difference between fourier series and fourier transform

furier transform

sir,
i wish to know about the difference between fourier series and fourier transform?

difference in furier series and furier transform

Basically Fourier Series is for periodic signals and Fourier Transform is for aperiodic.But, i feel, you cant get this concept readily. So i advise you to study some basics in books and from net and come back with doubts which you dont Understand well .

fourier series

The Fourier series is a mathematical tool used for analyzing periodic functions by decomposing such a function into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. The weights, or coefficients, of the modes, are a one-to-one mapping of the original function. Generalizations include generalized Fourier series and other expansions over orthonormal bases.


In mathematical physics, the Fourier transform of a signal x(t) can be thought of as that signal in the "frequency domain." This is similar to the basic idea of the various other Fourier transforms including the Fourier series of a periodic function.


hope it helped you!

fourier series and fourier transform

As it has been already hinted, Fourier Series is used for periodic signals. It represents the signal by the discrete-time sequence of basis functions with finite and concrete amplitude and phase shift. The basis functions, according to the theory, are harmonics with the frequencies, divisible by the frequency of the signal (which coincides with the frequency of the 1st main harmonic). All the harmonics with the number>1 are called higher harmonics, whereas the 1st one is called - the main harmonic. After reminding the mathematical properties of the signal we can maintain, that sometimes harmonics with even or odd numbers are absent at all. There phases are sometimes always equal to 0 and 180 degrees or to 90 and -90 degrees.

Fourier series are known to exist in sinus-cosinus form, sinus form, cosinus form, complex form. The choice depends on the problem solved and must be convenient for further analysis.

Fourier tranform is invented and adjusted for aperiodic signals with integrated absolute value and satisfaction of Diricle conditions. It's worth saying, that Dirichle conditions is the necessary requirement for Fourier series too. Fourier representation of aperiodic signals is not discrete, but continious and the amplitudes are infinitely small. They play the role of the proportional coefficients.

there are links between Fourier series of periodic signal and Fourier transform. These links may be easily found in almost all the books on classical Fourier analysis of signals. For example, see Oppenheim, Djervis and others.

With respect,

Dmitrij