[Matlab] 线性卷积&圆周卷积代码实现

时间：2024-03-09 15:20:18

1、线性卷积 周期卷积 圆周卷积的 关系：

 

 

2、Matlab实验及现象

圆周卷积：

 1 %% 圆周卷积实例程序
 2 %% Alimy 2014年11月21日 20:19:12
 3 clc;
 4 clear;
 5 %%准备数据
 6 N = 5;
 7 M = 5;
 8 L = N + M -1;
 9 x1n = [1,2,3,4,5];
10 x2n = [1,5,9,7,3];
11 kn_x1 = 0:1:N-1;
12 kn_x2 = 0:1:M-1;
13 kn_y = 0:1:L-1;
14 %%画原始有限长序列
15 subplot(4,2,1);
16 stem(kn_x1,x1n);
17 xlabel(\'n\',\'FontSize\',15);
18 ylabel(\'x1n\',\'FontSize\',15);
19 subplot(4,2,2);
20 stem(kn_x2,x2n);
21 xlabel(\'n\',\'FontSize\',15);
22 ylabel(\'x2n\',\'FontSize\',15);
23 
24 x1n_t = [x1n, zeros(1,L-N)];  %%补零
25 x2n_t = [x2n, zeros(1,L-M)];
26 kn_x1t = 0:1:(N+M-1)-1;
27 kn_x2t = 0:1:(N+M-1)-1;
28 %%画补0后序列
29 subplot(4,2,3);
30 stem(kn_x1t,x1n_t);
31 xlabel(\'n\',\'FontSize\',15);
32 ylabel(\'x1n补0后\',\'FontSize\',15);
33 subplot(4,2,4);
34 stem(kn_x2t,x2n_t);
35 xlabel(\'n\',\'FontSize\',15);
36 ylabel(\'x2n补0后\',\'FontSize\',10);
37 
38 x1n_t = [x1n_t,x1n_t,x1n_t,x1n_t];    %沿拓
39 x1n_t = fliplr(x1n_t);                %翻转 
40 [x1t_x,x1t_y] = size(x1n_t);
41 x1t_numbers = x1t_x * x1t_y;
42 kn_x1t = -17:1:18;
43 %%画沿拓翻转后的周期序列
44 subplot(4,2,5);
45 stem(kn_x1t,x1n_t);
46 xlabel(\'t\',\'FontSize\',15);
47 ylabel(\'x1n_t补0后再沿拓翻转后\',\'FontSize\',10);
48 
49 x2n_t = [zeros(1,L),zeros(1,L),x2n_t,zeros(1,L)];
50 kn_x2t = -18:1:17;
51 subplot(4,2,6);
52 stem(kn_x2t,x2n_t);
53 xlabel(\'t\',\'FontSize\',15);
54 ylabel(\'x2n_t补0后 沿拓翻转后\',\'FontSize\',15);
55 
56 
57 %%  乘 加 移位
58 yn = zeros(1,2*L);
59 for I = 1:1:18
60     x1n_t = circshift(x1n_t,[0,1]);
61     yn(I) = x2n_t*x1n_t\';
62 end
63 
64 kn_yn = 0:1:2*(N+M-1)-1;
65 subplot(4,2,7);
66 stem(kn_yn,yn);
67 xlabel(\'n\',\'FontSize\',15);
68 ylabel(\'圆周卷积结果\',\'FontSize\',15);
69 
70 %%取主值序列
71 ynmain = zeros(1,L);
72 for I = 1:1:9
73     ynmain(I) = yn(I);
74 end
75 kn_ynm = 0:1:8;
76 subplot(4,2,8);
77 stem(kn_ynm,ynmain)
78 xlabel(\'n\',\'FontSize\',15);
79 ylabel(\'主值序列\',\'FontSize\',15);
80 
81 %%
cycleConv.m

线性卷积：

 1 %% 线性卷积 
 2 clc;
 3 clear;
 4 %%
 5 N = 5;
 6 M = 5;
 7 L = N + M - 1;
 8 x1n = [1,2,3,4,5];
 9 kx1 = 0:1:N-1;
10 x2n = [1,5,9,7,3];
11 kx2 = 0:1:M-1;
12 
13 %% 线性卷积
14 yn = conv(x1n,x2n);
15 kyn = kx1(1)+kx2(1):1:kx1(end)+kx2(end);  % 0:1:(N+M-1)-1
16 
17 %% 循环卷积   To do 2014年11月20日 15:25:36 循环卷积怎么做
18 
19 %% 画图
20 subplot(2,2,1);
21 stem(kx1,x1n);
22 xlabel(\'n\');
23 ylabel(\'x1n\');
24 title(\'信号1\');
25 
26 subplot(2,2,2);
27 stem(kx2,x2n);
28 xlabel(\'n\');
29 ylabel(\'x1n\');
30 title(\'信号2\');
31 
32 subplot(2,2,3);
33 stem(kyn,yn);
34 xlabel(\'n\');
35 ylabel(\'yn\');
36 title(\'线性卷积结果\');
37 yn   %%  1     7    22    44    69    88    82    47    15
linConv.m

结果如下：

当 L = N + M -1时，圆周卷积和线性卷积的结果一致：

yn =

1 7 22 44 69 88 82 47 15

圆周卷积：

线性卷积：

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