Parseval’s Theorem provides a relationship between the total energy of a signal in the time domain and the energy contained in its frequency components (Fourier coefficients).
\[ \frac{1}{2L} \int_{-L}^{L} |f(x)|^2 dx = \frac{a_0^2}{4} + \frac{1}{2} \sum_{n=1}^{\infty} (a_n^2 + b_n^2) = \sum_{n=-\infty}^{\infty} |c_n|^2 \]