Lab_2_RTC_Stat

clear all;
load("lab2_coeff.mat");
MX = 0; %Constant value
SIGMAX = 0.3; %Mean square deviations
N = 10000; %Count samples
K = 100;%Count realizations of process
fs = 1000; %Freuency of sampling
amp = 10;
ansambles = zeros(K, N);
%TODO norming Fsampling with time value
x = normrnd(MX, SIGMAX, 1, N);
%Generate random process
for i = 1:K
    ansambles(i, :) =amp * normrnd(MX, SIGMAX, 1, N);
end
norm_time = zeros(1, N);
%Math time norming
for i = 1:N
   norm_time(i) = i/fs;
end
%Plot graph
%for i = 1: K
%Create array after circuits
c0 = filter([1, -0.5], 1, ansambles(1, :));
c1 = filter([1, 0.5], 1, ansambles(1, :));
%part2 of circuits
c2 = filter(1, [1, +0.9], ansambles(1, :));
c3 = filter(1, [1, -0.9], ansambles(1, :));
c4 = filter(Num, 1, ansambles(1, :));
i = 1;
   figure
   plot(norm_time, ansambles(i, :));
   hold on
   title("Реализация случайного процесса");
   xlabel("t, s");
   ylabel("x(t), V");
   plot(norm_time, mean(ansambles(i, :)) * ones(size(norm_time)));
   plot(norm_time, std(ansambles(i, :)) * ones(size(norm_time)));
   plot(norm_time, std(ansambles(i, :)) * -1 * ones(size(norm_time)));
   plot(norm_time, var(ansambles(i, :)) * ones(size(norm_time)));
   plot(norm_time, var(ansambles(i, :)) * -1 * ones(size(norm_time)));
   grid on;
%%end
   %c0
   figure
   plot(norm_time, c0);
   hold on
   title("Реализация случайного процесса после прохождения цепи");
   xlabel("t, s");
   ylabel("x(t), V");
   plot(norm_time, mean(c0) * ones(size(norm_time)));
   plot(norm_time, std(c0) * ones(size(norm_time)));
   plot(norm_time, std(c0) * -1 * ones(size(norm_time)));
   plot(norm_time, var(c0) * ones(size(norm_time)));
   plot(norm_time, var(c0) * -1 * ones(size(norm_time)));
   %c1
   figure
   plot(norm_time, c1);
   hold on
   title("Реализация случайного процесса после прохождения цепи");
   xlabel("t, s");
   ylabel("x(t), V");
   plot(norm_time, mean(c1) * ones(size(norm_time)));
   plot(norm_time, std(c1) * ones(size(norm_time)));
   plot(norm_time, std(c1) * -1 * ones(size(norm_time)));
   plot(norm_time, var(c1) * ones(size(norm_time)));
   plot(norm_time, var(c1) * -1 * ones(size(norm_time)));
   %c2
   figure
   plot(norm_time, c2);
   hold on
   title("Реализация случайного процесса после прохождения цепи");
   xlabel("t, s");
   ylabel("x(t), V");
   plot(norm_time, mean(c2) * ones(size(norm_time)));
   plot(norm_time, std(c2) * ones(size(norm_time)));
   plot(norm_time, std(c2) * -1 * ones(size(norm_time)));
   plot(norm_time, var(c2) * ones(size(norm_time)));
   plot(norm_time, var(c2) * -1 * ones(size(norm_time)));
    %c3
   figure
   plot(norm_time, c3);
   hold on
   title("Реализация случайного процесса после прохождения цепи");
   xlabel("t, s");
   ylabel("x(t), V");
   plot(norm_time, mean(c3) * ones(size(norm_time)));
   plot(norm_time, std(c3) * ones(size(norm_time)));
   plot(norm_time, std(c3) * -1 * ones(size(norm_time)));
   plot(norm_time, var(c3) * ones(size(norm_time)));
   plot(norm_time, var(c3) * -1 * ones(size(norm_time)));
       %c4
   figure
   plot(norm_time, c4);
   hold on
   title("Реализация случайного процесса после прохождения цепи");
   xlabel("t, s");
   ylabel("x(t), V");
   plot(norm_time, mean(c4) * ones(size(norm_time)));
   plot(norm_time, std(c4) * ones(size(norm_time)));
   plot(norm_time, std(c4) * -1 * ones(size(norm_time)));
   plot(norm_time, var(c4) * ones(size(norm_time)));
   plot(norm_time, var(c4) * -1 * ones(size(norm_time)));
%автокорреляция
figure
plot(xcorr(ansambles(1, :)));
title("Автокорреляция");
i = 1;
   figure
   [counts, bins] = hist(ansambles(i, :));
   hold on;
   est_pdf = counts / sum(counts * mean(diff(bins)));
   pd = fitdist(ansambles(1, :)','normal');
   x_pdf = linspace(min(ansambles(i, :)),max(ansambles(i, :)),length(norm_time));
   y_pdf = pdf(pd,x_pdf);
   bar(bins,est_pdf);
   plot(x_pdf, y_pdf, '-r');
   title("плотность вероятности и ее оценка");
   %c0
   figure
   plot(xcorr(c0));
   title("Автокорреляция");
   i = 1;
   figure
   [counts, bins] = hist(c0);
   hold on;
   est_pdf = counts / sum(counts * mean(diff(bins)));
   pd = fitdist(ansambles(1, :)','normal');
   x_pdf = linspace(min(ansambles(i, :)),max(ansambles(i, :)),length(norm_time));
   y_pdf = pdf(pd,x_pdf);
   bar(bins,est_pdf);
   plot(x_pdf, y_pdf, '-r');
   title("плотность вероятности и ее оценка");

   %c1
   figure
   plot(xcorr(c1));
   title("Автокорреляция");
   i = 1;
   figure
   [counts, bins] = hist(c1);
   hold on;
   est_pdf = counts / sum(counts * mean(diff(bins)));
   pd = fitdist(ansambles(1, :)','normal');
   x_pdf = linspace(min(ansambles(i, :)),max(ansambles(i, :)),length(norm_time));
   y_pdf = pdf(pd,x_pdf);
   bar(bins,est_pdf);
   plot(x_pdf, y_pdf, '-r');
   title("плотность вероятности и ее оценка");

   %c2
   figure
   plot(xcorr(c2));
   title("Автокорреляция");
   i = 1;
   figure
   [counts, bins] = hist(c2);
   hold on;
   est_pdf = counts / sum(counts * mean(diff(bins)));
   pd = fitdist(ansambles(1, :)','normal');
   x_pdf = linspace(min(ansambles(i, :)),max(ansambles(i, :)),length(norm_time));
   y_pdf = pdf(pd,x_pdf);
   bar(bins,est_pdf);
   plot(x_pdf, y_pdf, '-r');
   title("плотность вероятности и ее оценка");

   %c3
   figure
   plot(xcorr(c3));
   title("Автокорреляция");
   i = 1;
   figure
   [counts, bins] = hist(c3);
   hold on;
   est_pdf = counts / sum(counts * mean(diff(bins)));
   pd = fitdist(ansambles(1, :)','normal');
   x_pdf = linspace(min(ansambles(i, :)),max(ansambles(i, :)),length(norm_time));
   y_pdf = pdf(pd,x_pdf);
   bar(bins,est_pdf);
   plot(x_pdf, y_pdf, '-r');
   title("плотность вероятности и ее оценка");

   %c4
   figure
   plot(xcorr(c4));
   title("Автокорреляция для фильтра");
   i = 1;
   figure
   [counts, bins] = hist(c4);
   hold on;
   est_pdf = counts / sum(counts * mean(diff(bins)));
   pd = fitdist(ansambles(1, :)','normal');
   x_pdf = linspace(min(ansambles(i, :)),max(ansambles(i, :)),length(norm_time));
   y_pdf = pdf(pd,x_pdf);
   bar(bins,est_pdf);
   plot(x_pdf, y_pdf, '-r');
   title("плотность вероятности и ее оценка для фильтра");


   %
   figure
   hold on
   cdfplot(ansambles(i, :))
   histogram(ansambles(1, :), 'Normalization', 'cdf');
   title("Функция распределения и ее оценка");
   figure
   %PSD = periodogram(ansambles(1, :), [], length(ansambles(1, :)), fs, 'centered');
   PSD = 10 * log10(abs(fft(ansambles(1, :))).^2/N/fs);
   %PSD = fftshift(PSD);
   plot(PSD);
   title("СПМ");
   ans_mean = zeros(1, length(ansambles(1, :)));
   for i = 1: K
       ans_mean(1, :) = ans_mean(1, :) + ansambles(i, :);
   end
   ans_mean = ans_mean / K;
   figure
   PSD_M= 10 * log10(abs(fft(ans_mean(1, :))).^2/N/fs);
   plot(PSD_M);
   hold on;
   title("Усредненная СПМ");
%end

   %с0
   figure
   hold on
   cdfplot(c0)
   histogram(c0, 'Normalization', 'cdf');
   title("Функция распределения и ее оценка");
   figure
   %PSD = periodogram(ansambles(1, :), [], length(ansambles(1, :)), fs, 'centered');
   PSD = 10 * log10(abs(fft(c0)).^2/N/fs);
   %PSD = fftshift(PSD);
   plot(PSD);
   title("СПМ");
   ans_mean = zeros(1, length(c0));
   for i = 1: K
       ans_mean(1, :) = ans_mean(1, :) + c0;
   end
   ans_mean = ans_mean / K;
   figure
   PSD_M= 10 * log10(abs(fft(ans_mean(1, :))).^2/N/fs);
   plot(PSD_M);
   hold on;
   title("Усредненная СПМ");

   %c1
   figure
   hold on
   cdfplot(c1)
   histogram(c1, 'Normalization', 'cdf');
   title("Функция распределения и ее оценка");
   figure
   %PSD = periodogram(ansambles(1, :), [], length(ansambles(1, :)), fs, 'centered');
   PSD = 10 * log10(abs(fft(c1)).^2/N/fs);
   %PSD = fftshift(PSD);
   plot(PSD);
   title("СПМ");
   ans_mean = zeros(1, length(c1));
   for i = 1: K
       ans_mean(1, :) = ans_mean(1, :) + c1;
   end
   ans_mean = ans_mean / K;
   figure
   PSD_M= 10 * log10(abs(fft(ans_mean(1, :))).^2/N/fs);
   plot(PSD_M);
   hold on;
   title("Усредненная СПМ");


   %c2
   figure
   hold on
   cdfplot(c2)
   histogram(c2, 'Normalization', 'cdf');
   title("Функция распределения и ее оценка");
   figure
   %PSD = periodogram(ansambles(1, :), [], length(ansambles(1, :)), fs, 'centered');
   PSD = 10 * log10(abs(fft(c2)).^2/N/fs);
   %PSD = fftshift(PSD);
   plot(PSD);
   title("СПМ");
   ans_mean = zeros(1, length(c2));
   for i = 1: K
       ans_mean(1, :) = ans_mean(1, :) + c2;
   end
   ans_mean = ans_mean / K;
   figure
   PSD_M= 10 * log10(abs(fft(ans_mean(1, :))).^2/N/fs);
   plot(PSD_M);
   hold on;
   title("Усредненная СПМ");

   %c3
   figure
   hold on
   cdfplot(c3)
   histogram(c3, 'Normalization', 'cdf');
   title("Функция распределения и ее оценка");
   figure
   %PSD = periodogram(ansambles(1, :), [], length(ansambles(1, :)), fs, 'centered');
   PSD = 10 * log10(abs(fft(c3)).^2/N/fs);
   %PSD = fftshift(PSD);
   plot(PSD);
   title("СПМ");
   ans_mean = zeros(1, length(c3));
   for i = 1: K
       ans_mean(1, :) = ans_mean(1, :) + c3;
   end
   ans_mean = ans_mean / K;
   figure
   PSD_M= 10 * log10(abs(fft(ans_mean(1, :))).^2/N/fs);
   plot(PSD_M);
   hold on;
   title("Усредненная СПМ");


   %c4
   figure
   hold on
   cdfplot(c4)
   histogram(c4, 'Normalization', 'cdf');
   title("Функция распределения и ее оценка");
   figure
   %PSD = periodogram(ansambles(1, :), [], length(ansambles(1, :)), fs, 'centered');
   PSD = 10 * log10(abs(fft(c4)).^2/N/fs);
   %PSD = fftshift(PSD);
   plot(PSD);
   title("СПМ");
   ans_mean = zeros(1, length(c4));
   for i = 1: K
       ans_mean(1, :) = ans_mean(1, :) + c4;
   end
   ans_mean = ans_mean / K;
   figure
   PSD_M= 10 * log10(abs(fft(ans_mean(1, :))).^2/N/fs);
   plot(PSD_M);
   hold on;
   title("Усредненная СПМ");
%end