Why don't you use fourier series for analog signals?

Answer 1

Fourier Series Operations are done on Neumeric Set of Data.

Analog Signals inherently are Not in the Neumeric Domain. So it is Not Possible to Do any Fourier Operations directly on such Signals.

In the purely Analog World , some equivalent operations are done using Passive Networks of Resistors / Capacitors / Inductors together with some Non Linear Devices / Active Amplifiers etc. in different combinations to get the desired results , on analog signals in particular range of Frequency & Amplitudes. It is very difficult to Do such operations on a wide range signals using a particular combination od circuits.

Another alternative is to Digitise the Analog Signal , so that Any Suitable Mathematical Operations can be done easily & then reconvert the Processed Digital Signal back to Analog form when required.

An important fact to note is that Storage of the Purely Analog Signals & Retrival is an Expensive & Lossy affair ( signal stored may degrade / get corrupted ), as is evident in Magnetic Audio / Video Tapes , Phonographic Records etc.which were the Most Popular Methods of Analog Signal Storage.

So a Digitised Format would be vastly more convenient from today's technological point of view.