How can i calculate & plot amplitudes of first 40 harmonics of char and plot the letter ?

Question

Asia 2014-12-17

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https://ww2.mathworks.cn/matlabcentral/answers/166990-how-can-i-calculate-plot-amplitudes-of-first-40-harmonics-of-char-and-plot-the-letter

回答： Shoaibur Rahman 2014-12-18

t=0:0.005:1; x=0:5:200;

cu=0.5; au=zeros(1,201); bu=au; ampu=zeros(1,201); ampu(1)=0.5;

for n=1:40 au=au+1/(n*pi)*(cos(n*pi/4)-cos(n*2*pi/4)+cos(n*3*pi/4)-cos(n*4*pi/4)+cos(5*n*pi/4)-cos(n*6*pi/4)+cos(n*7*pi/4)-cos(n*8*pi/4)) *sin(n*2*pi*t);

 bu=bu+1/(n*pi)*(sin(n*2*pi/4)-sin(n*pi/4)+sin(n*4*pi/4)-sin(n*3*pi/4)+sin(n*6*pi/4)-sin(5*n*pi/4)+sin(n*8*pi/4)-sin(n*7*pi/4)) *cos(n*2*pi*t);
 ampu(n+1)=sqrt(au.^2+bu.^2);
 subplot(1,2,1),plot(t,cu+au+bu),grid
 subplot(1,2,2),plot(x,ampu),grid
 pause(0.01);

end

But the error is : In an assignment A(I) = B, the number of elements in B and I must be the same.

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Answer 1

Shoaibur Rahman 2014-12-18

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https://ww2.mathworks.cn/matlabcentral/answers/166990-how-can-i-calculate-plot-amplitudes-of-first-40-harmonics-of-char-and-plot-the-letter#answer_162679

在 MATLAB Online 中打开

I see a couple of problems in the code:

First, ampu(n+1) means a scaler, but sqrt(au.^2+bu.^2) is a vector. So, you can form ampu as a matrix whose rows corresponds to each harmonics, like: ampu(n,:)=sqrt(au.^2+bu.^2);

Second, in plot(x,ampu), x and ampu are not in same lengths. Look, you defined x=0:5:200; which has 41 elements, but ampu has 201 elements. Make them of same lenghts. For example define x=linspace(0,200,201); or as per your requirement.

So, run the following modified code, which produces animation-like plots of ampu for 40 times. You can increase the pause to make it slower. However, if you want to see all 40 harmonics at a time then plot them outside the for loop.

    t=0:0.005:1; x=linspace(0,200,201);
    cu=0.5; au=zeros(1,201); bu=au; ampu=zeros(1,201); ampu(1)=0.5;
    for n=1:40
       au=au+1/(n*pi)*(cos(n*pi/4)-cos(n*2*pi/4)+cos(n*3*pi/4)-cos(n*4*pi/4)+cos(5*n*pi/4)-
       cos(n*6*pi/4)+cos(n*7*pi/4)-cos(n*8*pi/4)) *sin(n*2*pi*t);
       bu=bu+1/(n*pi)*(sin(n*2*pi/4)-sin(n*pi/4)+sin(n*4*pi/4)-sin(n*3*pi/4)+sin(n*6*pi/4)-
       sin(5*n*pi/4)+sin(n*8*pi/4)-sin(n*7*pi/4)) *cos(n*2*pi*t);
       ampu(n,:)=sqrt(au.^2+bu.^2);
       subplot(1,2,1),plot(t,cu+au+bu),grid
       subplot(1,2,2),plot(x,ampu(n,:)),grid
       pause(0.01);
    end