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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6 ^# x1 V' r8 U4 I" O2 h6 Vfunction [y,n] = sigadd(x1,n1,x2,n2)
% implements y(n) = x1(n) + x2(n)
2 P  [& J8 E+ O$ |: E9 i% [y,n] = sigadd(x1,n1,x2,n2)
. a( _- D3 r# c. W6 C6 Q) B3 Y' _%——————————————————————————————
% y = sum sequence over n, which includes n1 and n2
- [8 `; {& {( O% x1 = first sequence over n1
$ N6 f- c  @, M0 Z  X% x2 = second sequence over n2( n2 can be different from n1)
%
( v- Z' ?. |5 ?" s) y, V5 E4 an = min( min(n1), min(n2) ):max( max(n1), max(n2) ); %duration of y(n)
/ @4 H6 t1 g+ P8 p8 Sy1 = zeros(1,length(n)); y2 = y1; %initialization
y1( find( ( n >= min(n1) )&( n <= max(n1) ) == 1  )  ) = x1; %x1 with duration of y1
- r' F3 ?' ^$ P. g, ry2( find( ( n >= min(n2) )&( n <= max(n2) ) == 1  )  ) = x1; %x2 with duration of y2
) N0 X0 W9 W% r% zy = y1 + y2;

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: x- k$ @& b6 I, \1 F( ]5 l5 M* z" l直接给出MATLAB脚本：

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clear
close all
. b' h  s$ |8 g# L. o. x
% help stepseq
%   generate x(n) = u(n - n0); n1 <= n <= n2
3 p. ]5 @: x; O3 C) t% o%  _____________________________________________
%  [x,n] = stepseq(n0, n1, n2);
[u1,n1] = stepseq(0,-5,45);
[u2,n2] = stepseq(10,-5,45);
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% generate signal x(n)
! G" Z! f" p* s  a[x,n] = sigadd(u1,n1,-u2,n2);
6 z7 Z+ d  ?8 B. _% s
% generate signal h(n)
7 E, H+ `" v- dm = -5:45;
h = ( (0.9).^m ).* u1;
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" ~# b+ B7 z, z! w; L4 S3 t% the convolution of x(h) and h(n)
, [0 T- m& M8 }& [y = conv(x,h);
' k6 h! W! E# [! g, M0 J% ensure the index
$ K) c* K8 M5 ^+ c$ z9 u+ jnyb = n(1)+ m(1);
. C/ E& _# }' {2 Pnye = n(length(x)) +n(length(h));
ny = nyb:nye;


; \/ ]9 z* k+ M5 [% Tsubplot(3,1,1);
stem(n,x);
" e. i6 G2 @7 J- o) m9 Ttitle('x(n)');
xlabel('n')
0 b% ?4 h% o# e" }
" r! E* x3 m0 o! s6 w( L6 C/ rsubplot(3,1,2);
/ K6 v: O' o( K8 xstem(m,h);
, D3 M" X2 V1 @1 [. v, ytitle('h(n)');
xlabel('n')

' ^2 M1 ~2 m1 M" O/ L/ Csubplot(3,1,3);
! X7 j7 J3 @" F) O" q* V2 i2 U+ Pstem(ny,y);
title('the conv of x(n) and h(n)');
xlabel('n')
! X3 _/ p4 y& j, i+ l+ V, mxlim([-5,45]);
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Heaven_1

subplot这个函数经常使用