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Ivan I. Ovchinnikov 88295b8345 cedd, vopra pics 2023-03-23 19:01:15 +03:00
Ivan I. Ovchinnikov bbf3344ca7 another week 2023-03-23 11:20:22 +03:00
17 changed files with 6049 additions and 12 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 ДПФ (есть оптимизации -- БПФ) $N = 1024$ отсчётов
\[X(k) = \frac{1}{N}\sum_{n=0}^{N-1} x(nT) e^{\frac{-j2\pi nk}{N}}\] \[X(k) = \frac{1}{N}\sum_{n=0}^{N-1} x(nT) e^{\frac{-j2\pi nk}{N}}\]
Получим 1024 градаций спектра. 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: подвох -- некогерентная дискретизация:
(2) \begin{figure}[H]
\centering
\fontsize{12}{1}\selectfont
\includesvg[scale=1.01]{pics/04-cedd-00-test-adc-incoherence.svg}
\end{figure}
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. 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}
\[X(k) = \frac{1}{N}\sum_{n=0}^{N-1} x(nT) x(W) e^{\frac{-j2\pi nk}{N}}\] \[X(k) = \frac{1}{N}\sum_{n=0}^{N-1} x(nT) x(W) e^{\frac{-j2\pi nk}{N}}\]
Тем самым мы достаточно сильно повлияли на входной сигнал. 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. 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} \section{Характеристики ЦАП}
Основные характеристики 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 смещения offset error -- подали 0, на выходе не 0 напряжение (аддитивная ошибка)
\item ошибка усиления gain error -- наклон шкалы (мультипликативная) \item ошибка усиления gain error -- наклон шкалы (мультипликативная)
\end{itemize} \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. Идеальная характеристика - каждому отсчёту соответствует точка равная определённому разному напряжению. Пропущенных кодов быть не может.
\subsection{Динамические характеристики ЦАП} \subsection{Динамические характеристики ЦАП}
\begin{itemize} \begin{itemize}
\item Время установления выходного напряжения (setting time). -- классический аналоговый параметр. Меняется код и на выходе переходной процесс \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. 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 \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). 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} \end{itemize}
\subsection{Архитектуры АЦП} \subsection{Архитектуры АЦП}
@ -544,8 +585,20 @@ $N=8$, $SNR=49,7dB$. реальный может быть 48,1 или 47,1 (пе
\item параллельные \item параллельные
\end{itemize} \end{itemize}
Основной элемент -- это компаратор. Это однобитный квантователь, перед ним стоит УВХ. Основной элемент -- это компаратор.
(10) получаем 255 уровней квантования. на выходе 255-разрядный (позиционный, температурный) код. \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. 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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@ -542,6 +542,51 @@ TS-Процесс.
Для того чтобы проверить распределение Дики-Фуллера нужно построить константы и тренд и понять значимый ли тренд Для того чтобы проверить распределение Дики-Фуллера нужно построить константы и тренд и понять значимый ли тренд
\section{Прогнозирование временных рядов}
\subsection{Прогнозирование временных рядов по параметрическим моделям}
Лучшее, что мы можем сделать -- это среднеквадратичное. Наилучший прогноз -- это матожидание
\begin{equation*}
\begin{gathered}
\tilde{y_{t+k|t}} = E{\tilde{y_{t+k|k}}|y_1...y_t}\\
\tilde{y_{t+k|t}} = E{\tilde{y_{t+k|k}}|y^t_1}
\end{gathered}
\end{equation*}
\[ y_{t} \to \tilde{\xi_t} = y_t-\tilde{y_{t|t-1}}\]
Можем оценить $\xi_t$ -- это будет модель вычисленная по величинам, но мы не можем вычислить $\xi_{t-1}$.
\[\tilde{y_{t|t-1}} = f(y_{t-1}...y_1)\]
\begin{equation*}
\begin{gathered}
y_t = \xi_t-\alpha\xi_{t-1}, \xi_t \sim N(0, \sigma^2)\\
y_{t+1} = \xi_{t+1}-\alpha\xi_{t}\\
\tilde{y_{t+1|t}} = -\alpha\tilde{\xi_t}\\
e_{t+1}(1) = y_{t+1} - \tilde{y_{t+1|t}} = \xi_{t-1}-\underbrace{\alpha\xi_t-(-\alpha\tilde{\xi_t})}_{0}\\
Var(e_{t+1}(1)) = Var(\xi_{t+1}) = \sigma^2\\
Var(\xi_t) = E(\xi_t^2-E\xi_t)
\end{gathered}
\end{equation*}
Дисперсия ошибки прогноза равна безусловной дисперсии процесса.
Прогнозирование авторегрессионных процессов
\begin{equation*}
\begin{gathered}
y_t = 0,4y_{t-1}+0,2y_{t-2}+\xi_t\\
y_{t+1}=0,4y_{t}+0,2y_{t-1}+\xi_{t+1}\\
\tilde{y_{t+1|t}} = 0,4y_{t}+0,2y_{t-1}\\
Var(e_t(1)) = \sigma^2\\
y_{t+2}=0,4y_{t+1}+0,2y_{t}+\xi_{t+2}=\\
= 0,4(0,4y_{t}+0,2y_{t-1}+\xi_{t+1})+0,2y_t+\xi_{t+2}=\\
= 0,16y_t + 0,08y_{t-1}+0,2y_t+0,4\xi_{t+1}+\xi_{t+2}\\
\tilde{y_{t+2|t}} = 0,36y_t + 0,08y_t\\
e_t(2) = 0,4\xi_t+1+\xi_{t+2}\\
Var(e_t(2)) = 0,16+1
\end{gathered}
\end{equation*}
В основном рассматриваются процессы прогнозирующие изменения доходности ARCH, GARCH.
\appendix \appendix
\setcounter{secnumdepth}{0} \setcounter{secnumdepth}{0}
\section*{Приложения} \section*{Приложения}

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@ -377,5 +377,89 @@ $S_x$ -- размер одного пикселя светочувствител
и тогда переход - это и есть размытие. Что сделать, чтобы найти сигма-размытие -- переразмываем один раз и получаем известное $\sigma_1 \Rightarrow i_1(x)$ находим первую производную для обоих изображений. Берём отношение производных и получаем некоторый график ($\Omega$-образный), по нему можем определить точки, где график будет около нуля и расстояние между ними это и будет размытие. и тогда переход - это и есть размытие. Что сделать, чтобы найти сигма-размытие -- переразмываем один раз и получаем известное $\sigma_1 \Rightarrow i_1(x)$ находим первую производную для обоих изображений. Берём отношение производных и получаем некоторый график ($\Omega$-образный), по нему можем определить точки, где график будет около нуля и расстояние между ними это и будет размытие.
\end{itemize} \end{itemize}
\section{Детектирование характерных точек объекта}
В первую очередь это контраст. то есть характерная точка это переход от контрастной к неконтрастной области, угловые, на рёбрах
\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.
\textbf{Детекторы} -- обнаружение. \textbf{Дескрипторы} -- обнаружение и описание. Мы всё будем называть детекторами. Хороший алгоритм должен быть инвариантен к шумам и деформациям.
\subsection{Детектор Моравеца}
Самый простой детектор углов на изображении.
\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.
\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}
\item [+] самый простой для интерпретации, программной реализации.
\item [-] не инвариантен к поворотам, если у объекта есть большое количество диагональных рёбер.
\end{itemize}
\subsection{Детектор Харриса}
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
\[ \left[\frac{dI}{dx} \frac{dI}{dy}\right] \cdot \begin{bmatrix} u\\v \end{bmatrix} \]
(формула ляма)
\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.
\item [-] более сложный по отношению к моравецу, восприимчив к шумам, не инвариантен к масштабированию
\end{itemize}
Модификация -- детектор Харриса-Лапласа -- инвариантен к масштабированию (из-за вторых производных).
\subsection{Детектор FAST}
Features from Accelerated Test
\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.
\[S =
\begin{cases}
d, I_x\leq I_p -t\\
s, I_p-t < I_x < I_p+t\\
b, I_p+t \leq I_x\\
\end{cases}
\]
Строим дерево решений. Множество которое соответствует узлу дерева разбивается на подмножества и на основе этих деревьев не рассматриваем всё, а проходим по дереву и находим характерные точки.
\subsection{Детектор MSER}
\end{document} \end{document}

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