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zKMjmL=ENWWzw>{R1V2N6-fjH}t-|}yr~hN`^|O_~yWT%-004U=0Kh*S@z3zTFO7eN ghdz4x|G@vfP%212d7NDU0Oj%L|LE&=K|h}U4;+_*{Qv*} literal 0 HcmV?d00001 diff --git a/3.6.1Спектр/Laba.py b/3.6.1Спектр/Laba.py new file mode 100644 index 0000000..ab2f637 --- /dev/null +++ b/3.6.1Спектр/Laba.py @@ -0,0 +1,258 @@ +# -*- coding: utf-8 -*- + +import numpy as np +import matplotlib.pyplot as plt +import csv +from scipy.optimize import curve_fit + + +def read_csv(file_name): + with open(file_name) as file: + reader = list(csv.reader(file, delimiter=';', + quotechar=',', quoting=csv.QUOTE_MINIMAL)) + return reader + + +def make_latex_table(data): + table = [] + table.append("\\begin{table}".replace('//', '\\')) + table.append("\label{}".replace('/', '\\')) + table.append('\caption{}'.replace('/', '\\')) + leng = len(data[0]) + stroka = 'c'.join(['|' for _ in range(leng+1)]) + table.append('\\begin{tabular}{'.replace('//', '\\')+stroka+'}') + table.append('\hline') + for i in range(len(data)): + table.append(' & '.join(data[i]) + ' \\\\') + table.append('\hline') + table.append("\end{tabular}".replace('/', '\\')) + table.append("\end{table}".replace('/', '\\')) + return table + + +def make_point_grafic(x, y, xlabel, ylabel, caption, xerr, yerr, + subplot=None, color=None, center=None, s=15): + if not subplot: + subplot = plt + if type(yerr) == float or type(yerr) == int: + yerr = [yerr for _ in y] + if type(xerr) == float or type(xerr) == int: + xerr = [xerr for _ in x] + + if xerr[1] != 0 or yerr[1] != 0: + subplot.errorbar(x, y, yerr=yerr, xerr=xerr, linewidth=4, + linestyle='', label=caption, color=color, + ecolor=color, elinewidth=1, capsize=3.4, + capthick=1.4) + else: + subplot.scatter(x, y, linewidth=0.005, label=caption, + color=color, edgecolor='black', s=s) + # ax = plt.subplots() + # ax.grid()) + if not center: + plt.xlabel(xlabel) + plt.ylabel(ylabel) + else: + ax = plt.gca() + ax.spines['top'].set_visible(False) + ax.spines['right'].set_visible(False) + ax.spines['bottom'].set_position('zero') + ax.spines['left'].set_position('zero') + ax.set_xlabel(ylabel, labelpad=-180, fontsize=14) # + + ax.set_ylabel(xlabel, labelpad=-260, rotation=0, fontsize=14) + + +def make_line_grafic(xmin, xmax, xerr, yerr, xlabel, ylabel, k, b, caption, + subplot=None, color=None, linestyle='-'): + if not subplot: + subplot = plt + x = np.arange(xmin, xmax, (xmax-xmin)/10000) + subplot.plot(x, k*x+b, label=caption, color=color, linewidth=1.4, + linestyle=linestyle) + + +def make_graffic(x, y, xlabel, ylabel, caption_point, xerr, yerr, k=None, + b=None, filename=None, color=None, koef=[0.9, 1.1], s=None): + if not color: + color = ['limegreen', 'indigo'] + if not s: + make_point_grafic(x, y, xlabel=xlabel, + ylabel=ylabel, caption=caption_point, + xerr=xerr, yerr=yerr, subplot=plt, color=color[0]) + else: + make_point_grafic(x, y, xlabel=xlabel, + ylabel=ylabel, caption=caption_point, + xerr=xerr, yerr=yerr, subplot=plt, color=color[0], s=s) + if k and b: + make_line_grafic(xmin=min(x)-1, xmax=max(x)+1, xerr=xerr, yerr=yerr, + xlabel='', ylabel='', k=k, b=b, + caption='Theoretical dependence', subplot=plt, + color='red') + if type(yerr) == float or type(yerr) == int: + yerr = [yerr for _ in y] + k, b, sigma = approx(x, y, b, yerr) + sigma[0] = abs(k*((sigma[0]/k)**2+(np.mean(yerr)/np.mean(y))**2 + + (np.mean(xerr)/np.mean(x))**2)**0.5) + if (b != 0): + sigma[1] = abs(b*((sigma[1]/b)**2+(np.mean(yerr)/np.mean(y))**2 + + (np.mean(xerr)/np.mean(x))**2)**0.5) + else: + sigma[1] = 0 + + make_line_grafic(xmin=min(x)*koef[0], xmax=max(x)*koef[1], xerr=xerr, + yerr=yerr, xlabel='', ylabel='', k=k, b=b, caption=None, + subplot=plt, color=color[1]) + plt.legend() + return k, b, sigma + + +def approx(x, y, b, sigma_y, f=None): + if sigma_y[0] != 0: + sigma_y = [1/i**2 for i in sigma_y] + else: + sigma_y = np.array([1 for _ in y]) + if f is None: + if b == 0: + def f(x, k): + return k*x + k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y) + sigma = np.sqrt(np.diag(sigma)) + return k, b, [sigma, 0] + else: + def f(x, k, b): + return x*k + b + k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y) + sigma_b = np.sqrt(sigma[1][1]) + b = k[1] + k = k[0] + sigma = np.sqrt(sigma[0][0]) + + return k, b, [sigma, sigma_b] + else: + k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y) + sigma = np.sqrt(np.diag(sigma)) + b = k[1] + k = k[0] + return k, b, sigma + + +def find_delivation(data): + data = np.array(data).astype(np.float) + s = sum(data)/len(data) + su = 0 + for i in data: + su += (i-s)**2 + return (su/(len(data)-1))**0.5 + + +def make_dic(filename): + data = np.array(read_csv(filename)) + data = np.transpose(data) + dic = {} + for i in range(len(data)): + dic[data[i][0]] = np.array(data[i][1:]).astype(np.float) + data = dic + return data + + +def make_fun(A0, T): + def f(t, k, b): + return A0/(1+A0*b*t)-k*0*A0*t/T + return f + + +def make_fun_grafic(xmin, xmax, xerr, yerr, xlabel, ylabel, f, k, b, caption, + subplot=None, color=None): + if not subplot: + subplot = plt + x = np.arange(xmin, xmax, (xmax-xmin)/10000) + subplot.plot(x, f(x, k, b), label=caption, color=color) + + + + +def make_all(): + part_1_1() + part_1_2() + part_2() + part_3() + + +def part_1_1(): + plt.figure(dpi=500, figsize=(8, 5)) + data = make_dic("dnu(tau).csv") + x = 1 / data["tau"]*100 + y = data['d_nu']/10**4 + xlabel = "1/"+greek_letters[48]+'$,10^4$Гц' + ylabel = greek_letters[0]+greek_letters[41]+'$,10^4$ Гц' + k, b, sigma = make_graffic(x, y, xlabel, ylabel, + caption_point='', xerr=0, yerr=0, s=40) + print(k, sigma[0]) + plt.savefig("dnu(tau)") + plt.show() + + +def part_1_2(): + fig, ax = plt.subplots(figsize=(10, 6)) + data = make_dic("a(n).csv") + v = 1000 + t = 50 * 10 **- 6 + T = 1 / v + N = 200 + V0 = 300 + vu = [n/T for n in range(2, N)] + c = [abs(V0*t/T*np.sin(n*t*np.pi/T)/(n*t*np.pi/T)) for n in range(2, N)] + for i in range(len(vu)): + plt.scatter(vu[i], c[i], linewidth=0.005, label='', + color='purple', s=15) + ax.vlines(vu[i], 0, c[i], colors='purple') + ax.set_xlabel(greek_letters[41]+', Hz') + ax.set_ylabel("$a_n$, мВ") + plt.savefig("a(n)") + plt.show() + +def part_2(): + plt.figure(dpi=500, figsize=(8, 5)) + data = make_dic("T(dnu).csv") + x = 1 / data["T"]*10**3 + y = data['dnu'] + xlabel = "1/"+greek_letters[48]+'$, $Гц' + ylabel = greek_letters[0]+greek_letters[41]+'$,10^4$ Гц' + k, b, sigma = make_graffic(x, y, xlabel, ylabel, + caption_point='', xerr=0, yerr=0, s=40) + print(k, sigma[0], -sigma[0]/k*100) + plt.savefig("T(dnu)") + plt.show() + +def part_3(): + plt.figure(dpi=500, figsize=(8, 5)) + data = make_dic("a(m).csv") + otn = data['a_b']/data['a_c'] + k, b, sigma = make_graffic(data['m']/100, otn, 'm', '$а_{бок}/a_{осн}$', + caption_point='', xerr=0, yerr=0, s=40) + print(k, sigma[0]) + plt.savefig("a(m)") + plt.show() + + + + + +greek_letters=[chr(code) for code in range(916,980)] +print(greek_letters) + +make_all() + + + + + + + + + + + + + + diff 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colorlinks=true, % false: ссылки в рамках + urlcolor=blue % на URL +} + +% Русский язык +\usepackage[T2A]{fontenc} % кодировка +\usepackage[utf8]{inputenc} % кодировка исходного текста +\usepackage[english,russian]{babel} % локализация и переносы + + +% Математика +\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools} +\usepackage{titlesec} +\titlelabel{\thetitle.\quad} + +\usepackage{wasysym} + +\author{Анна Назарчук Б02-109} +\title{3.6.1 Спектральный анализ электрических сигналов} +\date{} +\begin{document} +\maketitle +\section{Аннотация} +В работе исследуются спектры периодических сигналов: модулированный по амплитуде, прямоугольные импульсы и цуги. Проверяются теоретические зависимости параметров спектра на практике. + + +\section{Введение} +Задача описания поведения некоторой системы во времени зачастую +сводится к выяснению связи между "сигналом", подаваемым на "вход" +системы (обозначим его как $f(t)$), и её реакцией на "выходе" $g(t)$). Если произвольную функцию $f(t)$ удастся представить в виде +некоторой суммы ряда (конечного или бесконечного) гармонических +слагаемых, то при известной частотной характеристике $\lambda(\omega)$) задача +о связи воздействия и отклика системы будет решена. Такое разложение +называют спектральным. Оно имеет физический смысл: высоко добротный колебательный контур выделяет из подаваемого на него сигнала те спектральные компоненты, частоты которых близки к его собственной. Возможность разложить произвольную функцию $f(t)$ в ряд (или интеграл) +Фурье единственным и однозначным способом подразумевает и +возможность "собрать" сигнал любой формы, используя гармонические +колебания с подобранными амплитудами и фазами. В последнее время повсеместное распространение получила цифровая +обработка сигналов. Спектральный состав оцифрованного сигнала +может быть найден численно. Это и планируется проследить в работе. + + +\section{Поставка задачи} +Сгенерировать и получить на осциллографе спектры различных периодических сигналов. Проверить экспериментально соотношение неопределенности и отношения амплитуд гармоник при модулированных по амплитуде сигналах. + +\section{Теоретические сведения} +Задача описания поведения некоторой системы во времени зачастую +сводится к выяснению связи межу «сигналом», подаваемым на «вход» +системы (обозначим его как $f(t)$), и её реакцией на «выходе» ($g(t)$). +Для линейных стационарных фильтров: $g = \hat{\Lambda}[f]$, $\hat{\Lambda}$ - линейное преобразование. Из линейности системы: $f=\sum c_nf_n$, $g_n = c_n \cdot \hat{\Lambda}[f_n]$ +\begin{equation} +g(t) = \sum c_n \hat{\Lambda}[f_n] +\end{equation} +Выбор элементарных слагаемых - собственные векторы. +\begin{equation} +f(t) = \sum_n c_n e^{i\omega_n t} +\end{equation} +Такое представление - ряд Фурье. +\subsection*{Спект периодического процесса} +Периодический процесс - $f(t)=f(t+T)$ +\begin{equation} +f(t) = \sum_{n=-\inf}^{\inf} c_n e^{in\omega_0 t} +\end{equation} +Набор коэффициентов можно найти, домножив обе части прошлого равенства на $e^{-im\omega_0 t}$ и проинтегрировав по периоду: +\begin{equation} +c_n = \frac{1}{T}\int_0^T f(t)e^{-in\omega_0 t}dt +\end{equation} +\begin{figure}[h!] +\includegraphics[width=0.4\textwidth]{rect} +\caption{Периодическая последовательность прямоугольных импульсов} \label{rect} +\end{figure} +Рассмотрим спектр периодической последовательности прямоугольных импульсов (рис. \ref{rect}): +\begin{equation} +c_n = \frac{1}{T}\int_{-\tau / 2}^{\tau / 2} e^{-in\omega_0 t}dt = \dfrac{sin(\pi n \tau / T))}{\pi n} +\end{equation} + +\subsection*{Свойства спектров} +Справедливо для произвольного сигнала соотношение неопределенностей: +\begin{equation} +\Delta \omega \cdot \Delta t \sim 2\pi +\end{equation} +Рассмотрим спектр обрывка синусоиды (цуг): +\begin{equation} +f(t) = f_0(t)\cos(\omega_0 t) +\end{equation} +Из спектра прямоугольного импульса: +\begin{equation} +F(\omega) = \dfrac{\tau}{2}\left[\dfrac{\sin(\omega-\omega_0)\tau /2} +{(\omega-\omega_0)\tau /2} + + \dfrac{\sin(\omega+\omega_0)\tau /2}{\omega+\omega_0)\tau /2}\right] +\end{equation} +Получим спектр периодической последовательности цугов (рис. \ref{цуги}): +\begin{equation} +F(\omega) = \dfrac{\tau}{2T}\left[\dfrac{\sin(\omega-\omega_0)\tau /2} +{(\omega-\omega_0)\tau /2} + + \dfrac{\sin(\omega+\omega_0)\tau /2}{(\omega+\omega_0)\tau /2}\right] +\end{equation} + +\begin{figure}[h!] +\begin{center} +\includegraphics[width=0.4\textwidth]{цуги} +\caption{Периодическая последовательность цуг} \label{цуги} +\end{center} +\end{figure} +\subsection*{Модуляция} +Модулированные колебания: +\begin{equation} +f(t) = a(t) \cos (\omega_0 t+\varphi(t)) +\end{equation} +Простейшее амплитудно-модулированное колебание: +\begin{equation} +f(t)= a(t) \cos (\omega_0 t), \hspace{3mm} a(t) = a_0(1+m\cos(\Omega t)) +\end{equation} +В выражении $0 < m \leq 1$ - глубина модуляции, выражается: +\begin{equation} +m = \dfrac{a_{max}-a_{min}}{a_{max}+a_{min}} +\end{equation} +Из прошлой формулы можно получить: +\begin{equation} +f(t) = a_0 \cos (\omega_0 t) +\dfrac{ma_0}{2}\cos (\omega_0 +\Omega)t++\dfrac{ma_0}{2}\cos (\omega_0 -\Omega)t +\end{equation} + +\section{Методика измерений} +В работе используются генератор сигналов произвольной формы, цифровой осциллограф с функцией быстрого преобразования Фурье. + +\section{Измерения и обработка данных} +\subsection*{Исследования спектра периодической последовательности прямоугольных импульсов} +На генераторе создается сигнал с разными параметрами, по которому на экране осциллографа получается спектр (рис. \ref{прямоуг}) + +\begin{figure}[h!] +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{1_1}} a) $\nu_{повт} = 1000 Гц, \tau = 50 мкс$\\ +\end{minipage} +\hfill +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{1_2}} \\b) $\nu_{повт} = 1400 Гц, \tau = 50 мкс$ +\end{minipage} +\vfill +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{1_3}} c) $\nu_{повт} = 700 Гц, \tau = 50 мкс$ \\ +\end{minipage} +\hfill +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{1_4}} d) $\nu_{повт} = 1000 Гц, \tau = 70 мкс$ \\ +\end{minipage} +\caption{Спектры прямоугольных импульсов} +\label{прямоуг} +\end{figure} +При $\nu_{повт} = 700 Гц$ проведены измерения ширины спектра. Результаты +представлены в таблице \ref{dnu(tau)_tbl} и на рисунке \ref{dnu(tau)_img}. +\begin{table}[h!] +\caption{Зависимость ширины спектра от длительности спектра} \label{dnu(tau)_tbl} +\begin{tabular}{|l|l|} +\hline +$\Delta\nu$, Hz & $\tau$, мкс \\ \hline +50200 & 20 \\ \hline +25200 & 40 \\ \hline +17200 & 60 \\ \hline +13000 & 80 \\ \hline +10200 & 100 \\ \hline +8600 & 120 \\ \hline +7400 & 140 \\ \hline +6600 & 160 \\ \hline +5800 & 180 \\ \hline +5000 & 200 \\ \hline +\end{tabular} +\end{table} + +\begin{figure}[h!] +\begin{center} +\includegraphics[width=\textwidth]{dnu(tau)} +\caption{Зависимость ширины спектра от длительности спектра} \label{dnu(tau)_img} +\end{center} +\end{figure} +Рассчитаем коэффициент наклона прямой: +\begin{equation} +k = 0.9997 \pm 0.0039 +\end{equation} +Полученное значение близко к $1$, что подтверждает соотношение неопределенностей. + + +Для одного из сигналов (a) рассчитаем теоретическую зависимость и изобразим на графике \ref{теор}. Теоретический и экспериментальный спектр похожи. + +\begin{figure}[h!] +\begin{center} +\includegraphics[width=\textwidth]{a(n)} +\caption{Теоретический спектр прямоугольных импульсов} \label{теор} +\end{center} +\end{figure} + +\subsection{Исследование спектра периодической последовательности цугов гармонических колебаний} +На генераторе создается сигнал последовательности синусоидальных цугов с разными параметрами, по которому на экране осциллографа получается спектр. (рис. \ref{спектр_цуги}) + +\begin{figure}[h!] +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{2_1}} a) $\nu = 50 кГц, T = 1 мс, N = 5$\\ +\end{minipage} +\hfill +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{2_2}} \\b) $\nu = 50 кГц, T = 1 мс, N = 3$ +\end{minipage} +\vfill +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{2_3}} c) $\nu = 50 кГц, T = 3 мс, N = 5$ \\ +\end{minipage} +\hfill +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{2_4}} d) $\nu = 30 кГц, T = 1 мс, N = 5$ \\ +\end{minipage} +\vfill +\begin{minipage}[h!]{0.47\linewidth} +\center{\includegraphics[width=1\linewidth]{2_5}} \\e) $\nu = 70 кГц, T = 1 мс, N = 5$ +\end{minipage} +\caption{Вид спектра при разных параметрах спектра} +\label{спектр_цуги} +\end{figure} + +При фиксированной длительности импульсов $\tau$ = 50 мкс измерим расстояния между соседними спектральными компонентами от периода повторения импульсов (табл. \ref{dnu(T)_tbl}, рис. \ref{dnu(T)_img}) + +\begin{table}[h!] +\caption{Зависимость расстояния между соседними спектральными компонентами от периода повторения импульсов} \label{dnu(T)_tbl} +\begin{tabular}{|l|l|} +\hline +T, ms & $\delta \nu$, Hz \\ \hline +0.2 & 6250 \\ \hline +1 & 2778 \\ \hline +1.5 & 4167 \\ \hline +2 & 1042 \\ \hline +2.5 & 1190 \\ \hline +3 & 735 \\ \hline +3.5 & 893 \\ \hline +4 & 1000 \\ \hline +4.5 & 1042 \\ \hline +5 & 1190 \\ \hline +\end{tabular} +\end{table} + +\begin{figure}[h!] +\begin{center} +\includegraphics[width=0.9\textwidth]{T(dnu)} +\caption{Зависимость расстояния между соседними спектральными компонентами от периода повторения импульсов} \label{dnu(T)_img} +\end{center} +\end{figure} + +Точки должны хорошо ложиться на прямую, однако из графика видно, что это не так. Проблема заключается в снятии данных (был выбран неверный канал при курсорных измерениях). Поэтому подтвердить справедливость соотношения неопределенности невозможно. + +\subsection{Исследование спектра гармонических сигналов, модулированных по амплитуде} +На генераторе создается сигнал, модулированных по амплитуде, по которому на экране осциллографа получается спектр (\ref{мод}). +\begin{figure}[h!] +\begin{center} +\includegraphics[width=\textwidth]{3} +\caption{Спектр сигнала, модулированного по амплитуде} \label{мод} +\end{center} +\end{figure} +Измерим с помощью осциллографа глубину модуляции: +\begin{equation} +m = \dfrac{A_{max}-A_{min}}{A_{max}+A_{min}} = \dfrac{1.54 - 0.04}{1.54 + 0.04} = 0.5, что сходится с установленным на генераторе +\end{equation} +Изменяя глубину модуляции, измерим $\dfrac{a_{бок}}{а_{осн}}$ (табл. \ref{mod_tbl} и рис. \ref{mod_img}). + +\begin{table}[h!] +\caption{Зависимость $\dfrac{a_{бок}}{а_{осн}}$ от $m$} +\label{mod_tbl} +\begin{tabular}{|l|l|l|} +\hline +m & a\_бок & a\_центр \\ \hline +50 & 186 & 738 \\ \hline +10 & 38 & 738 \\ \hline +20 & 74 & 738 \\ \hline +30 & 110 & 738 \\ \hline +40 & 150 & 738 \\ \hline +60 & 222 & 738 \\ \hline +70 & 258 & 738 \\ \hline +80 & 298 & 738 \\ \hline +90 & 334 & 738 \\ \hline +100 & 370 & 738 \\ \hline +\end{tabular} +\end{table} +\begin{figure}[h!] +\begin{center} +\includegraphics[width=0.9\textwidth]{a(m)} +\caption{Зависимость $\dfrac{a_{бок}}{а_{осн}}$ от $m$} \label{mod_img} +\end{center} +\end{figure} +Определим коэффициент наклона прямой: +\begin{equation} +k = 0.502 \pm 0.002 +\end{equation} +Результат сходится с предсказанным теоретически (0.5). + +\section{Выводы} + + +1. При исследовании последовательности прямоугольных импульсов получена зависимость ширины спектра от длительности импульса, что подтверждает соотношение неопределенностей: $\tau \cdot \Delta\nu \sim 1$. + +2. Проверены теоретические расчеты спектра при прямоугольных импульсах (теоретическая и экспериментальная картины схожи). + +3. При обработке данных от спектра периодической последовательности цугов была обнаружена ошибка при снятии данных, что не позволило проверить соотношение неопределенностей. + +4. Получен угол наклона графика зависимости $\dfrac{a_{бок}}{а_{осн}}$ от $m$ (0.5), подтверждено теоретическое значение этого угла (0.5). + +\end{document} \ No newline at end of file diff --git a/3.6.1Спектр/Цуги.png b/3.6.1Спектр/Цуги.png new file mode 100644 index 0000000000000000000000000000000000000000..adf6c8b9f0c71d4b6429df356a10c9bffa6d9d0f GIT binary patch literal 19171 zcmdpecQ~8x8*lp6(qXjKVbthQI*gh{t!im&*J=^7wnSADBS=+gwN)*(ca;bwb}B|{ zxAq7@klG_6idYfO>-+m%=Q@9#>zwQScmCk@8qa+{_jB*(bBi=K)a5!Za2x~zaXox+ z?=cAU&lm`F==M=|;5%YTkcR@v67Z!k*!>(EeS|CtK^od=EBf$Hy=MSFx zf?`fI&+tS8PjDGRm+yA>+$ouG;USHLhF7e;juEk%lIIYav zKv5Av&~}t>4oX$WN8N9iI<3c@a{QD^eqQ0U)R`QZ+5DghoTRqTRNdt4$9cLGO$8@1 z89{dws|M~G!7H3j$mGbSz z_|u#xjt^z1<@Q4r_{}oLMKxiNsKi|*&=(B7e5)cCmu)F*DqQTmpiip;k^ zoXe+hps5M_iP^83YWr>wb9b%bQ|@s2KT!oR1g-cVzsEi+P*~YA5|U;+&rsq5TPHr@ z21%TF4F#>-%x&nV_tK%M+06+yXkA0^tdS$#i$>^lOuO#)ekE!BehyV$KZDDa6Xt3@ zoomV4Ly#S7vQ=b`LqQR~R-`YnAY)L{uO@4_NcYbnki%sd+e_CI@)MC00=1YD0TJ>; zq18%i^);hKX^}4$kY7Dw0)3gDSg5$y2)G?{nt|Qbc+*T%voa zWh6IUN1v+!QAI?B&BEUA8X9OI{f0P$BsCIaIRCCcQ6_BV6a16>b1D19JeK~ql32xs>mfIPg6;**x zRN;lxzigj8ZF^SU5KKGQjEMXdwTkuRa>Tf9vSX3rd|?Q9GfEon6dlh7?|SN4zK-z` zs7|XI0~wDT9Rs~+doNwbx4-}GVeI5S4|qwgGi4XD>ro+GNbEJefq&XQj(jNXb;qK0 z)4d=tGH1E42W_emg_3(@OVJ)^*K_Npe#_nw`fAm$ySR`<%l# zm~&V0H&9p{H`R5IZ!y}np`O+Q77aUCv}V0eFVeG5JR>OP$GM`f&c5<$>bU8XaEOUg zT}K66WFdPKcMVH1QOWwaIg6Wr@2B9Bo+R+%wV_%AGiXIES){-YG5Woe-qB~4n+Vdx zT!OLv;-A(2@=(=pnbY;%Z+t7G+5#ydEiD~_>059&h}w53PhU1$L(c>Ru;AM@l79)e zZ}iOu(A}SDfd{BVHl3&S`bW0w($%v9+osS(Omnqf1ojI7-fQAr7`ZQ&EdUwVSW(Ma zkdt@c-e|fD(sUO+ASvhCrEe39SQ^TjXnZ3MJz~6hX>6zKPG^ROogIo5I$kGvi?^C$ zTw59x5EQUmI`6JF>OhYnD35%LJ3;7qp`tG=~E%>djYBx)I{x$B*z@OaH|Hsr+mUq?BEBOqg|gJXZiKT~8|8#rkZ=`+TMl#`TP;l4y8>%Oz_nE8h{IVInj zB_P&*M`CAD+rS1|1UJEcWXJ{a_+K3`$2m+*y4qzj?6AFlkvX83^9P3i8b=9H^?_JA zguv~+W-hR#(Me8V<>Pzv?8XyGy-QJoX>$^9HU~oQkCX<5&Ng9jmZWnEQzRQ}!rdGC zZH0cB0t0`y!c?rXq+PLZ?Fs@Nl^E+6Mo^WlAyLEzn{AImiL$}QZH7aLrpx!0vjX#2Ldt%u1 z;@QgrV-;5lL;t%{&9vo_^x%!*zx#sQ+uMKt)I!LWpK=p}3eMWa@1AzHjXvi=g%_*5 z{3;g92-#&;g>}ragT9CX(m&oEWd0{$E^V{l=%*laxteZNulfZzgYEFTEjQD@XA>x8 zLdk_YS5XnUDFvakzHFej(^-O=;VwE=99#nBdVdTbvD3eP{n``*3VD)wBqOQSXIqV2 zDF8PkP4PU5e}Xw8NB9!S)SC09f7L3yY3Fkkbd>jCfx#TT^IU?8H+?+)uKM%v%UPsQsxVpXDuzk*u-Bs*KxbTx|ep#&U^PAC!%G}!73#Il@13Sz>X1WhZ zQxx#KzdUN|Y*);K-n|JdHz$p#CwHj{QU6N(Cc85{1^nh!7h{V$`1BMVOiMP@E1xDgRCUWrR`y3Oj+#JlFMac79Lx5HYqB zquj157>YO*xbk≺`<|cH!{%-gn`Y^ZS&!8W`xM_rZoI=Q2><*^OkHI(8&2e*_IS zVicNZ!pqLNWfi!OA@f|K>+v~$3hoS?m5JM4Z}iSY83&B)BjVn^rsTeINI2x1>)c(* z#LA~Ci+l`7y(P~-n(lzF)zrDRmM;i{CtA{M$F+h7Hm3#NMWqy86SN75niyw;b)GQt zbgOQK2fTM0sAB~P$dpC}Mk60=`i+qK4{3TWJTpkOHdQcMEJ`0>38{cUyT9L`)wAJv zd0bi=dqqEjR1WDmZ-nT-XentiE{46fpCmU>?`J#q-C6oV&c^wHejkyVqF%MIkb-yT zovWZA&}Beoz1Jm^aJgIik^_qg-~p)~kdJ}Fa&QFuvfR@t@sJ{TWKPbdcgpVYm&`^z>^o>O%TKGwMj{j4A@_EC-t(oSinWyN*-K**$ zXIzy!Vbk~L7T3e27eD*lFjFZ(#?993lVY&L0H4l+LX?}C*D&kK(ItSFy*YB}F>nd&yCi(42c^BBJ&j1|7Y4@y

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