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).
. y" Q* N  A2 Z2 j
0 N8 z$ Z) [: j; J0 @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：

' I; n/ [  e9 ]6 @+ D# u/ z, yfunction [y,n] = sigadd(x1,n1,x2,n2)
% implements y(n) = x1(n) + x2(n)
+ d$ U9 z7 I. V8 t, Y# @% [y,n] = sigadd(x1,n1,x2,n2)
%——————————————————————————————
+ a1 `* k& m" j) }  w% y = sum sequence over n, which includes n1 and n2
% x1 = first sequence over n1
4 v" ^0 j  C, Z* I% x2 = second sequence over n2( n2 can be different from n1)
%
# e/ j' a  ^$ Y6 `1 T0 u2 kn = min( min(n1), min(n2) ):max( max(n1), max(n2) ); %duration of y(n)
& A# h$ W8 r  j6 Q5 ]" h* ty1 = 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;

* v0 g# ?! v4 J4 w
4 `- y) p/ B5 N3 N( @" W: u直接给出MATLAB脚本：
1 O: t: `& N  Y3 S
0 ]( ?+ w5 W2 o  ?; Hclc
1 d' a) I% a" a, d9 sclear
close all
9 i1 ~2 B. T* L. ]
5 I: Q  M: ~. u% ~& e  }% help stepseq
5 p! v3 }4 v; e. l%   generate x(n) = u(n - n0); n1 <= n <= n2
%  _____________________________________________
) B8 Q6 j) g0 m  K%  [x,n] = stepseq(n0, n1, n2);
[u1,n1] = stepseq(0,-5,45);
[u2,n2] = stepseq(10,-5,45);

% generate signal x(n)
2 G: a2 q9 H  l9 {$ X: {' _- x[x,n] = sigadd(u1,n1,-u2,n2);
7 c, h: |, o0 q$ c
) n3 Q1 r' H0 T0 F, U/ r% generate signal h(n)
* q2 v/ p5 P9 gm = -5:45;
h = ( (0.9).^m ).* u1;
" X. u! \- s$ i* E; U$ x" z( L

% the convolution of x(h) and h(n)
" E% @" t% k: s4 C3 g5 ty = conv(x,h);
( P/ U  g2 N0 t  j+ i3 j% ensure the index
nyb = n(1)+ m(1);
) B$ R8 K; o/ h5 x* b' R- ?& B& P. Fnye = n(length(x)) +n(length(h));
- p: K6 w! Y  B7 J, }/ Yny = nyb:nye;


9 N$ X% O# ]+ k$ E+ ssubplot(3,1,1);
stem(n,x);
title('x(n)');
0 ?# u* b* r  |; q  \9 e0 w% `xlabel('n')

subplot(3,1,2);
stem(m,h);
0 a4 g) A: [' N" x; y4 Ytitle('h(n)');
* k1 m2 W1 ^6 M1 J1 mxlabel('n')
' i) \. u  t( p! e0 ?5 A
# V4 w1 a; r! ?' Y2 ^( bsubplot(3,1,3);
: p2 \& e, P" C* l  w1 istem(ny,y);
title('the conv of x(n) and h(n)');
7 n- I2 H' y4 O1 g8 Uxlabel('n')
xlim([-5,45]);



2 q8 U+ C  G* M( b6 A+ B( C
# B2 y! @, Z. y' ^( z
/ a& R2 ]6 Q8 Y' }* N

Heaven_1

subplot这个函数经常使用