Lab_3

clear all;
load("lab2_coeff.mat");
MX = 3; %Constant value
SIGMAX = 0.5; %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 = ansambles(1, :).^2;
c0 = ansambles(1, :).^2;
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 квадратичного преобразователя");
   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)));

%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 после квадратичного преобразователя");
   i = 1;
   figure
   [counts, bins] = hist(c0);
   %hist(c0);
   hold on;
   est_pdf = counts / sum(counts * mean(diff(bins)));
   pd = fitdist(c0','normal');
   x_pdf = linspace(min(c0),max(c0),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 после квадратичного преобразователя");

   %
   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 после квадратичного преобразователя");
   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 после квадратичного преобразователя");
   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 после квадратичного преобразователя");
%end