What are the application of Fourier series?

Answer 1

There are many applications for this complex theory. One of these include the determination of harmonic components in a complex waveform. This is very helpful in analyzing AC waveforms in Electrical Engineering.

Answer 2

any signal can be represented by sum of sine and cosine signals...when fs is applied to a signal it is represented by a function containing only sine and cosine signals...mixing 2 signals produces a diff 1..like tat wen sine and cosine is mixed a diff required signal is produced..

ao/2+summation{(ancos(nx)+bnsin(nx)}...

here ao is DC component which gives the amplitude of a signal..

fs of square wave is 4/pi summation(1/n*sin(nwot)

Answer 3

In electrical engineering, the Fourier series is used to analyse signal waveforms to find their frequency contest. This is needed to design communication systems that will deliver the signal to the receiver in good shape.

If you go on to study the next step, the Fourier Transform, that is really interesting for electrical engineering because a signal can be a function of time and it can also be a function of frequency. These two representations of the same signal form a Fourier-Transform pair. So the spectrum is the FT of the waveform, while the waveform is reverse-FT of the spectrum.

Fourier series are also good because they are the simplest example of the whole new subject of orthogonal polynomials, and these are also important in engineering because they are used to find solutions of the differential equations that are thrown up by physical systems.

So, while a violin string can be analysed by a Fourier series which explains the harmonics that give a violin its distinctive sound, something more complex like a drum-skin can also be analysed, but the answer comes out in terms of another type of orthogonal function, the Bessel functions, instead of circular functions (sines and cosines). This explains why you get a note from a drum but it's less well defined, because the upper modes are not harmonically related to the fundamental.