Orthogonality is the Key to Understand Fourier Series Expansion
Video Available I would say that "orthogonality" is the key to understand Fourier series expansion. In engineering and science, we deal with waveforms. A waveform may represent a characteristic of a phenomenon with respect to a certain variable, or variation of a quantity with the evolution of a certain variable for instance time. In order to apply a mathematical method to a given waveform, the waveform must be represented by a simple mathematical expression. If a given waveform is represented by a complicated equation or just by numerical data, then applying a certain mathematical method would be quite complicated. For representing a given waveform by a simple mathematical expression, note that there are basically three different categories. If you are interested in local behavior of a waveform, use Taylor series. If a given waveform is periodic and you want to capture the entire behavior of the waveform, then use Fourier series. If a given waveform is single-shot and...