The Fourier Series representation of a continuous-time signal has a variety of properties that are noted/investigated in this three-part video sequence. We investigate the following properties in this video:
1. The FS exists for all signals that meet the weak and strong Dirchlet conditions (i.e. must be absolutely integrable on the T0 time interval and have finite number of min/max and discontinuities.
2. When a continuous-time signal is an even signal, all bn = 0 and a simplified equation can be used to compute a0 and an.
3. When a continuous-time signal is an odd signal, all an = 0 and a simplified equation can be used to compute bn.
4. Continuous-time signals with half-wave symmetry have no even harmonics in their FS representation (i.e. a2 = a4 = ... = b2 = b4 = ... = 0).