Calculating Fourier Series Coefficients Using Custom Matlab Function

Question

ha9981 2012-10-19

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https://ww2.mathworks.cn/matlabcentral/answers/51350-calculating-fourier-series-coefficients-using-custom-matlab-function

评论： Parul Saini 2019-7-26

My attempt at creating such a function where it must have the three inputs x, w0, and N:

function[ak] = cal_fs(x, w0, N)
ak = zeros(1,2*N+1); %intialize a row vector of 2N+1 zeros
T = 2*pi/w0; %calculate the period and store in T
syms t;
for k = -N:N
ak = 1/T * int(x * exp(-1i*k*w0*t), t); % ak is fourier coefficient
end

Above is my attempt. I am trying to make a vector ak that contains all the fourier series coefficents as calculated by the equation above. I am new to Matlab and highly confused as to why i do not get an output of a matrix when I do the following:

syms x;
syms t;
x = 2*t;
w0 = 62;
N = 20;
cal_fs(x,w0,N)

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ha9981 2012-10-19

The problem is the output of cal_fs is not coming as a vector but rather a symbolic matrix 1x1. What am I doing wrong friends?

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Answer 1

Alexander 2012-10-22

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You forgot the index for assigning to ak. Also do you want the indefinite integral or an integral from 0 to 2*pi/w0? I added the index and changed the integral:

function[ak] = cal_fs(x, w0, N)
ak = zeros(1,2*N+1); %intialize a row vector of 2N+1 zeros
T = 2*pi/w0; %calculate the period and store in T
syms t;
for k = -N:N
ak(1,1+k+N) = 1/T * int(x * exp(-1i*k*w0*t), t, 0, T); % ak is fourier coefficient
end