傅里叶3D可视化绘图技巧

一路上

三维数据可视化为学习者提供直观影像，应用广泛。3D折线图旨在展示三维空间的曲线分布，采用MATLAB函数plot3。与二维折线绘制plot函数的差异在于，需要设定x,y,z方向坐标向量，其他绘图属性两者基本一致。与之类似的还有3D散点图scatter3，3D杆状图stem3等。

下面，我们以傅里叶级数展开（Fourier series expansion）3D可视化作为代码示例。

1. clc; clear; close all;
   
2. %----------------------
   
3. m = 15; % Series
   
4. N = 512; % Period
   
5. T0 = 4;
   
6. T = 2;
   
7. t1 = linspace(-T/2, T/2, N);
   
8. t2 = linspace(T/2, T0-T/2, N);
   
9. t = [(t1-T0)'; (t2-T0)'; t1'; t2'; (t1+T0)'];
   
10. %----------------------
    
11. % Construct periodic signals
    
12. %----------------------
    
13. % s = zeros(5*N,1);
    
14. % s(1:N)=1; s(2*N+1:3*N)=1; s(4*N+1:5*N)=1;
    
15. s = [ones(N,1);zeros(N,1);ones(N,1);zeros(N,1);ones(N,1)]';
    
16. y = zeros(m+1, length(s));
    
17. y(m+1,:) = s-0.5;
    
18. plot3(t-(t+2), t, y(m+1,:),'LineWidth',2); % Period square wave
    
19. hold on;
    
20. axis([-2,m+1,-T0-1,T0+1,-1,2])
    
21. set(gca,'XTick',-T0-1:2:m);
    
22. set(gca,'YTick',-T0-1:1:T0+1);
    
23. set(gca,'ZTick',-1:0.5:T0);
    
24. title('Fourier series expansion','FontSize',15);
    
25. grid on;
    
26. view(-49,23)
    
27. fsamp = 1028;
    
28. f = linspace(1, m+1, fsamp);
    
29. A = 0.5; % Coefficient
    
30. freq = 1:1:m;
    
31. plot3(f,T0+f-f+1,A*sinc(A*f)*5,'LineWidth',3)
    
32. mag = A*sinc(A*freq)*5;
    
33. h=stem3(freq,T0+freq-freq+1,mag,'filled','LineWidth',3);
    
34. set(h,'Marker','o',...   
    
35. 'MarkerFaceColor','g')
    
36. x = A*ones(size(t));%  Harmonic signals
    
37. X = A*ones(size(t));% Synthesis signals
    
38. for k = 1:m
    
39. x = 2*A*sinc(A*k)*cos(2*pi*t*k/T0);
    
40. X = X+2*A*sinc(A*k)*cos(2*pi*t*k/T0);
    
41. y(k, :) = x;
    
42. plot3(k+t-t, t, y(k,:),'LineWidth',1.5); % Harmonic
    
43. end
    
44. plot3(k+1+t-t, t, X-0.5,'LineWidth',2);
    
45. grid on;
    
46. xlabel('Frequency view','Rotation', 15);
    
47. ylabel('Time duration','Rotation', -10);
    
48. zlabel('Amplitude/Magnitude');
    
49. set(gcf,'Color','White');  % Background is white
    
50. %----------------------

复制代码

程序运行如图-1所示。

图-1 傅里叶级数展开的三维可视化