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Design >> Mixed-Signal Design >> Difficult fundamental question about sampling
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Message started by tony_taoyh on Sep 22^nd, 2009, 1:27am

Title: Difficult fundamental question about sampling
Post by tony_taoyh on Sep 22^nd, 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.

Title: Re: Difficult fundamental question about sampling
Post by MarcoC on Sep 22^nd, 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

Title: Re: Difficult fundamental question about sampling
Post by raja.cedt on Sep 22^nd, 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.

Title: Re: Difficult fundamental question about sampling
Post by raja.cedt on Sep 22^nd, 2009, 2:40am

one more thing normally we will keep anti-alias filter to avoid this only

Title: Re: Difficult fundamental question about sampling
Post by tony_taoyh on Sep 22^nd, 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.

Title: Re: Difficult fundamental question about sampling
Post by raja.cedt on Sep 22^nd, 2009, 3:19am

hi,
i feel it is five times because of five times noise folding

Thanks,
Rajasekhar.

Title: Re: Difficult fundamental question about sampling
Post by MarcoC on Sep 22^nd, 2009, 5:13am

around five times is correct.
1MHz/200KHz

Title: Re: Difficult fundamental question about sampling
Post by thechopper on Sep 22^nd, 2009, 7:23pm

raja.cedt wrote on Sep 22^nd, 2009, 2:37am:

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

Title: Re: Difficult fundamental question about sampling
Post by raja.cedt on Sep 22^nd, 2009, 9:33pm

hi tosie,
excellent correction man, but here whose low pass filter action we have to consider here?

Thanks,
Rajasekhar.