設矩形脈衝  是脈衝響應  的LTI系統的輸入，求輸出 y(n).

下面的指令碼中用到了一個自定義的函式，也就是兩個訊號相加的函式：

function [y,n] = sigadd(x1,n1,x2,n2)
% implements y(n) = x1(n) + x2(n)
% [y,n] = sigadd(x1,n1,x2,n2)
%——————————————————————————————
% y = sum sequence over n, which includes n1 and n2
% x1 = first sequence over n1
% x2 = second sequence over n2( n2 can be different from n1)
%
n = min( min(n1), min(n2) ):max( max(n1), max(n2) ); %duration of y(n)
y1 = zeros(1,length(n)); y2 = y1; %initialization
y1( find( ( n >= min(n1) )&( n <= max(n1) ) == 1  )  ) = x1; %x1 with duration of y1
y2( find( ( n >= min(n2) )&( n <= max(n2) ) == 1  )  ) = x1; %x2 with duration of y2
y = y1 + y2;
 

直接給出MATLAB指令碼：

clc
clear
close all

% help stepseq
%   generate x(n) = u(n - n0); n1 <= n <= n2
%  _____________________________________________
%  [x,n] = stepseq(n0, n1, n2);
[u1,n1] = stepseq(0,-5,45);
[u2,n2] = stepseq(10,-5,45);

% generate signal x(n)
[x,n] = sigadd(u1,n1,-u2,n2);

% generate signal h(n)
m = -5:45;
h = ( (0.9).^m ).* u1;


% the convolution of x(h) and h(n)
y = conv(x,h);
% ensure the index
nyb = n(1)+ m(1);
nye = n(length(x)) +n(length(h));
ny = nyb:nye;


subplot(3,1,1);
stem(n,x);
title('x(n)');
xlabel('n')

subplot(3,1,2);
stem(m,h);
title('h(n)');
xlabel('n')

subplot(3,1,3);
stem(ny,y);
title('the conv of x(n) and h(n)');
xlabel('n')
xlim([-5,45]);