Hi, I am new to signal processing and have very simple question. Where can I find a brief explanation about sub-Nyquist and irregular sampling. I searched the web by almost all possible keywords, but what I found is not so useful. It would be very nice if you give me some book titles. Thanks in advance!

# Information request about sub-Nyquist and irregular sampling

Started by ●October 1, 2009

Reply by ●October 1, 20092009-10-01

>Hi, > >I am new to signal processing and have very simple question. Where can I >find a brief explanation about sub-Nyquist and irregular sampling. I >searched the web by almost all possible keywords, but what I found isnot>so useful. It would be very nice if you give me some book titles.I don't think a brief explanation is possible, because considerable complexity is normally needed to make these techniques workable. Sub-Nyquist sampling is used in lots of applications, especially military ones, but there is normally something fairly complex going on to allow such sampling to be usable. For example, many radar and sonar systems use sub-Nyquist sampling, and a selection of sampling rates. By correlating across the different aliases at the various sampling rates, the true range/velocity/whatever can be resolved. The basic idea is pretty simple, but the details quickly get quite messy. There are books which cover these topics. I guess the most widely used application for irregular sampling is in oscilloscopes. I expect you can find material on that topic. Steve

Reply by ●October 2, 20092009-10-02

Hi, As Steve have mentioned subNyquist sampling problems are detailed in many textbooks, for example in R.Lyons "Understanding Digital Signal Processing". There is also a fundamental article on sampling frequency selection and noise issues: R.G.Vaughan, N.L.Scott and D.R.White "The Theory of Bandpass Sampling" in IEEE trans. on Signaд Processing, vol.39,no.9. What do you mean by irregular sampling here? If you mean time-interleaved sampling, which is in fact irregular because of timing mismatches between individual channels, then you can use this article as a starting point: http://www.analog.com/library/analogDialogue/cd/vol37n3.pdf#page=5 -- Alexander

Reply by ●October 3, 20092009-10-03

On Oct 2, 4:11 am, "Alexander Sotnikov" <sotni...@scideco.ru> wrote:> Hi, > > As Steve have mentioned subNyquist sampling problems are detailed in many > textbooks, for example in R.Lyons "Understanding Digital Signal > Processing". There is also a fundamental article on sampling frequency > selection and noise issues: R.G.Vaughan, N.L.Scott and D.R.White "The > Theory of Bandpass Sampling" in IEEE trans. on Signaд Processing, > vol.39,no.9. > > What do you mean by irregular sampling here? If you mean time-interleaved > sampling, which is in fact irregular because of timing mismatches between > individual channels, then you can use this article as a starting point:http://www.analog.com/library/analogDialogue/cd/vol37n3.pdf#page=5 > > -- > AlexanderI wrote a paper on a very simple technique that can be explained without much fany math, back in 1992. It only covers the periodic missing-sample case. http://www.aes.org/e-lib/browse.cfm?elib=7022# Bob Adams

Reply by ●October 3, 20092009-10-03

>Hi, > >As Steve have mentioned subNyquist sampling problems are detailed inmany>textbooks, for example in R.Lyons "Understanding Digital Signal >Processing". There is also a fundamental article on sampling frequency >selection and noise issues: R.G.Vaughan, N.L.Scott and D.R.White "The >Theory of Bandpass Sampling" in IEEE trans. on Signaд Processing, >vol.39,no.9.What has bandpass sampling to do with sub-Nyquist sampling? Bandpass sampling (unless it is screwed up) complies with the sampling theorem requirements for sampling rate.>What do you mean by irregular sampling here? If you meantime-interleaved>sampling, which is in fact irregular because of timing mismatchesbetween>individual channels, then you can use this article as a starting point: >http://www.analog.com/library/analogDialogue/cd/vol37n3.pdf#page=5Steve

Reply by ●October 3, 20092009-10-03

On 3 Okt., 16:15, Robert Adams <robert.ad...@analog.com> wrote:> I wrote a paper on a very simple technique that can be explained > without much fany math, back in 1992. It only covers the periodic > missing-sample case. > > http://www.aes.org/e-lib/browse.cfm?elib=7022#That was an excellent article! It taught me two things: 1. From an oversampled signal, any finite number of "missing" samples can be reconstructed (using the "eigen-filter" approach outlined in your article). This implies that any discrete signal with only a finite number of non-zero samples is _never_ oversampled (the discrete version of the finite-bandwidth-infinite-time-support theorem). 2. Even an infinite amount of missing samples can be reconstructed if the oversampling factor is sufficient. You showed the particlar case where 1-out-of-M samples was missing. It was a neat exercise to extend this result to the N-out-of-M case for periodic missing samples patterns. I wrote this up in a DSP Tips and Tricks article in the November 2007 issue of the Signal Processing Magazine. To the OP: your question is not simple at all. Use google books to have a look at "Nonuniform sampling: theory and practice" from Farokh A. Marvasti. Regards, Andor

Reply by ●October 5, 20092009-10-05

>What has bandpass sampling to do with sub-Nyquist sampling? Bandpass >sampling (unless it is screwed up) complies with the sampling theorem >requirements for sampling rate.I was wrong about that. I confused sub-Nyquist sampling with subsampling, the term which is sometimes used for bandpass sampling. -- Alexander