两个序列的卷积和运算的MATLAB实现（1）

mytomorrow

设矩形脉冲 是脉冲响应 的LTI系统的输入，求输出 y(n).

下面的脚本中用到了一个自定义的函数，也就是两个信号相加的函数：
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function [y,n] = sigadd(x1,n1,x2,n2)
0 X$ J6 ^0 b# p) q% implements y(n) = x1(n) + x2(n)
) ]2 ]5 j& J5 d8 h- [% [y,n] = sigadd(x1,n1,x2,n2)
%——————————————————————————————
% y = sum sequence over n, which includes n1 and n2
6 \* T8 K1 Y) g  w' D0 [% D& N% x1 = first sequence over n1
! v- C/ q; h/ {6 p2 e" N7 m# g% x2 = second sequence over n2( n2 can be different from n1)
; ^3 W: u. j' N* {+ ?( }%
: {1 z( U+ Y+ Y0 Fn = min( min(n1), min(n2) ):max( max(n1), max(n2) ); %duration of y(n)
y1 = zeros(1,length(n)); y2 = y1; %initialization
6 V: @" V! G6 Y# ?y1( find( ( n >= min(n1) )&( n <= max(n1) ) == 1  )  ) = x1; %x1 with duration of y1
, S$ F+ T, F1 U- d8 k! Yy2( find( ( n >= min(n2) )&( n <= max(n2) ) == 1  )  ) = x1; %x2 with duration of y2
y = y1 + y2;
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直接给出MATLAB脚本：
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; {! F, ]. e# Z. W5 h7 D& T7 oclc
clear
close all
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% help stepseq
+ w; g% _" V4 j+ J! l: ~%   generate x(n) = u(n - n0); n1 <= n <= n2
%  _____________________________________________
%  [x,n] = stepseq(n0, n1, n2);
$ g3 D* Y! k2 K1 q( B[u1,n1] = stepseq(0,-5,45);
[u2,n2] = stepseq(10,-5,45);

6 J7 J$ J; ^' a. ?& B5 a% generate signal x(n)
[x,n] = sigadd(u1,n1,-u2,n2);
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% generate signal h(n)
5 x: o. ^; p0 C' R9 V/ P6 A& g, a* |m = -5:45;
& l' n* v" }. @& ~4 {h = ( (0.9).^m ).* u1;
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% the convolution of x(h) and h(n)
8 ^% m6 q! N0 z: _  x- e: g% Zy = conv(x,h);
( G( V9 j0 H; i/ T% ensure the index
nyb = n(1)+ m(1);
nye = n(length(x)) +n(length(h));
ny = nyb:nye;
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subplot(3,1,1);
- @- p) }1 u8 [) ?5 N8 Y4 ?* H/ pstem(n,x);
# L$ {/ D. [; t% S/ T! X: ltitle('x(n)');
xlabel('n')
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/ m; D3 ]! K$ I, t5 u1 b! B! Rsubplot(3,1,2);
$ W7 S2 \" c4 V( |stem(m,h);
title('h(n)');
1 \3 E$ `, L. d! y$ Axlabel('n')

. X1 |8 U( |9 _  V6 ~3 P+ vsubplot(3,1,3);
stem(ny,y);
title('the conv of x(n) and h(n)');
xlabel('n')
xlim([-5,45]);
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Heaven_1

subplot这个函数经常使用