The Fourier Series Only Applies to Periodic Waves
The Fourier Series only applies to "periodic" waves. This is a key point that must be understood to understand the Fourier Series versus the Fourier Transform. A periodic wave is a wave with a repeating pattern. It is that repeating pattern that determines the wave's frequency, or wavelength. This frequency is referred to as the "fundamental frequency" (and the corresponding wavelength is the "fundamental wavelength"). Non-periodic waves will be dealt with later (the job of the Fourier Transform). Below are examples of periodic and non-periodic waves.
Above: Diagram of periodic wave above. Repeating Pattern.
Above: Diagram of non-periodic wave. Non-repeating pattern.
Note: the non-periodic wave above does not repeat over the visible portion of the wave. It may be that it does repeat if you extend the length of the graph. There is no fundamental frequency for a non-periodic wave.
