如何将离散信号扩展为傅里叶级数？

Question

u_i(x_j,t) is an array of numbers:
let's say {      0.1 0.3 0.5 0.2 0.4;      <-- i = 1
                 0.5 0.3 0.6 0.3 0.1;      <-- i = 2
                 0.6   1   7 0.4  9;       <-- i = 3 
                                      }
each number in a row corresponds to given time 
let's take first row: 0.1 is t = 0.1 sec 
                      0.3 is t = 0.2 sec
                      0.5 is t = 0.3 sec
                      0.2 is t = 0.4 sec
                      0.4 is t = 0.5 sec

u_i可以表示为图片上给出的。是否有可能找到图片上圈出的系数？ a_i_n，k_n_j，omega_n，b_i_n？