Convolution Demo

Contents

Show f(x) and h(x)

References: f.m, h.m

x = linspace(-4,4,161);
% plot f(x)
y = f(x);
subplot(2,1,1);
plot(x,y,'k','LineWidth',2);
ylabel('f(x)');
axis([-4 4 0 4]);
% plot h(x)
subplot(2,1,2);
y = h(x);
plot(x,y,'k','LineWidth',2);
ylabel('h(x)');
axis([-4 4 0 4]);

Show convolution

Reference: g.m (analytic result)

subplot;
x = linspace(-8,8,321);
dx = x(2)-x(1);
g1 = g(x);
g2 = convn(f(x),h(x),'same')*dx;
plot(x,g1,x,g2,'LineWidth',2);
axis([-8 8 0 4]);

Another example

x = linspace(-8,8,321);
dx = x(2)-x(1);
f1 = rect(x);
f2 = rect(x,4);
g3 = convn(f1,f2,'same')*dx;
subplot(3,1,1);
plot(x,f1,'b','LineWidth',2);
ylabel('f1(x)');
axis([-8 8 0 2]);
subplot(3,1,2);
plot(x,f2,'g','LineWidth',2);
ylabel('f2(x)');
axis([-8 8 0 2]);
subplot(3,1,3);
plot(x,g3,'k','LineWidth',2);
ylabel('f1(x)*f2(x)');
axis([-8 8 0 2]);

polynomial

 x^2 - x + 3
      2x + 1
------------
2 x^3 -2 x^2 + 6 x
        x^2 -   x + 3
----------------------
2 x^3 -  x^2 + 5 x + 3

subplot;
p1 = [1 -1 3];  % x^2 - x + 3
x = linspace(-8,8,321);
y = polyval(p1,x);
plot(x,y);
p2 = [2 1]; % 2x+1
p3 = conv(p1,p2);
disp('results of polynomial convolution');
disp(p3)

results of polynomial convolution
     2    -1     5     3

Published with MATLAB® 7.6