Formula for calculating nyqist frequency

nyqist frequency ?

It's two times the bandwidth, not two times the highest frequency. Common misquote of Nyquist theorm, and it makes a big difference in some applications.

Re: nyqist frequency ?

Dear comsians,
To not to be confused i will recommend you to read the first two chapters of Digital Signal Processing Book by John G. Proakis.

-Regards

Re: nyqist frequency ?

I saw quite some responses about how sine wave when sampled at Nyquist rate gives only zeroes... But I expected someone to point out the phases as well...
When you sample the sine wave you should also remember the phase of the signal. Hence, a sine wave when sampled at Nyquist rate gives zeroes with alternate phases. This, I argue, is a "complete" representation of a sine wave. Of course, to regain the sinewave from the samples, one would need the "ideal" filter. Hence, the practice of going a little beyond two times. On paper, twice the maximum freq. is perfect.
Please let me know if I am mistaken.

Re: nyqist frequency ?

Dear asymbian,
I think it is infered that phases are to be considered, as far as the question of twice lies it is on magnitude.
So if one has 5 khz frequency sample not less that 10khz and definitly the phase restrictions are always there.

-Best Regards

nyqist frequency ?

8khz
sample frequency must no less then 2 times of signal frequency

Re: nyqist frequency ?

Hi,

I aggree to the answers posted so far but I think when we apply the same thery in digital domain it might not work.

With regards,
R.Lakshmikanth

nyqist frequency ?

Lakshmikanth !!

What u mean by digital domian ... This topic is fully on Nyquist rate which hold good in analog/ digital and even when u try to sample a big array in matlab.
pls understand wats going here and post a reply ...( hope u replied this post to increase u r points ;-) )

Re: nyqist frequency ?

comsians

If any body know that signal has fs=4Khz wht wil be the nyqist frequency plz tell me the formula also

Click to expand...

The nyquist frequency is 1/2 the sampling frequency. That's all. In this case, nyquist frequency is 2-kHz. Nyquist frequency is sometimes known as the maximum of highest frequency in the signal bandwidth of interest.

Not so much mentioned in DSP or Signal and System books, but in books that teaches Analog-to-Digital Converters, there are ADCs that belong to the Nyquist-Rate ADCs and Nyquist frequency is the maximum frequency of input signal that is concerned.

nyqist frequency ?

Just a reminder - the Nyquist theorm applies to the signal bandwidth, not necessarily the signal frequency.
For example, a digital receiver's ADC sample rate is typically much slower than its input signal frequency.

Re: nyqist frequency ?

That's why I have already stated, "maximum of highest frequency in the signal bandwidth of interest".

nyqist frequency ?

SkyHigh, you are probably saying the right thing, but your sentence structure is unclear.
Signal bandwidth is important. Signal frequency is (almost) not important.
For example, a 10 MHz signal with 1 kHz bandwidth can be sampled at slightly over 2 kHz sample rate. Later, the original signal can be fully restored.

Re: nyqist frequency ?

echo47 said:

SkyHigh, you are probably saying the right thing, but your sentence structure is unclear.
Signal bandwidth is important. Signal frequency is (almost) not important.
For example, a 10 MHz signal with 1 kHz bandwidth can be sampled at slightly over 2 kHz sample rate. Later, the original signal can be fully restored.

Click to expand...

According to nyquist we have to sample the signal with "atleast twice the highest frequency available in signal" suppose we have a modulated signal and having spectrum within 570 KHz ~ 580 KHz then we have sampling frequency equal to 2*580 KHz

Re: nyqist frequency ?

khubaibahmed said:

echo47 said:

SkyHigh, you are probably saying the right thing, but your sentence structure is unclear.
Signal bandwidth is important. Signal frequency is (almost) not important.
For example, a 10 MHz signal with 1 kHz bandwidth can be sampled at slightly over 2 kHz sample rate. Later, the original signal can be fully restored.

Click to expand...

According to nyquist we have to sample the signal with "atleast twice the highest frequency available in signal" suppose we have a modulated signal and having spectrum within 570 KHz ~ 580 KHz then we have sampling frequency equal to 2*580 KHz

Click to expand...

Actually, this phrasing of the nyquist criterion is only valid for baseband signals. The more accurate version of nyquist should be a minimum sampling frequency of twice single-sided bandwidth of the signal. So for a bandwidth of 570-580kHz, sampling frequencies must be at least 20kHz.
The reason is that for perfect reconstruction to occur, all you have to ensure is that there is no spectrum overlap, ie aliasing. If the spectrum is only 10kHz wide, repeating these spectrums at 20kHz intervals will ensure that no spectrum overlap occurs. It's just that during the reconstruction stage, you will have to remove the redundant spectrums through a bandpass filter, as the true spectrum is no longer a basband one in the first place.

As to why there is a widely published misconception on nyquist being twice the highest frequency component of the signal, I'm too quite perplexed about it, but my take on it is that firstly, it has borne out of habit, and secondly, most people refer "frequencies" by default to baseband frequencies rather than absolute frequencies.

nyqist frequency ?

I've seen that "twice highest frequency" error countless times, even in classrooms. It has caused some engineers to abandon perfectly good projects because they mistakenly believe it would require too high sample rate or too expensive signal processing.

I think you are correct about the origin of the error. Most sampled systems are baseband, where "twice highest frequency" is the same as "twice bandwidth". When a new student studies sampling theory, it's easier to understand "twice highest frequency". The "twice bandwidth" concept seems counter-intuitive, like some mathematical trick with no practical application. I probably learned it in college, and could do the math, but I never really understood it until years later when I somehow rediscovered it while planning my first digital receiver system.

nyqist frequency ?

I probably learned it in college, and could do the math, but I never really understood it until years later when I somehow rediscovered it while planning my first digital receiver system

Click to expand...

could you explain more 'bout your system echo47.

Istill culdn't grab the idea about this topic...

any other application who could best describe this nyquist freq?

nyqist frequency ?

Try reading this page, especially the "undersampling" section:
https://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem

If you find this concept confusing at first, that's ok. It helps to actually build a system (or simulate one) and observe what's happening.

Re: nyqist frequency ?

Hi
I do not know whether somebody has said this before. However,
The sine wave of fs freq can be reconstructed back if the sampling is not done starting from zero but by some amount of offset.
But in practical scenarios we cannot assure that our sampler to sample perfectly, the 2*fmax component i.e for voice band of 4Khz if there is an input signal of freq 4Khz and our sampler works at 8Khz. And if unfortunately if the zero of the input signal coincides with the zero of the sampler that component of signal is lost.
This I feel is the reason to sample signals at slightly higher frequency than the sampling frequency.
Therefore by theory for a signal with max freq. of fmax the nyquist frequency is 2*fmax. But in practical scenarios it is slightly more.

regards,
KJN

Added after 7 minutes:

Hi
I do not know whether somebody has said this before. However,
The sine wave of fs freq can be reconstructed back if the sampling is not done starting from zero but by some amount of offset.
But in practical scenarios we cannot assure that our sampler to sample perfectly, the 2*fmax component i.e for voice band of 4Khz if there is an input signal of freq 4Khz and our sampler works at 8Khz. And if unfortunately if the zero of the input signal coincides with the zero of the sampler that component of signal is lost.
This I feel is the reason to sample signals at slightly higher frequency than the sampling frequency.
Therefore by theory for a signal with max freq. of fmax the nyquist frequency is 2*fmax. But in practical scenarios it is slightly more.

regards,
KJN

Re: nyqist frequency ?

nitthilan said:

Hi
I do not know whether somebody has said this before. However,
The sine wave of fs freq can be reconstructed back if the sampling is not done starting from zero but by some amount of offset.
But in practical scenarios we cannot assure that our sampler to sample perfectly, the 2*fmax component i.e for voice band of 4Khz if there is an input signal of freq 4Khz and our sampler works at 8Khz. And if unfortunately if the zero of the input signal coincides with the zero of the sampler that component of signal is lost.
This I feel is the reason to sample signals at slightly higher frequency than the sampling frequency.
Therefore by theory for a signal with max freq. of fmax the nyquist frequency is 2*fmax. But in practical scenarios it is slightly more.

regards,
KJN

Click to expand...

What you have said is correct, but the reason behind higher than nyquist sampling rates have been mentioned before. Sampling at exactly nyquist rates would require analog filters (both the anti-aliasing and reconstruction filters) that are rectangular (ie zero roll-off). Realworld filters always have rolloffs.