fft - How to expand a discrete signal into a Fourier series? -

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

u_i may represented given on picture. possible find coefficients circled on picture? a_i_n, k_n_j, omega_n, b_i_n?