Observations

• Any periodic signal can be represented as a sum of sines (and cosines) with frequencies equal to multiples of the fundamental frequency.
• The result is called Fourier Series decomposition.
• The Fourier series indicates how much of a sinusoid of a particular frequency is contained in the signal.
• To represent non-periodic signals, the idea of the Fourier series must be generalized to the Fourier Transform.
• The Fourier series and transform of a signal are unique, i.e., each signal has a different Fourier representation.
• The ability to represent any signal as a sum of sinusoids is extremely important and will be pursued further.