\[X(k) = \frac{1}{N}\sum_{n=0}^{N-1} x(nT) e^{\frac{-j2\pi nk}{N}}\]
Получим 1024 градаций спектра.
(1)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-test-adc-dpf.svg}
\end{figure}
подвох -- некогерентная дискретизация:
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-test-adc-incoherence.svg}
\end{figure}
подвох --некогерентная дискретизация:
(2)
Окно (на неполном или более чем единицном периоде) формирует фазовый сдвиг. Эффект Гибса. Каждый скачок -- это гармоники. Точно рассчитать спектр вообще невозможно. Добавляют умножение на весовую функцию на этапе ДПФ -- операцию взвешивания. Фильтр RAMP, Хэмминга, Хана.
(3)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-test-adc-ramp-hamming.svg}
\end{figure}
\[X(k) = \frac{1}{N}\sum_{n=0}^{N-1} x(nT) x(W) e^{\frac{-j2\pi nk}{N}}\]
Тем самым мы достаточно сильно повлияли на входной сигнал.
Для тестирования АЦП необходимо применить когерентную дискретизацию -- один или несколько периоддов дискретизации точно укладываются в окно наблюдения.
(4)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-test-adc-good.svg}
\end{figure}
\section{Характеристики ЦАП}
Основные характеристики
@ -523,18 +543,39 @@ $N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (пе
\item ошибка смещения offset error -- подали 0, на выходе не 0 напряжение (аддитивная ошибка)
\item ошибка усиления gain error -- наклон шкалы (мультипликативная)
\end{itemize}
(5)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-dac-signal.svg}
\end{figure}
Идеальная характеристика - каждому отсчёту соответствует точка равная определённому разному напряжению. Пропущенных кодов быть не может.
\subsection{Динамические характеристики ЦАП}
\begin{itemize}
\item Время установления выходного напряжения (setting time). -- классический аналоговый параметр. Меняется код и на выходе переходной процесс
(6)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-setting-time.svg}
\end{figure}
Время установления является фактической ответной частью частотой дискретизации.
\item Форма переходного процесса может отличаться. Эмпирический показатель Область глитч импульса glitch impulse area. Максимальный переходной процесс -- в середине шкалы
(7)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-transfer-form.svg}
\end{figure}
Измеряется в $V\cdot pS$. Иногда измеряют не только площади, но разницы площадей. Проблему решает деглитчер (УВХ).
(8)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-psd-control.svg}
\end{figure}
\end{itemize}
\subsection{Архитектуры АЦП}
@ -544,8 +585,20 @@ $N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (пе
\item параллельные
\end{itemize}
Основной элемент -- это компаратор. Это однобитный квантователь, перед ним стоит УВХ.
(10) получаем 255 уровней квантования. на выходе 255-разрядный (позиционный, температурный) код.
Основной элемент -- это компаратор.
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-compare.svg}
\end{figure}
Это однобитный квантователь, перед ним стоит УВХ.
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-seq-zoom.svg}
\end{figure}
получаем 255 уровней квантования. на выходе 255-разрядный (позиционный, температурный) код.
Приоритетный шифратор формирует N-разрядный код. Слишком много компараторов (дорого, размер, потребление), зависит от точности резисторов (интегральная нелинейность), разброс задержек компараторов (решается цифровыми средствами), паразитные ёмкости.

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@ -379,7 +379,11 @@ $S_x$ -- размер одного пикселя светочувствител
\section{Детектирование характерных точек объекта}
В первую очередь это контраст. то есть характерная точка это переход от контрастной к неконтрастной области, угловые, на рёбрах
(1)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-vorpa-00-1-aperture.svg}
\end{figure}
Если объект сливается с фоном в видимом спектре его обнаружить не удастся.
@ -387,14 +391,23 @@ $S_x$ -- размер одного пикселя светочувствител
\subsection{Детектор Моравеца}
Самый простой детектор углов на изображении.
(2)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-vorpa-00-1-moravets.svg}
\end{figure}
Чтобы найти объект проходим окном (3х3,5х5,9х9) по изображению и смотрим на изменение интенсивности центрального пикселя и окружающих. Пиксель характеризуется координатами $x$, $y$. Получаем 8 направлений смещения относительно пикселя ($u$, $v$).
\[(u, v) \in \{(-1,0), (-1,-1), (0,-1), (1,-1), (1,0), (1,1), (0,1), (-1,1) \}\]
\[V_{u,v}(x,y) = \sum_{\forall a,b}(I(x+u+a, y+v+b)-I(x+a, y+b))^2\]
Если интенсивность одинаковая -- получим значение около нуля. Чем больше эта функция, тем характернее точка.
(3)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-vorpa-00-1-corners.svg}
\end{figure}
Самое максимальное изменение мы увидим на углу объекта.
\begin{itemize}
@ -406,10 +419,20 @@ $S_x$ -- размер одного пикселя светочувствител
улучшение моравеца, инвариантен к поворотам. Рассматриваем первые производные от детектора моравеца. Ряд тейлора
\[ I(x+y+a, y+v+b)\approx I(x+a, y+b) + u\frac{dI}{dx}+v\frac{dI}{dy}\]
Сумма квадратов разностей и остаётся только часть со смещениями в векторном (транспонируемый вектор) виде
\[ [\frac{dI}{dx} \frac{dI}{dy}] \cdot [u v] \]
\[ \left[\frac{dI}{dx} \frac{dI}{dy}\right] \cdot \begin{bmatrix} u\\v \end{bmatrix} \]
(формула ляма)
\[V_{u,v}(x,y) = \sum_{\forall a,b}([\frac{dI}{dx} \frac{dI}{dy}] \cdot [u v])^2 = \sum[u v][u\frac{dI}{dx} v\frac{dI}{dy}]\cdot [\frac{dI}{dx} \frac{dI}{dy}][uv] = [uv](\sum[\frac{dI}{dx} \frac{dI}{dy}]\cdot[\frac{dI}{dx} \frac{dI}{dy}])\cdot [u v]\]
\begin{equation*}
\begin{gathered}
V_{u,v}(x,y) = \sum_{\forall a,b}\left(\left[\frac{dI}{dx} \frac{dI}{dy}\right] \cdot
\begin{bmatrix} u\\v \end{bmatrix} \right)^2 =\\
= \sum_{\forall a,b}[u v] \begin{bmatrix} \frac{dI}{dx}\\\frac{dI}{dy} \end{bmatrix}
\cdot \left[\frac{dI}{dx} \frac{dI}{dy}\right] \begin{bmatrix} u\\v \end{bmatrix} =\\
= [u v]\left(\sum \begin{bmatrix} \frac{dI}{dx}\\\frac{dI}{dy} \end{bmatrix}
\cdot\left[\frac{dI}{dx} \frac{dI}{dy}\right]\right)\cdot \begin{bmatrix} u\\v \end{bmatrix}
\end{gathered}
\end{equation*}
получаем автокорреляционную матрицу $A_{u,v}(x,y)$. глядя на числа из неё можно понять характерны ли числа. Если числа большие -- пиксель можно характеризовать как угол. Если число $\lambda_1 \gg \lambda_2$ то это пиксель ребра. Если оба близки к нулю -- это не характерная точка.
\begin{itemize}
\item [+] инвариантен к поворотам.
@ -420,7 +443,11 @@ $S_x$ -- размер одного пикселя светочувствител
\subsection{Детектор FAST}
Features from Accelerated Test
(4)
\begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-vorpa-00-1-FAST.svg}
\end{figure}
Рассматривается точка и окружность, а не прямоугольник. Окружность вписана в квадрат 7х7. Каждый пиксель тестовой выборки изображений $X\in[1...16]$ ищем три состояния -- темнее(D) светлее(B) и такой же(S), раскидываем в три множества.
\[S =

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