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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# j7 D' f5 J( x% D8 J7 }7 K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：

% T0 e) z9 }. Gfunction [y,n] = sigadd(x1,n1,x2,n2)
/ A, ^: _* t6 u. i, G1 `, ^% implements y(n) = x1(n) + x2(n)
# k3 E& O# k7 e! ~% [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)
4 W: _% h5 J' p% k: }: Ty1 = zeros(1,length(n)); y2 = y1; %initialization
; Q( T5 A$ W3 R' E2 s! ]0 Uy1( 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
8 T( O) a& T0 V' i/ i: b: Q3 ?3 Sy = y1 + y2;
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直接给出MATLAB脚本：

) S3 f% n% @* w+ q+ H2 y- @" ~clc
. P" g+ l! u/ I  ]clear
close all
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. y) r, Y1 s- I, p9 N% help stepseq
" @7 e6 M1 k9 f, u/ f3 P. N* _%   generate x(n) = u(n - n0); n1 <= n <= n2
%  _____________________________________________
1 G/ h: F2 |& N! C9 C0 s4 v9 m- N%  [x,n] = stepseq(n0, n1, n2);
[u1,n1] = stepseq(0,-5,45);
3 v8 _( w& u1 k0 V$ q' Z[u2,n2] = stepseq(10,-5,45);

! Q- v& N! S7 u0 M! S% generate signal x(n)
* _7 t4 @" {7 t# A& v[x,n] = sigadd(u1,n1,-u2,n2);

; e" b' D7 H* y7 b0 i% generate signal h(n)
( f3 P/ ^. R0 ]- Z3 Z" em = -5:45;
h = ( (0.9).^m ).* u1;
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2 @' d/ g& S) W1 B% the convolution of x(h) and h(n)
y = conv(x,h);
% ensure the index
# a1 r6 m# Q3 u; p1 Z. Jnyb = n(1)+ m(1);
nye = n(length(x)) +n(length(h));
ny = nyb:nye;


2 T" {0 H& e/ F. t2 `- wsubplot(3,1,1);
, P8 z1 @+ u: D* ^/ H7 jstem(n,x);
title('x(n)');
xlabel('n')

subplot(3,1,2);
stem(m,h);
6 p3 ]3 d. C- F! ]% Xtitle('h(n)');
8 D5 t3 ~) y. Z5 ]xlabel('n')

3 \$ L0 x, D* I1 R; U' O6 csubplot(3,1,3);
+ l& p' f0 ]7 @  U0 Xstem(ny,y);
title('the conv of x(n) and h(n)');
xlabel('n')
6 n" X! ?5 y  D4 X0 |4 [xlim([-5,45]);


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Heaven_1

subplot这个函数经常使用
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