Irregular Sampling
Irregular sampling or non-uniform sampling is a tricky one because it involves iterative algorithms. However, if you work in signal processing you may deal with the problem of signals that were sampled in an irregular way and you would need to reconstruct them, by also meeting the conditions of the Nyquist Theorem.
The methods used to solve this problem are still in development and from Behind The Sciences we have found several resources that will make you easily understand what is going on, how to deal with it and, of course, how to implement it in Matlab, so have a look to the following list of FREE resources:
- If you want to easily understand how irregular sampling works, definitely you need to start by having a look at this tutorial: https://www.math.ucdavis.edu/~strohmer/research/sampling/irsampl.html
- This is another tutorial for those who want to learn the basic concepts: http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/PIRODDI1/NUFT/node7.html
- If you want to go deeper and learn how to implement it in Matlab, this aticle is your answer: H.G. Feichtinger, K. Grochenig, “THEORY AND PRACTICE OF IRREGULAR SAMPLING”. With the key methods explained and Matlab examples, you can request it for free here: https://www.researchgate.net/publication/265543129_Theory_and_practice_of_irregular_sampling
Figure 1. Example from the first referenced tutorial
Mathworks also has tutorial that explains how to re-sample a non-uniformly sampled signal in Matlab: http://uk.mathworks.com/help/signal/examples/resampling-nonuniformly-sampled-signals.html
Now, if you want to go deeper into the algorithms used to reconstruct irregularly sampled signals, google the following names:
- Voronoi-Allebach algorithm
- Marvasti algorithm
- Adaptive Weights Algorithm
Another detailed tutorial explaining this, can be found here:
We hope this was helpful! If you think we missed something, please, leave a comment or send us an email to contact@behindthesciences.com
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behindthesciences
We are two engineers who work in the Electronic and Telecommunication industry. We regularly blog in our spare time.