自相关函数仿真理解demo

背景介绍

利用MATLAB程序互动理解自相关函数，相关函数的工程应用可以看这里。
随意按键原始移动信号，造成不同时延与原函数自相关分析得到不同的相关程度。

完整代码

1. 调用函数

fs = 1000;
T = 1/fs;
N = 500; % desired length of signal
t = [0:N-1]*T; %time vector
f1 = 8; f2=f1*2;
x = sin(2*pi*f1*t) + sin(2*pi*f2*t);

% To step though each sample use the following:
autocorrelation(x,x)

% to step through using 50 steps use:
autocorrelation(x,x, 50)

2. 自相关函数demo

% This function illustrates the cross correlation process in action

function autocorrelation(x, y, varargin)
if(length(x) > length(y))
    y(end+1:length(x)) = 0; %zero pad so the signals are the same length
else
    x(end+1:length(y)) = 0; %zero pad so the signals are the same length
end

    num_steps = 2*length(x)-1;
if(nargin ==3)
    arg = varargin{1};
    if(isnumeric(arg))
        num_steps = ceil(abs(arg));
    end
end
if(nargin > 3)
    error('See help on this function to see how to use it properly')
end

[rxy lags] = xcorr(x,y); %cross correlate signals

disp('The signal being autocorrelated is shown in blue (two instances)')
disp('As you hit the space bar the lower plot will move into different lag positions')
disp('The correlation function shown in red is updated for each lag position');
disp('keep pressing the space bar to step through the illustration ...');

figure
plot_width = 0.3; plot_height = 0.25;

top_ax_h = subplot(3,1,1);
plot(x)
axis tight
set(top_ax_h, 'visible','off', 'units', 'normalized')
set(top_ax_h,'position', [0.5-plot_width/2 5/6-plot_height/2 plot_width plot_height])

mid_ax_h = subplot(3,1,2);
plot(y)
axis tight
set(mid_ax_h, 'visible','off', 'units', 'normalized')
set(mid_ax_h,'position', [0.5-plot_width/2-plot_width 5/6-3*plot_height/2-0.01 plot_width plot_height])

bottom_ax_h = subplot(3,1,3);
corr_h = plot(lags,rxy,'r');
axis tight
set(bottom_ax_h,'units', 'normalized','Ytick',[])
set(bottom_ax_h,'position', [0.5-plot_width*3/2 0.2-plot_height/2 plot_width*3 plot_height])
set(corr_h, 'Ydata', ones(1, length(rxy))*NaN); %clear the correlation funciton plot once its set up

normalised_shift_size = 2*plot_width/(num_steps-1);
corr_seg_len = length(rxy)/num_steps;
for k = 1 : num_steps
    if(k > 1)
        new_pos = get(mid_ax_h,'position') + [normalised_shift_size 0 0 0];
        set(mid_ax_h,'position', new_pos);
    end
    set(corr_h, 'Ydata', [rxy(1:round(corr_seg_len*k)) ones(1,length(rxy)-round(corr_seg_len*k))*NaN])
    pause
end