The Fourier series represents periodic, continuous-time signals as a weighted sum of continuous-time sinusoids. It is widely used to analyze and synthesize periodic signals. This lesson shows you how to compute the Fourier series coefficients, or weights, from the signal. It also introduces you to the conditions that must be met for a signal to have a convergent representation. You will learn both the general and trigonometric forms. The general form expresses the signal as a weighted sum of harmonically related complex sinusoids. The trigonometric form expresses real-valued signals as weighted sums of harmonically related sines and cosines.

The Fourier series is an essential tool and will enable you to work effectively with periodic signals in the frequency domain.