Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Register Log in

How the sampling frequency depends on the band width?

Status
Not open for further replies.
R

roykyn

Full Member level 5
Joined
Sep 15, 2006
Messages
253
Helped
12
Reputation
24
Reaction score
5
Trophy points
1,298
Activity points
2,704
i dont understand how the sampling frequency depends on the band width .... and not the maximum frequency component.....according to document by national semicon.
can anyone explain it in detail or suggest some document related to it.
 

undersampling images with matlab

Have you ever heard about fundamental theorem of Shannon-Kotelnikov?

This theorem maintains, that when the signal is continious-time (analogue) and has finite spectrum, limited by the frequency f_upper, it may be represented by its discete samples, taken with the sampling interval, which satisfies the following condition:

T<=1/2f_upper

Signal's reconstruction is done afterwards without any loss of useful information.

However, all real signals are finite in time domain, therefore they should have unlimited Fourier spectrum (Heisenberg's uncertainty principle). In order to apply Shannon's theorem, you need to limit the spectrum by the frequency f_upper.

The more this frequency is, the more is the sampling frequency:

f_sampling = 1/T >=2*f_upper

According to this formula, the wider is the spectrum (the effective band width of the signal) the more you have to take the sampling frequency in order to avoid information losses.

With respect,

Dmitrij
 

undersampling matlab

A signal must be sampled at greater than twice its bandwidth. It's wrong to say a signal must be sampled at greater than twice its highest frequency, unless the highest frequency and bandwidth happen to be equal. Those two values are equal in many common measurement situations, so most people develop the habit of saying "highest frequency" instead of "bandwidth". This unfortunately causes widespread misunderstanding.

For example, if you have a signal centered at 200 MHz with 30 kHz bandwidth, and there's no signal outside that bandwidth, you can sample it at slightly over 60 ksps without losing any information. If you wanted to, you could convert the sampled data back into the original 200 MHz signal.

You may find this helpful:
https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem
 

aliasing effect due to undersampling using matlab

if ur signal is 5Mhz band limeted and its located at 20Mhz freq(17.5Mhz to 22.5 Mhz).

still ur sampling freq is >=10Mhz as echo47 stated. thats correct.

how? most fundamental interview question.


as u said that sampling freq should be 2*(22.5MHz) = 45MHz.

Now u think if ur input signal in frq domain. so its 5MHZ band is located -20Mhz(-17.5 to -22.5) and 20 MHz(17.5 to 22.5).

Consider the effect if the sample rate is 17.5 MHz .Note that the original spectral components remain located at ±fc = 20Mhz, and spectral replications are located exactly at baseband, i.e., butting up against each other at zero Hz.

Draw by hand spectral replications.

now u reduce sample rate as 10MHz and draw spectral replications. its repeated but not overlap each other.

or better u read the book

understanding of DSP by Richard Loyns
chapter 2 bandpass sampling.
 

principle of undersampling

I should have pointed out that the sample rate needs to be greater than twice the signal bandwidth, and you must carefully select the sample rate to avoid aliasing of the duplicated positive and negative frequency components.

To clarify, a real (not complex) signal contains a positive frequency component and a mirror image negative frequency component. When you sample any signal, you create infinite duplicate images that are spaced along the frequency axis at a spacing equal to the sample rate. You need to choose a sample rate so the positive and negative duplicates don't overlap, otherwise you get aliasing.

In naresh850's example of a 5 MHz bandwidth signal centered at 20 MHz, the lowest range of non-aliasing sample rates is between about 11.3 and 11.6 MHz. The next range is between about 15.1 and 17.5 MHz.
 

Re: undersampling

Of course, when saying "sampling frequency must be taken twice as much as the highest frequency in signal's spectrum" I mean't that the signal refers to the class of video-processes, which are known to have amplitude spectrum grouped around the zero frequency. in this case, which is collided with very often in practice, bandwidth and highest frequency coincede.

If the signal is radio-signal, then we should consider it bandwidth, as echo47 mentioned. That will be true.

This misunderstanding may be caused by incorrect formulation of Shannon-Kotelnikov theorem in some books on DSP. Nevertheless, it doest't mean that there is a serious mathematical error.

But still I don't agree, that the inequality must be strict always. Theorem states, that f_sampling>=2*bandwidth. So the equality, in general, is also possible.

With respect,

Dmitrij
 

Re: undersampling

this thing is more complicated than i thought.......ok here is my question......as the guy states 200Mhz can be reconstructed using 60ksps .....how is that possible .....i mean i have an adc of 60ksps ...how can i reconstruct 200Mhz wave.....???????
And also consider a single frequency in freq domain.....what is the structure of the wave in time domain....cos i have heard...all practical signals are a mixture of signals....like sine wave...square wave...and so on....
 

undersampling

Hi roykyn, when you sample that 200 MHz signal at about 60 ksps, the sampler basically mixes it down to low frequency, so if you wish to reconstruct the original signal from the 60 ksps data, you must provide a local oscillator and mix it back up to 200 MHz.
 

Re: undersampling

Code: 
For example, if you have a signal centered at 200 MHz with 30 kHz bandwidth, and there's no signal outside that bandwidth, you can sample it at slightly over 60 ksps without losing any information. If you wanted to, you could convert the sampled data back into the original 200 MHz signal



no no .... i am talking about this statement......i ll simplify my question.....i have a digital oscilloscope running at 60ksps.....can i view 200Mhz wave form on that....
if yes ..... HOW??????


and what about this question
consider a single frequency in freq domain.....what is the structure of the wave in time domain....cos i have heard...all practical signals are a mixture of signals....like sine wave...square wave...and so on....
 

undersampling

Not in the way we've been discussing here. An ordinary sampling oscilloscope doesn't have the oscillator, mixer, and filters to convert the sampled data back up to 200 MHz.

However, a sampling oscilloscope can store thousands of those 60 ksps points and plot them at the correct places on the screen to gradually build up the original waveform, assuming the waveform is repetitive. (Some non-repetitive signals can be viewed too, such as an eye pattern of a digital bitstream.) It's called equivalent-time sampling. Lots of ultra-fast sampling scopes provide this sampling mode. You need to carefully adjust the sample rate so each sample occurs at a different point on the input waveform.

"A single frequency in freq domain" -- that's a simple sinewave in the time domain.
 

    R

    roykyn

    Points: 2
    Helpful Answer Positive Rating
Re: undersampling

i still dont understand....where is the mixer here(i mean after ADC)......all i am seeing is a adc and 150-190Mhz signal....please see the figure3 in the pdf..and also statement above it....[/img]
 

undersampling

You don't need a mixer/LO after the ADC unless you want to reconstruct the original RF waveform. Most communication receivers don't need to do that. They only care about the information contained within the signal's bandwidth (the modulation). The information contains relatively low frequencies, so a slow sample rate is sufficient.
 

Re: undersampling

that what i thought the information rate is less hence reduced sampling freq...
thank you.....i think you are the only active member in this forum.....
 

undersampling

Hi I have a question,

Why should signals be sampled at rates higher than twice the max freq (some sources mention up to 10 times) in DSOs to view the signal correctly on the screen, doesn't this contradict the nyquist theorem?
 

Re: undersampling

nyquist criteria specifies only the minimum sampling frequency required... hence there is no contradiction.... also higher sampling rate means better resolution,,,,,
 

Re: undersampling

A.Anand Srinivasan said:
nyquist criteria specifies only the minimum sampling frequency required... hence there is no contradiction.... also higher sampling rate means better resolution,,,,,
Click to expand...

Why can't I view (reconstruct) let's say a sinusoid correctly using two samples per cycle if they are enough to reconstruct my signal as Nyquist theorem claims.
 

Re: undersampling

well try this..... sample sine wave using the nyquist sampling rate then you will get just 2 samples per cycle and if it doesn't coincide with the peak of the sine wave then how would you know about the amplitude of the signal... this is where additional samples help,.....
 

undersampling

But nyquist theorem says I can reconstruct the signal with ONLY two samples per cycle.
 

Re: undersampling

In principle, a Nyquist frequency just larger than the signal bandwidth is sufficient to allow perfect reconstruction of the signal from the samples. However, this reconstruction requires an unrealizable filter that passes some frequencies unchanged while suppressing all others completely (commonly called a brickwall filter). When realizable filters are used, some degree of oversampling is necessary to accommodate the practical constraints on anti-aliasing filters. That is, frequencies close to the Nyquist frequency may be distorted in the sampling and reconstruction process, so the bandwidth should be kept below the Nyquist frequency by some margin.
 

undersampling

Hi cmos babe, Although it's possible to build, for example, a 500 MHz oscilloscope with 1.1 Gsps sample rate, it would require a low-pass anti-aliasing filter that passes everything below 500 MHz and blocks everything above 550 MHz. Such a sharp filter would have significant ringing (Gibbs phenomenon). That's very distracting when viewing common signals such as digital pulses. Also, it just doesn't "feel right" to use a scope with such sharp frequency cutoff.

If you didn't mind those drawbacks, you could build the scope and see a nice smooth displayed waveform, even though the ADC acquires only two or three samples per waveform cycle. The scope's display processor would use a digital interpolation low-pass filter to "connect the dots" with a smoother curve.
 

Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top