Frequency Domain Representation of Signals

Fourier Theory uniquely relates the time and frequency domain representations of signals. It is a particularly satisfying theory, being mathematically precise and elegant, and yet having a very clear physical interpretation and application. Like most worthwhile studies its understanding requires a certain amount of initial effort. It has been said that ‘Fourier Theory grows on you’ but unfortunately this is rather undermined by the reply ‘like warts or spots’. Most subjects become easier with use, of course, but this is particularly true of Fourier Theory. It is very difficult to find an examination question that someone well versed in the subject cannot do in less than about ten minutes; indeed, this is probably the best academic reason for not teaching it!