sampling theorem.............

hi everyone..

what is meant by sampling theorem,sampling frequency..

what we do with sampling theorem and why do this one..can any one tel me deeply pls..

Very simply put- Sampling theorem has its significance in Digital conversion of Analog signals. And it states that the signal must be sampled at twice the highest frequency of Analog spectrum so as to successfully reconstruct the signal at a far end. Meaning a 4KHz signal must be sampled more than 8Kbps (PCM)

Please go through **broken link removed**, a starter course on this topic

Can you say as why it has to be sampled at that rate?

Sampling is 1 st step of convering analog to digital.sampling theorem is described by nyquist in order to fathfully recoveir analog signal from digital.sampling is taking sample of continuos signal at discrete time or regualr interval of time.but this interval should be chosen carefully.
If u have any signal which is existing for 10msecond u should atleast sample at 2 instant. if sampling time is 40 msec means u are going to miss the signal.in 2nd case if sampling time is 4ms sec u can get atleast two samples of 10ms signal.this means sampling freq should be greater than frequency present in signal. in this example 10ms will set freuency of 100hz if sapling freq is 250Hz(corresponding to 4ms) u are going to get good samples but if sampling frequency is 25hz corresponding to time 4omsec samples are not good.

That I understood very well. But my question is "why"? Explain the qualitative analysis for it. Thank you!

Sampling is done to convert continuous time signal to discrete time signal, it is done because, by getting the samples with respect to time and amplitude(quantization) of the signal we can get the digital form of the analog signal....By getting digital signals we can do noise free, memory efficient signal(compressed) signal in various applications.

Did you get the style of the discussion going here?

Sampling at 2x the maximum frequency does not guarantee signal reconstruction. At best it will detect the presence of the maximum frequency Fourier component , but the amplitude estimation is not guaranteed. It can vary from zero to the actual amplitude of the fmax Fourier component. (depends on the sampling phase, Sampling at less than 2x the maximum frequency will generate / spill "mathematical " aliasing signals at Fmax. The harmonic components will down from fmax if the sampling frequency is reduced from 2x

Yes. It's a nice concept indeed. Before learning about sampling you should know two things: digital and analog frequency. Many people learn sampling without knowing the difference between these two. That's the main reason why everyone finds this difficult. Take a sine wave with a frequency. This is analog frequency. Now if you sample (i.e. take value only at some particular points) then it is know as sampling. Read this very carefully- In the above signal that I have mentioned take only a period in that signal(i.e. from 0 to 2pi). Digital frequency depends on how many times you sample in that period. You can clearly see that if you want to reconstruct the wave you should atleast have 2 lines in a periods (i.e. you should have taken samples atleast 2 times in a period). Just draw a wave yourself and try what I have said. If you sample only one time in a period you will not get the original wave when you join all the samples. Instead you would get a new wave and it would be having some other frequency. This is aliasing. Hence sampling theorem says that you should atleast sample 2 times in a single period of a wave. In other words your sampling frequency should be twice that of the analog frequency.

If you still have doubts please notify me.

Regards,
iVenky.

Thank you all for your valuable discussions.