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).
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  i8 p3 P4 z5 u9 }9 s$ U- V$ D/ d" I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)
2 x7 Y1 w: Z6 L3 s4 z2 g. J/ o- L% implements y(n) = x1(n) + x2(n)
8 q- p. Z2 {8 _4 M+ I2 `" o1 r6 R% [y,n] = sigadd(x1,n1,x2,n2)
%——————————————————————————————
5 ]1 v+ t2 D  a! b& {8 l# d: Z% y = sum sequence over n, which includes n1 and n2
% x1 = first sequence over n1
' N( T+ W. g8 F/ o! h% 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
  T, L( v  R4 }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;


直接给出MATLAB脚本：
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clc
7 ~, b& H6 Z( ?5 L' T; rclear
3 Y' i! l& H/ \  [+ z5 Bclose all
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% help stepseq
%   generate x(n) = u(n - n0); n1 <= n <= n2
7 X; [: t4 {$ X%  _____________________________________________
% s% A- x* t1 T  i%  [x,n] = stepseq(n0, n1, n2);
[u1,n1] = stepseq(0,-5,45);
/ Z0 [# M! L4 K# B5 M. [[u2,n2] = stepseq(10,-5,45);

8 o" `7 l! a, M5 |# l% generate signal x(n)
[x,n] = sigadd(u1,n1,-u2,n2);
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% generate signal h(n)
* W8 Z" j! k1 b. zm = -5:45;
- F. F% U7 @( K/ xh = ( (0.9).^m ).* u1;


# {: K1 N5 p- u% the convolution of x(h) and h(n)
y = conv(x,h);
% ensure the index
1 }# K7 f& K8 Vnyb = n(1)+ m(1);
nye = n(length(x)) +n(length(h));
* f* [$ k$ k0 C* v. w# ]$ a& Hny = nyb:nye;

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subplot(3,1,1);
/ [! x, r% \) Z2 a7 Estem(n,x);
title('x(n)');
% v& ~; R( k, O  H; x. g% H" X. W; bxlabel('n')

subplot(3,1,2);
( N! q% k+ R# S! w9 q+ lstem(m,h);
; s$ t" c3 B5 F* Xtitle('h(n)');
xlabel('n')

subplot(3,1,3);
& d+ N  G( a9 M" q8 E: \stem(ny,y);
- D9 K! v% N1 M  Z& ~title('the conv of x(n) and h(n)');
4 q$ F5 A# K# Q6 }4 w; p7 sxlabel('n')
xlim([-5,45]);


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Heaven_1

subplot这个函数经常使用
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