Multiplication Property of Continuous - Time Fourier Series
Suppose that x(t) and y(t) are both periodic with Period T and that
- $ x(t)\Longleftrightarrow a_k $, and...
- $ y(t)\Longleftrightarrow b_k $
Since the product $ x(t)y(t) $ is also periodic with period T, we can expand it in a Fourier series with Fourier series coefficients $ h_k $ expressed in terms of those for x(t) and y(t). The result is..
- $ x(t)y(t)\Longleftrightarrow h_k = \sum_{l=-\infty}^\infty a_lb_{k-l} $
