Contents

decompose signal

n = -15:15;
x = stepseq(0,-15,15) - stepseq(10,-15,15);
stem(n,x)

[xe,xo,m] = evenodd(x,n);
subplot(2,2,1); stem(n,x); title('rectangular pulse'); axis tight;
subplot(2,2,2); stem(m,xe); title('even part'); axis tight;
subplot(2,2,3); stem(m,xo); title('odd part'); axis tight;
subplot(2,2,4); stem(m,xo+xe); title('odd+even'); axis tight;

correlation

correlation is convolution after folding conv(x,y) = x{l)*y(l) corr(x,y) = x(l)*y(-l)

x = [3 11 7 0 -1 4 2];
nx = -3:3;

h = [2 3 0 -5 2 1];
nh = -1:4;

[y,ny] = conv_m(x,nx,h,nh);

subplot(3,1,1); stem(nx,x); xlim([-5 8]);
subplot(3,1,2); stem(nh,h); xlim([-5 8]);
subplot(3,1,3); stem(ny,y); xlim([-5 8]);

x = [3 11 7 0 -1 4 2];

y(n) = x(n-2)+w(n), w(n) is sequence of random noise compute the cross-correlation between y(n) and x(n)

x = [3 11 7 0 -1 4 2];
nx = -3:3;

[y,ny] = sigshift(x,nx,2);

w = randn(1, length(y));
nw = ny;

[y,ny] = sigadd(x,nx,w,nw);

figure
subplot(3,1,1); stem(nx,x); xlim([-7 7]);
subplot(3,1,2); stem(ny,y); xlim([-7 7]);

% [x,nx] = sigfold(x,nx);
% [rxy,nrxy] = conv_m(y,ny,x,nx);
[rxy, nrxy] = xcorr_m(x,nx,y,ny);
subplot(3,1,3); stem(nrxy,rxy); xlim([-7 7]);

hold on

[rxy, nrxy] = xcorr_m(y,ny,x,nx);
subplot(3,1,3); stem(nrxy,rxy); xlim([-7 7]);

covolution properties

nx1 = -5:25;
x1 = cos(pi/4*nx1).*(stepseq(-5,-5,25)-stepseq(25,-5,25));
figure
subplot(4,1,1); stem(nx1,x1); xlim([-10 30]);

nx2 = 0:20;
x2 = (0.9).^nx2.*(stepseq(0,0,20)-stepseq(20,0,20));
subplot(4,1,2); stem(nx2,x2); xlim([-10 30]);

nx3 = -10:10;
x3 = round(5*randn(size(nx3)));
subplot(4,1,3); stem(nx3,x3); xlim([-10 30]);

% commutation
% x1*x2=x2*x1
[y1,ny1] = conv_m(x1,nx1,x2,nx2);
[y2,ny2] = conv_m(x2,nx2,x1,nx1);
subplot(4,1,4); stem(ny1,y1,'k'); hold on; stem(ny2,y2,'r'); hold off;

% association
[yl,nyl] = conv_m(x1,nx1,x2,nx2);
[yl,nyl] = conv_m(yl,nyl,x3,nx3);
[yr,nyr] = conv_m(x2,nx2,x3,nx3);
[yr,nyr] = conv_m(yr,nyr,x1,nx1);
subplot(4,1,4); stem(nyl,yl,'k'); hold on; stem(nyr,yr,'r'); hold off;

% distribution
[yl,nyl] = sigadd(x2,nx2,x3,nx3);
[yl,nyl] = conv_m(x1,nx1,yl,nyl);
[yr1,nyr1] = conv_m(x1,nx1,x2,nx2);
[yr2,nyr2] = conv_m(x1,nx1,x3,nx3);
[yr,nyr] = sigadd(yr1,nyr1,yr2,nyr2);
subplot(4,1,4); stem(nyl,yl); hold on; stem(nyr,yr); hold off;

% identity
n0 = 10;
[yl,nyl] = impseq(10,-10,30);
[yl,nyl] = conv_m(x1,nx1,yl,nyl);
[yr,nyr] = sigshift(x1,nx1,n0);
subplot(4,1,4); stem(nyl,yl); hold on; stem(nyr,yr); hold off;

Published with MATLAB® R2016b