firsthomework.m

产生高斯白噪声并估计自相关序列

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%实验一：产生高斯白噪声并估计自相关序列
%% 作者： 李从娟 070628
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc;
clear all;
N = 1000;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  产生1000点零均值单位方差高斯白噪声序列   %%%%
X = randn(1,N);
r = 1;
r = [1,zeros(1,99)];
for k = 1:100
    ra(k) = 0;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%   用整体数据估计自相关序列   %%%%%%%%%%%
for k = 0:99
    n = k+1;
    for m = n:1000
        ra(n) = X(m)*X(m-k) + ra(n);
    end
    ra(n) = ra(n)/1000;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%   将数据分段之后估计自相关序列  %%%%%%%%%%           
for k = 1:100
    rb(k) = 0;
end
for k = 0:99
    L = k+1;
    for m = 0:9
        for n = L:99
            rb(L) = rb(L) + X(n+100*m)*X(n-k+100*m);
        end
    end
rb(L) = rb(L)/1000;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%   画图   %%%%%%%%%%%%%%%%%%%
n = [0:999];
figure(1);
stem(n,X);
xlabel('n');
ylabel('X[n]');
title('White noise sequence');
m = [0:99];
figure(2);
plot(m,r,'c>',m,ra,'m*',m,rb,'b+');
xlabel('m');
ylabel('Rx[n]');
title('autocorrelation');
grid;
legend('Real autocorrelation','autocorrelation with all','autocorrelation with part');