What Should be Sampling Frequency Fs in Practical Circuits ?

[starfish]

how sampling frequency decided

In theory we study that 2 samples per cycle in a periodic sine wave are enough to reconstruct it back in Analog form. I wana know what should be the values for sampling frequency Fs in practical circuits ? Is it taken 2 samples per cycle ? 10 / cycle or what is the deciding factor ??

If by theory 2 samples / cycle are appropriate to represent information of a periodic sinosoidal then why should we use higher sampling frequency ?? wouldn't it be much complex to handle more samples like 20 , 50 Samples / cycle than 2 samples / cycle.

 

[PaulHolland]

what is sampling frequency fs

Hi, If the world was perfect it would be possible buit since it is not we have to do our best !.

If you sample a signal than there should be no energy at frequencies 1/2 the sampling rate, if there is some signal above that frequency level and the signal is strong you will get it back in the sampled signal but at a different location. If we would be able to filter the input signal perfectly we would only need 2 samples per period, but since we do not have this possibility we sample higher and reduce in digital domain the sampling rate. This is the cheapest way of getting an almost perfect system.

Paul.

 

[Miguel Gaspar]

frequency fs

Well, sampling frequency must be twice the maximumfrequency of your signal, thats theorical one. That doesn't work in reality.

At least you must use 4 times, if you want a better reconstruction use 10 times or 20 times, but that increases your cost.

 

[starfish]

Re: What Should be Sampling Frequency Fs in Practical Circui

Thanks for clarification. Plz tell me that can a pure Analog Cosine Wave be reconstructed from cos ( pi n ) which has 2 samples per cycle in digital domain???

 

[Kral]

Re: What Should be Sampling Frequency Fs in Practical Circui

starfish,
Regarding your first question:
.
Steps in determining minimum sampling frequency;
.
Calculate, estimate, or measure the amplitudes of frequencies above the maximum frequency of interest.
.
Decide what amplitude of aliased components can be tolerated in the sampled signal. This, along with the info determined above will determine the amount of attenuation that must be provided by the anti-aliasing filter at the Nyquist (fs/2) frequency.
.
Decide the maximum number of poles you can accept in your anti-aliasing filter. This will be determined by economics, size, etc. Then calculate the frequency at which this filter will provide the minimum acceptable attenuation (determined above). The minimum acceptable sampling frequency is twice this value.
.
Regarding your 2nd question:
Yes. A zeroth order hold circuit, followed by a low pass filter will reconstruct the waveform.
Regards,
Kral

 

[KT4YE]

Re: What Should be Sampling Frequency Fs in Practical Circui

Theoretically 2x is OK. There are a couple of problems if we use this theoretical (Nyquist) criterion.

One is that you need to be sure that the input has negligible frequency content above the frequency of interest. Otherwise, these signals will be sampled at a rate below the Nyquist rate, and will appear at the output as spurious signals. (This is called "aliasing.") Once a spurious component is mixed in with the desired signal, it is VERY difficult (or impossiblle)

Another is that, on the output, the filtering must be robust enough to eliminate any residual (and often robust) sampling frequency while maintaining the integrity of the desired signal.

So, the issue is one of filter design.

In the dawn of Digital Video, we used 10.7 MHz (roughly 3X the NTSC subcarrier frequency) for sampling. This allowed reasonable filter designs. 14 MHz was better, however since the filter design was easier. (I do not know what is used today.)

Hope this helps!

 

[sheraz.pervaiz]

Re: What Should be Sampling Frequency Fs in Practical Circui

Fs=2.2 * Fmax

 

[farhantariq]

Re: What Should be Sampling Frequency Fs in Practical Circui

Fs should be twice of the Max. frequency of the input signal. thats what a sampling theorem says. Mostly Samplig is done in communication field w.r.t this theorom.