Explain to me the Nyquist Rate!

What is Nyquist Rate

I have a problem about sampling theorem and Nyquist Rate...
I working from Oppenheim but ı cant understand easily because my englist isnt very good.

Please
can you explain me Nyquist Rate??

Re: What is Nyquist Rate

Simply:
If you want to sample a signal and then want to reconstruct as the original from of it ,you must take samples at rate that 2*f .f is the frequency of the highest frequency component of that signal.Maybe other guys can tell the theorem's mathematical proof.

Re: What is Nyquist Rate

umutguncan,
To restate what coshkun (accurately) said, the Nyquist rate, or Nyquist frequency is half the sampling rate. It is the highest input frequency that can be reconstructed from the samples, taken at the sampling rate.
Regards,
Kral

Re: What is Nyquist Rate

So, the sampled signal has periodic spectrum. (So it will be infinity)
It will be periodic with the sampling frequency.
Try it, for example draw a simple spectrum, and pushing along the spectrum with sampling frequency. If the sampling frequency isn't large enough then the spectrum will be "aliasing".(Subsampling) But in some application the subsampling is useful.
Shannon has the theory about sampling. This is true, if your signal is real and bandlimited.
So, if you use Nyquist rate as sampling frequency, you can take it for sure, that no loss of information will occur subsequent upon aliasing.
Nyquist frequency(rate)=2* highest frequency in your signal (baseband signal) , so the two-sided bandwith of the signal

And then you can use a low pass filter to reduce the bandwith from infinity



In the Communication Theory, there's an idea of Nyquist channel characteristics. It's because of avoid ISI (Inter Symbol Interference)

Re: What is Nyquist Rate

Very thanks your usefull Answers but ı am afraid ı dont know exactly what is fourier transform..
I know all the formules but it is not important to understand main idea...
Can you explain me spectrum and fourier transform...

Re: What is Nyquist Rate

I hope you know Fourier series ( and function series, power series, Taylor series,... these are very important for an engineer , because an engineer always approximate, i think)
Fourier series:
So we have two orthonormal base function ( sin and cos), and we can generate a periodic function (signal) from the sum of sin and cos functions.
(other orthonormal base functions are possible for example the Walsh functions.)

And you can imagine the Fourier transform as the extension of the Fourier series for non-periodic signals. (you exchange the sum to an integral)
And the Fourier transform is a transfrorm from time domain to frequency domain.
If you characterize a signal in the frequency domain, then you give its spectrum.
From its spectrum you can read for example the bandwidth of the signal.
(There's an instrument called spectrum analyzer which can determine the spectrum of a signal)

In the measurement theory engineers like use the time domain and in communication theory enginners like to use the frequency domain.( according to my experience)
And I think it's the best if you learn some rules for example if a signal is finite in the time domain it will be infinity in the frequency domain. If a signal is narrow in either domain it will be wide in the other domain. Rectangular signal has a sin(x)/x spectrum. Gauss signal has a Gauss spectrum. Multiplication in the either doman will be convolution in the other domain. multiplication with exp() <-> offset
I think these are the most important. ( I can remember these rules now, but I had learned it a long time ago)

Re: What is Nyquist Rate

Very thanks Dragos..
But what can we know from spectrum another..

I learned Spectrum let us know the which Cos Ans Sın signals are in my signal.(sorry for my bad english.) Is it true.....

İs is it true HOW?

Re: What is Nyquist Rate

Nyquist Rate:
In signal processing, the Nyquist Rate is the minimum sampling rate (in samples per second) required to avoid aliasing when sampling a continuous signal. If the input signal is real and bandlimited, the Nyquist rate is simply twice the highest frequency contained within the signal. In other words, the Nyquist rate is equal to the two-sided bandwidth of the signal.

,

where

, is the highest frequency component contained in the signal.

To avoid aliasing, the sampling rate must exceed the Nyquist rate:

for more information, refer below mentioned links:
1) https://www.efunda.com/designstandards/sensors/methods/dsp_nyquist.cfm
2) https://cnx.org/content/m10791/latest/
3) https://www.facstaff.bucknell.edu/mastascu/elessonshtml/Signal/SignalNoteNyquistSampling.htm

cheers...

What is Nyquist Rate

nyquist rate is twice the highest freqency contained in the signal

Re: What is Nyquist Rate

I learned Spectrum let us know the which Cos Ans Sın signals are in my signal.(sorry for my bad english.) Is it true.....

Click to expand...

If you have a periodic signal, then you will have a discrete spectrum. So you can read what frequencies of sin and cos signals will produce your signal. If your signal is even, then just cos if your signal is odd then just sin signal will produce the signal.

Think that many signal has infinity continuous spectrum. these signals will contain all the frequencies of sin and cos signals, you can thik about it this way. (for example an ideal pulse)

What is Nyquist Rate

2 times of your smaple rate

Re: What is Nyquist Rate

It is the minimum frequency at which the signal which is band limited has to be sampled so as to get back the original CT signal by reconstruction formula.

thnx

purna

Re: What is Nyquist Rate

the Nyquist rate is twice the highest frequency of the signal ,you can get the highest frequency from FT. In signal processing ,the sampling frequengy must not less than the Nyquist Rate if you want to recover the original signal.