How to solve this equation

Dear all,

For the following equations:

sum(a(i)*sin(2*pi*f(i)*t(j)+phi(i),i=1,...,m)=s(j) , j=1,...,2*m

how to solve the unknowns
a(i),phi(i), i=1,...,m?


Thanks

Have you heard of fourier series.

Its a summation of sine waves of which are integer multiples of a frequency, which are called harmonics.

Refer to this document for a better understanding

http://www.complextoreal.com/chapters/fft1.pdf

Regards
Elchiquito

Hi Elchiquito,

Thank you very much for your kindly reply. Now the problem is that the sampling points are limited. For example, when the unknows are A1, A2, A3 and phi1, phi2 phi3, and the number of unknowns is only 6, can I also get the solution by FFT?

Thanks