Nyquist Rate question?

The sampling theorem tells us that aliasing can be avoided if the Nyquist frequency is greater than the bandwidth, or maximum frequency, of the signal being sampled. And Nf=2*B; B=BW or the Highest freq. component

Why BW should be equivalent to the highest freq. component? We can have a 1 MHz-1.5 Mhz band with BW=500 Khz and highest freq. component as 1.25 Mhz? Is there any relation between BW and highest freq. component in the band?

I think it should be based on maximum frequency. Maximum frequency has to be below 1/2 sampling frequency or else aliasing would occur.

I can't see how bandwidth has anything to do with it.

WEL INFACT BANDWIDTH AND NYQUIST RATE ARE TWO TOTALLY DIFFERENT THINGS THE BANDWITH TELLS THAT IN WHICH BAND U CAN TRANSMIT A SIGNAL LET SAY U R ASSIGNED A BAND OF 10MHZ ,IT CAN BE AT ANY WHERE FROM 1HZ TO LET SAY SOME GIGA HERTZ SO THE SECOND THING U NEED IS THE CENTRAL FREQUECY OF UR BANDWITH TO LOCATE UR BAND IN THE SPECTRUM
AND ABOUT NYQUIST CRITERIAN U ALL NEED TO KNOW IS HIGHEST FREQUENCY OF UR SIGNAL THAT U R TRANSMITTING WHICH U CAN GET AFTER HAVING THE FREQUECY BAND ALLOCATED WITH CENTRAL FREQUENCY.

There is a bunch of theory on another topic comming from:

https://groups.google.com/group/sci.electronics.design/browse_thread/thread/b8a58d07e0e3f968/#

However the Nyquist is quite simple if you really want to undestand it.

If the signal frequency is small enough you may sample it with any frequency greater than 2f. Usually this sampling frequency could be 10f or 20f or even more.
On software you can resample the signal at your own fingertip. But everytime you need an antialising filter between the signal and AD converter input, that one should be below the nyquist frequency. The filter must be as flat as possible in amplitude (like butterworth) and as sharpen as possible in swing between passband and stop band (like Cauer) and as flat in time response (as Bessel). You realize there wasn't invented yet such analogic filter, so the equivalent digital filter simulating all of these coulde be parttially the FIR.

If your signal frequency is already high, you can't sample it only with a frequency egual with 2f because you have no computational speed. So here the problems are quite clear.

In relative terms, if nyquist is 1 and theoretical input frequency is 0.5, then practical input frequency is 0.45 and the antialising should be designed at 0.4.
The same theory for signal reconstruction and theoreticaly you'll have no problems.


greetings,

The above definition of Nyq. Freq. is not mine, I found it in Wikipedia. So is it that BW should not be equivalent to the highest freq. in this case?

pmonon said:

The above definition of Nyq. Freq. is not mine, I found it in Wikipedia. So is it that BW should not be equivalent to the highest freq. in this case?

Click to expand...

The bandwidth must be understood without any carrier. Than it's correct.

Yes...But can you explain a little more?

pmonon said:

Yes...But can you explain a little more?

Click to expand...

An analogic signal could vary between say 1KHz and 100MHz.
According to Nyquist, the sampling frequency must be in this situation at least 200MHz. Could be also 1GHz if your computing system could read the samples at this frequency. You can't sample a carrier of 2.4GHz which contain a signal whith a bandwith of 11MHz using 22MHz sampling frequency. You need to demodulate the signal, get the baseband which is 0-11MHz and only after that apply Nyquist sampling at least 22MHz.
I hope now is much clear.

A huge number of people, included many teachers and book authors, incorrectly say that sampling frequency must *always* be greater than twice the signal's highest frequency to avoid aliasing loss of information. The correct requirement is "greater than twice the signal's bandwidth". If the signal contains information around zero hertz, then the two requirements are equivalent. (That's probably the source of the widespread misinformation.)

If an example signal is 100MHz with a 10kHz bandwidth, then you only need to sample it at a little over 20 kHz to fully recover the information. Be aware that the ADC would need a sample-and-hold that has over 100MHz bandwidth. Melc says demodulation is required first, but that's not a requirement if your sample-and-hold is fast enough. For more information, read a book that describes digital receivers and IF sampling.

echo47 said:

If an example signal is 100MHz with a 10kHz bandwidth, then you only need to sample it at a little over 20 kHz to fully recover the information. Be aware that the ADC would need a sample-and-hold that has over 100MHz bandwidth. Melc says demodulation is required first, but that's not a requirement if your sample-and-hold is fast enough. For more information, read a book that describes digital receivers and IF sampling.

Click to expand...

How do you understand an "100MHz signal with 10KHz bandwidth" ?
This is the key of the whole explanation.

Oops, I could have said that more clearly. I meant a signal with a 100MHz center frequency and a 10kHz bandwidth. For example, a radio broadcast.

echo47 said:

Oops, I could have said that more clearly. I meant a signal with a 100MHz center frequency and a 10kHz bandwidth. For example, a radio broadcast.

Click to expand...

100 center freq., then 5 khz for each side of it?

Yes, from 99.995 MHz to 100.005 MHz.

There's nothing special about the numbers I chose for my example. We could also use melc's example - a 2.4GHz signal having 11MHz bandwidth could be sampled at a little over 22MHz. However, that would require an extremely high performance sample-and-hold.

Another way of looking at this technique: the ADC's sample-and-hold is simply performing decimation.

echo47 said:

Yes, from 99.995 MHz to 100.005 MHz.

There's nothing special about the numbers I chose for my example. We could also use melc's example - a 2.4GHz signal having 11MHz bandwidth could be sampled at a little over 22MHz. However, that would require an extremely high performance sample-and-hold.

Click to expand...

So, the type of modulation does not count in your explanation ?
Could be AM, 256QAM, QPSK or FM ? Just sampling at 22MHz and bingo ?

Dreams.

melc said:

echo47 said:

Yes, from 99.995 MHz to 100.005 MHz.

There's nothing special about the numbers I chose for my example. We could also use melc's example - a 2.4GHz signal having 11MHz bandwidth could be sampled at a little over 22MHz. However, that would require an extremely high performance sample-and-hold.

Click to expand...

So, the type of modulation does not count in your explanation ?
Could be AM, 256QAM, QPSK or FM ? Just sampling at 22MHz and bingo ?

Dreams.

Click to expand...

I think Melc is right...for sampling you need to consider modulation scheme also..

Yes, you can sample at (a little over) 22MHz and demodulate afterwards. The modulation type doesn't matter - all the information is intact, it's just shifted to a new frequency band. However, you may need to modify the demodulation algorithm to account for the frequency shift (maybe easy, maybe difficult).

The concept is similar to an analog receiver. You can directly demodulate the RF signal (rather uncommon), or you can add a local oscillator and mixer that converts the RF to IF and then demodulate the IF (very common).

In both systems, you may want to carefully select the sample rate (or the IF frequency) to simplify demodulation. The arithmetic is usually simple, but can be confusing. I draw myself little diagrams showing the signal band being shifted, inverted, duplicated, or whatever.