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Interpreting the asymptotic increment of Jeffrey's divergence between some random processes
- Source :
- Digital Signal Processing. 75:120-133
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- In signal and image processing, Jeffrey's divergence (JD) is used in many applications for classification, change detection, etc. The previous studies done on the JD between ergodic wide-sense stationary (WSS) autoregressive (AR) and/or moving average (MA) processes state that the asymptotic JD increment, which is the difference between two JDs based on k and ( k − 1 ) -dimensional random vectors when k becomes high, tends to a constant value, except JDs which involve a 1st-order MA process whose power spectral density (PSD) is null for one frequency. In this paper, our contribution is threefold. We first propose an interpretation of the asymptotic JD increment for ergodic WSS ARMA processes: it consists in calculating the power of the first process filtered by the inverse filter associated with the second process and conversely. This explains the atypical cases identified in previous works and generalizes them to any ergodic WSS ARMA process of any order whose PSD is null for one or more frequencies. Then, we suggest comparing other random processes such as noisy sums of complex exponentials (NSCE) by using the JD. In this case, the asymptotic JD increment and the convergence speed towards the asymptotic JD are useful to compare the processes. Finally, NSCE and pth-order AR processes are compared. The parameters of the processes, especially the powers of the processes, have a strong influence on the asymptotic JD increment.
- Subjects :
- 0209 industrial biotechnology
Stochastic process
Applied Mathematics
Null (mathematics)
Spectral density
020206 networking & telecommunications
02 engineering and technology
Exponential function
020901 industrial engineering & automation
Computational Theory and Mathematics
Autoregressive model
Artificial Intelligence
Moving average
Signal Processing
0202 electrical engineering, electronic engineering, information engineering
Ergodic theory
Applied mathematics
Computer Vision and Pattern Recognition
Electrical and Electronic Engineering
Statistics, Probability and Uncertainty
Divergence (statistics)
Mathematics
Subjects
Details
- ISSN :
- 10512004
- Volume :
- 75
- Database :
- OpenAIRE
- Journal :
- Digital Signal Processing
- Accession number :
- edsair.doi...........0e7a19e5dadb8a1f1550bbc03864cbb6