regarding the sample frequency calculation

[sridivya pathapati]

hiii..can u tell me the sample frequency if the frequency inputs are of 1.2khz and 2.2khz?????

 

[D.A.(Tony)Stewart]

if say an A/D convertor, your sampling rate must be> 2x the highest f , so 5kHz min with a high order LPF @ 2.2kHz to prevent aliasing and IM distortion. If this is an issue, then sample at a higher frequency. This assumes both signals are sine waves. If NOT, then all the harmonics must be considered that are useful.
These are the common rates for a dialup modem 1.2, 2.4kHz. Most common solution for voice is 4kHz 7th order LPF with 8ksps with a nonlinear µ Law or A Law logarithmic curve on ADC. For data similar LPF but modulation is linear 16n QPSK within 4KHz BW. So modem signals can pass thru 8Ksps DS0 SLIC converter and yield 64kbps output with 8 bit log scale data.

 

[Petre Petrov]

Hello!

May be the "At Least 4x" rule will work for you.

May be that will help you at least when you sample sinusoidal and co-sinusoidal signals:

“A New Approach to Sampling Sinusoidal and Cosinusoidal Signals”, P T Petrov,
https://www.ieindia.org/pdf/88/88ET104.pdf

Also may be it will be useful to know:
“Sampling of the Simplest Signals” P T Petrov
https://www.ieindia.org/pdf/89/89CP109.pdf

Any feedback is welcomed

BR

Petre Petrov

 

[D.A.(Tony)Stewart]

Petre, I read part of your articles.

**added** if I see your graph of a sine wave and discussion of triangle waves , I see harmonic content. The Sine wave is actually an elliptical wave, with significant harmonic content and the triangle waves have the same harmonics as square waves except the phase is not complementary but rather in phase, so Shannon's theorem cannot apply without some discussion as the the sampling of the harmonic content and preservation of the original signal. Your Rule of Thumb of 4x f based on 3db approximation neglects the harmonic content and Fourier transform or at least some discussion on Spectral Density of the signal. The conclusion is not valid since the assumptions are not stated correctly **end**
= - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - = - =
The 4x is not a rule but merely a practical suggestion for wideband use.

However the Theorem on Information Theory is clear.
You also stated "The proof that with N = Fd / Fs = 2 and the angle of the first sample equal to zero ( ϕ0 = 0 ), s"

But N should be >2 rather than =2 ??

Of course the assumptions must be reviewed.

WHat is the highest frequency present?

If there is no modulation, then the sinewaves will be preserved.

If there is modulation, then the sampling rate must be increased to cover the sidebands.

ALso one must consider if you need a synchronous detection and you have optimally matched filter data. If you sample any signal value and shape, with an offset to the frequency or a harmonic of it, then the output say of an analog Sample & Hold will be the diference frequency, which matches the original waveshape due to behaviour of an ideal mixer. With the phase and waveform appear forward or reverse according to the relative frequency error. THis is how Doppler works.

if 2.2KHz is a sine wave and is the highest frequency content, you can reconstruct the orignal amplitude and phase using a sampling rate >4.4KHz

Of course then we have latency. Faster the sampling rate for ADC then DAC, the lower the latency as there is memory in the sample interval.
Sampling is ideally done with the autocorrelation function describing both the channel information bandwidth and pass band shape with maximally flat group delay being ideal.

 

[Petre Petrov]

Hi SunnySkyguy,
Thank you for the attention to may post and to the papers.

4x is rule based on theorems guarantying -3bB band width
Please see the theorems and the tables in the paper.
Please accepted my apologize if my English or stile is not comprehensible.

-3dB bandwidth is accepted rule and standard
Testing with sine and co-sine signals is accepted rule and standards

2x is giving error from 0 to 100% and has no practical value.
Please see the theorems and the tables in the paper.

I hope that is clearing the situation.
Any comments and questions are welcomed
BR
Petre Tzv. Petrov