Nyquist Theorem for fiber optics

[Hamidzia]

Assalam o Alekum !

Plz give detailed answer

Is Nyquist theorem

i.e.

Sampling frequency shud be greater than max component of freq

also true for Fiber Optics or only for copper wire.

Thankx

 

[Cluricaun]

nyquist theorem

Hi Hamidzia

The Nyquist Theorem is a mathermatical expression, so it is independent of what material the frequence is measured
When sampling a frequence with freq f then the sampling frequency must be twice the measured one (2f).
To be more precise the signal should not contain a Fourier spectrum with sine or cosines above frequnce f, then by sampling at 2f you can reconstruct the signal.

If you do not sample at twice the frequency you cannot reconstruct the signal properly because you get aliasing.


http://www.digital-recordings.com/publ/pubneq.html
**broken link removed**

/Cl

 

[acai]

nyquist theroem

if a signal is band pass signal or band limited signal. you can use the band sampling theory so you dont need to sample the signal at the twice the maximum frequency of the signal. you just need to sample the signal at the twice the signal band.
but application of the band sampling theory have some restriction on the signal. so if RF or the carrier frequency is very high, you can think if it can using the band sampling theory. In the software design, because the AD is near the front, the frequency of the RF signal is very high, practical apllication usually use the band sampling.

 

[DrDolittle]

nyquist theorem fiber optics

Even if we sample the signal at the Nyquist rate we cannot exactly reconstruct the signal. This is because time limited signals and not bandlimited and vice versa. This is why we cannot even have an ideal filter.

Regards
drdolittle

 

[aramisss]

nyquist theorem in matlab

and, you can use a prealias filter before sampling. this a low pas filter which the cutoff freq. equal to the sşgnal bandwith.

 

[svicent]

nyquist theorem lecture

acai wrote:

if a signal is band pass signal or band limited signal. you can use the band sampling theory so you dont need to sample the signal at the twice the maximum frequency of the signal. you just need to sample the signal at the twice the signal band.
but application of the band sampling theory have some restriction on the signal. so if RF or the carrier frequency is very high, you can think if it can using the band sampling theory. In the software design, because the AD is near the front, the frequency of the RF signal is very high, practical apllication usually use the band sampling.

Imagine a sine wave of frequency 1 MHz, passing through a bandpass filter with limiting frequencies 999,999 Hz and 1,000,001 Hz. This is a band limited signal and the bandwidth is 2 Hz. Are you saying that is possible to sample this signal a little more than 4 Hz, and reconstruct it?

Can you explain it?

svicent

 

[masai_mara]

nyquist theorem matlab

To answer the question asked- Yes nyquist theroem always requires that you sample the input at >= twice the frequency of signal of interest in the input. This is required when we do processing in digital domain and not applicable in analog processing. So fibre or coper or wave guide like microstrip or whatever that carries a signal if you want to sample the input then follow nyquist to ensure no loss of information.

 

[checkmate]

understanding nyquist

To put it in simple words, if your system has to support signals up to a certain frequency, for complete reproduction of the signals, they have to be sampled at at least twice of that frequency.

 

[svicent]

nyquist theorem program

David Salomon in his book Data Compression, Third Edition, wrote (page 697):

The solution to the sampling problem is to sample sound at a little over the Nyquist
rate (page 522), which is twice the bandwidth of the sound (the bandwidth is the difference
between its maximum and minimum frequencies). Thus, if a sound contains
frequencies between 500 Hz and 2 kHz (the bandwidth of the human voice), it should
be sampled at a little more than 3 kHz. (Previous editions of this book, as well as many
other sources, erroneously state that the Nyquist rate is twice the maximum frequency.
The author is indebted to Alfred Fuchs for clearing up this point.

Is this theory correct?. My opinion is: not

 

[checkmate]

prealias filter in sampling

It is correct if additional signal processing is done before it is sampled. It's similar to comms systems, where a message signal is sampled AFTER demodulation, not BEFORE.

Anyway, the issue is that such a Nyquist sampling rate is the minimum possible sampling frequency required to extract the original signal given the chance to throw whatever dsp tricks you have up your sleeve at it. One must realise that the Nyquist frequency is a bound, not a rule.

In other words, the theorem only states that it's possible, but does not otherwise specify how it is to be achieved.

 

[me2please]

nyquist sampling theory

David Salomon in his book Data Compression, Third Edition, wrote (page 697):

The solution to the sampling problem is to sample sound at a little over the Nyquist
rate (page 522), which is twice the bandwidth of the sound (the bandwidth is the difference
between its maximum and minimum frequencies). Thus, if a sound contains
frequencies between 500 Hz and 2 kHz (the bandwidth of the human voice), it should
be sampled at a little more than 3 kHz. (Previous editions of this book, as well as many
other sources, erroneously state that the Nyquist rate is twice the maximum frequency.
The author is indebted to Alfred Fuchs for clearing up this point.

Is this theory correct?. My opinion is: not

I think if you are looking back into What exactly does sampling mean?, you will be able to find the answer yourself.
The quote from the book is correct. Why?
Sampling :
In time domain: = multiply by impulse train.
In frequency domain: = convolution by another impulse train.
For perfect reconstruction, the requirement is not to have "aliasing" in frequecy domain. This means as long as impulse train in frequency domain has enough spacing (no 2 impulses are on the signal bandwidth at the same time), no aliasing will occur. Draw picture of convolution process and you will see it clearer.

 

[cedance]

nyquist theorem fiber optic

but, a simple program in matlab with sampling at exactly sampling at twice the signal frequency, i see that it couldnt be perfectly reconstructed. is it a bug in matlab or the mathematical expression is sampling rate greater than twice the highest frequency component of the signal? i remember an iit professor lecture telling that the nyquist rate actually doesnt contain the = sign... and is given wrong in text books...

regards,
arunmit168.

 

[me2please]

nyquist theorem for bandpass signals

I don't know how you do it in matlab but matlab is a numerical environment which always operates in discrete fashion (unless you do it symbolically).

From my understanding, Nyquist should be valid for =. In the case of continuous spectrum, there shouldn't be any problem getting back the signal at all since the aliasing at the point of the band boundary (periodical points) has zero measure.

The only problem could occur in the case of discrete spectrum. In the bandpass filter to recover original signal spectrum, the discrete spectrum will fall exactly at the boundary points. In this case, if the filtering at boundaries is defined correctly (half of magnitude), the original spectrum will be recovered correctly.

 

[chandreou]

alfred fuchs sound

Niquist says that sampling frequency must be at least two times greater that the frequency of the signal

 

[checkmate]

log 2 mean in the nyquist theorem

Niquist says that sampling frequency must be at least two times greater that the frequency of the signal

Exactly. Take for example, the theory of relativity states that nothing can travel faster than light. That does not imply everything travels at the speed of light. Neither does the theory provide the means as to how we can make things travel at the speed of light. As I said, it's just a bound. Sometimes, bounds can be reached in practice. Sometimes, they can't. But in theory, if this bound is violated, no amount of DSP can help you recover the original signal.

 

[cedance]

nyquist theory rf

I don't know how you do it in matlab but matlab is a numerical environment which always operates in discrete fashion (unless you do it symbolically).

From my understanding, Nyquist should be valid for =. In the case of continuous spectrum, there shouldn't be any problem getting back the signal at all since the aliasing at the point of the band boundary (periodical points) has zero measure.

The only problem could occur in the case of discrete spectrum. In the bandpass filter to recover original signal spectrum, the discrete spectrum will fall exactly at the boundary points. In this case, if the filtering at boundaries is defined correctly (half of magnitude), the original spectrum will be recovered correctly.

Will this suffice?

the Nyquist rule states that the sampling frequency should be more then twice of the highest signal frequency.

Consider sine wave with frequency let say f. Its period is T=1/f
If you sample with frequency 2f then your time step is T/2.
No assume that some sampling point is exactly at zero of our sine wave.
The next sampling point will be after time T/2 which is again zero of the sine wave, ... so following this assumption we will have zero signal after the sampling. (If we shift the sampling grid will get constant DC level instead of this zero sampled signal). This effect is the well known aliasing of the DC level over the Nyquist frequency.

regards,
arunmit168.

 

[Cluricaun]

nyquist theorem example

Hi

Topic is closed, the originall question is answered long time ago.

PM me if you need it opened.