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.
In order to recover all Fourier components of a periodic waveform, it is necessary to sample at least twice as fast as the highest waveform frequency . So if is the sampling rate, the Nyquist frequency, also called the Nyquist limit, is the highest frequency that can be coded at a given sampling rate in order to be able to fully reconstruct the signal, i.e.,
I am not in the position to aruge the Nyquist qurterion that states that .. bla bla bla 2 x Fmax.
You can buy it, or not, it is up to you .. but I am open to discuss any other options ..
in this context, i would also not like 2 argue but express my opinion with a simple example.. i have already posted.
cedance said:
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.
I am not in the position to aruge the Nyquist qurterion that states that .. bla bla bla 2 x Fmax.
You can buy it, or not, it is up to you .. but I am open to discuss any other options ..
You and the_jackal are both correct. To be able to reconstruct the signal without mistakes you indeed need 2 x Fmax but because you dont have a perfect squere filter you take a bit more in practice.
fs here is actually signal frequency, so the nyquist frequency is twice of fs i.e. 8 KHz. Now in order to sample the signal in such a way that no information is lost the sampling frequency should be greater than Nyquist frequency.
So,
We have
Signal frequecny as 4KHz.
Nyquist Frequency as 8 KHz
and the signal sampling frequency as >8KHz.
If we say that fs is actually sampling frequency that in no case it does guarantee that Nyquist frequency would be 2KHz i.e. half of sampling frequency. The rule is just that the sampling frequency must be somewhat higher than that of the Nyquist frequency and off course you wouldn't like to make it too high to waste your bandwidth.
Adding to all the above i have some idea added here
When an analog signal is concedered it will have many frequencies. The maximum frequency content in that signal is taken as fm(fmax)
Now the sampling frequency is called as fs(sampling freq)
When a analog signal is sampled u have to sample at a rate of twice or greater the maximum frequency content in that particular analog signal
For example
In our speech signal the signal is band limited to 3.4KHz. It seems no human voice exceed a freq content greater than that. So we use a sampling frequency of 8KHz.
so Nyquist Frequency = 2 * Maximum frequency content in the signal
but fs >= 2fm
When we sample less than 2fm the effect called strobing occurs
Strobing:
This effect is that u can see some times in fan rotation or in rotation of car wheel.
In that ur eye has a sample rate of 16Hz. So u visualize things at that rate. if your car rotates at the speed just less than 32Hz than you can see that car wheel is revolving backwards. To avoid it u have to same at greater frequencies
Problem in Sampling at Nyquist rate
If you sample at Nyquist rate for eg in case of sine you will be sampling only two times in a cycle. That two points will be having only zero value if you start sampling at the initial points. So finally the sampled signal will contain only zeros
Problem in Sampling at Nyquist rate
If you sample at Nyquist rate for eg in case of sine you will be sampling only two times in a cycle. That two points will be having only zero value if you start sampling at the initial points. So finally the sampled signal will contain only zeros
ok all the confusion here was the way that the question was asked, I beleive that the person who asked the original question actually means that the frequency of the wave measured was f = 4Khz, not fs, fs is normally means the sampling frequency which is what we want to find out. having the sampling frequency twice the frequency of the signal you want to sample will let you reconstruct the original signal, it's not necessary to have the sampling frequency higher than that, except for a safe guard in case the highest frequency to be sampled actually turns out to be higher than you thought. there are many reasons as to why you would want to put your sampling frequency higher than the nyquist frequency, but i'm not going to go into those now.
all the best.
if you look at the signal after smapling in frequency domain, you will find if sampling rate less than 2 times singal frequency, the singals will overlap.
I think anto summed it up nicely....simple answer the same one...if highest component freq in the signal is f then the sampling freq will be >=2*f but in practice its always more than 2f
more than 2 the frequency is not directly for anti aliasing, it's for 1 the simplification of the anti aliasing filter, 2 a reduction in the adc noise floor by spreading the quantization noise over a wider bandwidth. (improves snr performance) etc etc etc
we can not determine the nyqist frequency of a singal if we only know the signal freq itself instead of
the sample freq. or we can say the nyqist frequency
is the signal freq itself(fi) so we can use the sampls signal freq greater than 2*fi to get a reconstuctable
sample.
HI,
The minimum sampling rate allowed by the sampling theorem, that is, fs=2Fmax,is called the Nyquist rate. For arbitrary value of fs, the quantity fs/2 is called the Nyquist frequency or the fold frequency.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.
