The Designer's Guide Community
Forum
Welcome, Guest. Please Login or Register. Please follow the Forum guidelines.
Mar 29th, 2024, 4:22am
Pages: 1
Send Topic Print
Difficult fundamental question about sampling (Read 5643 times)
tony_taoyh
New Member
*
Offline



Posts: 7

Difficult fundamental question about sampling
Sep 22nd, 2009, 1:27am
 
Hi, All,

The nyquist sampling theorem is well "known".

Also, the aliasing is also "known".

However, what will happen if we are sampling a wideband noise using a lower sampling frequency?

For example, the wideband noise has spectrum from 1 to 1MHz, however, the sampling frequency is only 100kHz, what will be inside the output spectrum? How to calculate the output spectrum with the input spectrum?

Thanks a lot.


Back to top
 
 
View Profile   IP Logged
MarcoC
Junior Member
**
Offline



Posts: 20
Cesena, Italy
Re: Difficult fundamental question about sampling
Reply #1 - Sep 22nd, 2009, 2:00am
 
Hi Tony,
Quote:
However, what will happen if we are sampling a wideband noise using a lower sampling frequency?


The noise is folded. In the output spectrum you will see a white spectrum of value around USF*Sin(f) where USF is the under-sampling factor and Sin(f) is the input spectrum.
This is a quick reply but I don't have much time today.

If you wish more understanting take a look to these:
- "Circuit Techniques for reducing the effects of op-amp imperfections: autozeroing, correlated double sampling and chopper stabilization" by G. Temes (this is a paper about CDS and so on but it answers quite well to your question)

- I suggest you also these material:
       http://www.designers-guide.org/Theory/cyclo-paper.pdf
       http://www.cadence.com/rl/Resources/white_papers/tdnoise.pdf

Hope to be helpful.  ;)
Bye
Back to top
 
 
View Profile MarcoC   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: Difficult fundamental question about sampling
Reply #2 - Sep 22nd, 2009, 2:37am
 
hi,
  answer seems very clear because according to sampling theorem noise will be aliased with sampling frequency rate, and fortunately additional noise is uncorrelated so you will get white spectrum  

Thanks,
Rajasekhar.
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: Difficult fundamental question about sampling
Reply #3 - Sep 22nd, 2009, 2:40am
 
one more thing normally we will keep anti-alias filter to avoid this only
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
tony_taoyh
New Member
*
Offline



Posts: 7

Re: Difficult fundamental question about sampling
Reply #4 - Sep 22nd, 2009, 3:04am
 

How to calculate them?

For example, before sampling, the noise power density is:

1 v^2/Hz (1~1MHz), what is the power spectrum density after sampling @ 200KHz?

Thanks.
Back to top
 
 
View Profile   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: Difficult fundamental question about sampling
Reply #5 - Sep 22nd, 2009, 3:19am
 
hi,
  i feel it is five times because of five times noise folding

Thanks,
Rajasekhar.
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
MarcoC
Junior Member
**
Offline



Posts: 20
Cesena, Italy
Re: Difficult fundamental question about sampling
Reply #6 - Sep 22nd, 2009, 5:13am
 
around five times is correct.
1MHz/200KHz
Back to top
 
 
View Profile MarcoC   IP Logged
HdrChopper
Community Fellow
*****
Offline



Posts: 493

Re: Difficult fundamental question about sampling
Reply #7 - Sep 22nd, 2009, 7:23pm
 
raja.cedt wrote on Sep 22nd, 2009, 2:37am:
hi,
  answer seems very clear because according to sampling theorem noise will be aliased with sampling frequency rate, and fortunately additional noise is uncorrelated so you will get white spectrum  

Thanks,
Rajasekhar.


Hi Rajasekhar,

This is about correct. However the bandlimited noise is not totally white: a low pass filtered noise has some degree of correlation, as opposed to an infinite bandwidth noise, which is an idealization we call "white noise" (I´m assuming a flat spectrum).
The aliased noise will then have an about flat spectrum but that does not convert it into white noise, since it will also have a degree of correlation due to the low pass filtering. This correlation will be stronger if after sampling such noise is further filtered.

Concerning the noise aliasing ratio, there is a correction factor that should be considered. For a 1-pole like noise spectrum the equivalent noise BW is 1.57 time the pole frequency. Therefore for the 1MHz case you should consider 1.57MHZ instead (again, assuming 1 pole BW). Therefore the ratio is more like 7.85 times.

Regards
Tosei
Back to top
 
 

Keep it simple
View Profile   IP Logged
raja.cedt
Senior Fellow
******
Offline



Posts: 1516
Germany
Re: Difficult fundamental question about sampling
Reply #8 - Sep 22nd, 2009, 9:33pm
 
hi tosie,
           excellent correction man, but here whose low pass filter action we have to consider here?

Thanks,
Rajasekhar.
Back to top
 
 
View Profile WWW raja.sekhar86   IP Logged
Pages: 1
Send Topic Print
Copyright 2002-2024 Designer’s Guide Consulting, Inc. Designer’s Guide® is a registered trademark of Designer’s Guide Consulting, Inc. All rights reserved. Send comments or questions to editor@designers-guide.org. Consider submitting a paper or model.