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Automatic Control and Computer Sciences
Erschienen in: Automatic Control and Computer Sciences 3/2019

01.05.2019

Trellis-Based Postprocessing for Short Delay Measurement Using NDFT

verfasst von: Karel Dudáček, Karel Dudáček

Erschienen in: Automatic Control and Computer Sciences | Ausgabe 3/2019

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Abstract

For digital measurement of short delays between fast analogues signals can be used phase shift method with non-uniform sampling and non-uniform Fourier transform (NDFT), but if the signals are short, non-uniform sampling causes random spurious peaks in the spectrum. In case we have sequence of spectrograms with slow frequency change, correct peaks could be found using evaluation of such sequence. Our new Trellis-based postprocessing selects several greatest peaks from each spectrogram in the sequence and interprets them as nodes of an acyclic directed graph. These nodes are weighted and correct ones are found by graph algorithm. Experiments showed that our method provides correct results in cases when ordinary peak detection is not able to distinguish correct and spurious peaks.
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Fußnoten
1
Phase shift computed using Fourier transform is in range \(\left\langle { - \pi , + \pi } \right\rangle \).
 
2
According to [9], the bandwidth of analogue inputs of common AD converters is typically 4 to 8 times higher than half of the maximal (periodic) sampling frequency of the AD converter.
 
3
Change of the frequency fp and of the random sampling instants causes different cross-interference in every burst; therefore, spurious peaks appear at the different positions.
 
4
We also tried p = 1/2.
 
5
Asterisk (*) in indexes (e.g. \({{P}_{{{i,}^{*}}}}\) or \({{w}_{{{0,}^{*}}}}\)) is used as a placeholder saying any valid value.
 
6
It would be formally more proper to weight the nodes by \(\sqrt[p]{{{{w}_{{i + 1,\,k}}}}}\), but for purposes of our method, it is enough to use \({{w}_{{i + 1,\,k}}}\) since for any a < b < c; a, b, c > 0 holds ap < bp < cp ; p > 1.
 
7
There could be more non-converging paths, but it is improbable due to random distribution of the most of the nodes.
 
8
It would be formally more appropriate to use \({{w}_{c}} = \sqrt[p]{{k{{{(\lambda )}}^{p}}}}\), but we must use the same norm as we use for path weighting, i.e. \({{w}_{c}} = k{{(\lambda )}^{p}}\).
 
9
Generator of pseudorandom numbers was also initiated to the same state.
 
10
In the spectrogram, there is no local maximum for useful frequency fp , or it is to small.
 
11
In case of increasing N, take care about ratio of λ and B/2N.
 
Literatur
1.
2.
3.
4.
Dudáček, K., Jr., Dudáček, K., and Vavřička, V., Short delay measurement using non-uniform Fourier transform, Proceedings of the 14th Biennial Baltic Electronics Conference, 2014, pp. 165–168.
5.
Dudáček, K., Jr., Dudáček, K., and Vavřička, V., Comparison of short delay measurement methods, 2015 International Conference on Applied Electronics (AE), 2015, pp. 27–32.
6.
Dudáček, K., Short Time Delay Measurement. Technical Report, Pilsen: University of West Bohemia, 2015.
7.
8.
9.
Bilinskis, I., Digital Alias-Free Signal Processing, Chichester: John Wiley & Sons, Ltd., 2007.CrossRefMATH
10.
Artyukh, Yu., Bilinskis, I., Boole, E., Rybakov, A., and Vedin, V., Wideband RF signal digititising for high purity spectral analysis, Proceedings of the 2005 International Workshop on Spectral Methods and Multirate Signal Processing (SMMSP 2005), 2005, 123–128.
Metadaten
Titel
Trellis-Based Postprocessing for Short Delay Measurement Using NDFT
verfasst von
Karel Dudáček
Karel Dudáček
Publikationsdatum
01.05.2019
Verlag
Pleiades Publishing
Erschienen in
Automatic Control and Computer Sciences / Ausgabe 3/2019
Print ISSN: 0146-4116
Elektronische ISSN: 1558-108X
DOI
https://doi.org/10.3103/S0146411619030039

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