It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.
yes
Colour is a property that is not a periodic function.
no.
As you have described it, this sounds very similar to an annuity.
The Fourier series can be used to represent any periodic signal using a summation of sines and cosines of different frequencies and amplitudes. Since sines and cosines are periodic, they must form another periodic signal. Thus, the Fourier series is period in nature. The Fourier series is expanded then, to the complex plane, and can be applied to non-periodic signals. This gave rise to the Fourier transform, which represents a signal in the frequency-domain. See links.
no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.
Consider a periodic function, generally defined by f(x+t) = f(x) for some t. Any periodic function can be written as an infinite sum of sines and cosines. This is called a Fourier series.
David Anton Frederick Robinson has written: 'Fourier expansions of pseudo-doubly periodic functions and applications' -- subject(s): Fourier series, Periodic functions
An aperiodic signal cannot be represented using fourier series because the definition of fourier series is the summation of one or more (possibly infinite) sine wave to represent a periodicsignal. Since an aperiodic signal is not periodic, the fourier series does not apply to it. You can come close, and you can even make the summation mostly indistinguishable from the aperiodic signal, but the math does not work.
Fourier series and the Fourier transform
what are the limitations of forier series over fourier transform
yes a discontinuous function can be developed in a fourier series
Fourier transform. It is a calculation by which a periodic function is split up into sine waves.
no
Yes. For example: A square wave has a Fourier series.
Fourier series is series which help us to solve certain physical equations effectively