The difference between raised cosine and sync functions

mathematical sync function

can anyone please give me difference between raised cosine and sync functions.
what is the purpose for going to raised cosine in case of base band communication.?

fourier transform of sync functions

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try this link

fourier transform sync function

Sync function has a side band existing widely but cosine doesnt it only has the main lobe

Re: sync function

Raised cosine is generally used in baseband communication because it is practically realisable whereas ideal lowpass filter is not practically realizable.both functions have different fourier transform.

Re: sync function

Raised Cosine Impulse with Roll-Off alfa, have temporal shape similar to Sinc(x) impulse. The substantial difference is that sinc(x) is only a mathematical function (it's in practice impossible to realize an impulse withe infinite duration; an other interpretation is that the TCF of a sinc(x) is a rectangular function and in practice is impossible realize filter with frequency response of that shape).

It is important notice that RRC(alfa) impulse must be limited in the time domain (the transmission impulse must be of finite duration): the great advantage respect sinc(x) is that the quasi-all energy is addensated around the origin. You can control by the parameter alfa, the effective practical duration of the RRC(alfa) impulse, so when truncated, is loss only a trascurable quantity of energy.

You ask the why to use RRC(alfa) in BB communications: it's a limitative ipotesi to work in BB, because You can represent a Transmission System who work at RF, by the Representation in Base Band by use the Complex Envelope of all the signals and the Equivalent Model in Base Band of Your Radio Frequency System.
So, You can use the RRC(alfa) impulses like in PAM (works in BB) like, for example, in QAM (works at RF).

sync function

it can be used in rejecting the crosstalk between codes. and then it can help save the signal band.

sync function

Sinc waveform has large bandwidth and in timedomain its perfect rectangular function so impossible to acheive.So Raised cosine waveform is adapted whos bandwidth can be adjusted by the factor called roll off and its better suited for practice.