Linear predictor and autocorrelation for noisy and delayed digital signal

G Vinu Priya, R Jothilakshmi


This paper deals with the association between the linear prediction and digital signal modeling and ends up with the suitable ways to predict the signal by considering a stationary signal $y_{n}$. The linear prediction of signal modeling based on the finite past and the solutions are arrived in a recursive manner. Further we analyzed the wiener filter along with spectral theorem and autocorrelation in terms ofpredictive analysis.This estimates the gap function along with delay and noise. The delayed signal’sproperties are analyzed like causal, stability and applied these into optimum filtering. Finally the predicted error is compared with linear predictor and Wiener filter. Then transfer function is applied to estimate the interval function and gap function along with delay.


Linear Predictor, Weiner filter, gapped function, delay, autocorrelation, orthogonal.

Full Text:



J. Chen, J. Benesty, Y. Huang, and S. Doclo. New insights into the noise reduction

Wiener filter. Audio, Speech, and Language Processingn, volume 14. IEEE

Transactions, 2006.

L. Dogariu, J. Benesty, C. Paleologu, and S. Ciochina. An insightful overview of the wiener filter for system identification. Appl. Sci., 11(7774), 2021.

F. L. Gland and N. Oudjane. A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo- mixingsignals. Stochastic Processes and their Applications, 106(2):279–316, 2003.

J. Makhoul. Linear prediction a tutorial review. Proceedings of the IEEE, 63(4):561–580, 1975.

J. Mao, D. Ding, Y. Song, and FE. Alsaadi, event-based recursive filtering for time-delayed stochastic nonlinear systems with missing measurements. Signal Processing, 134:158–165, 2017.

M. Pituk. A criterion for the exponential stability of linear difference equations, volume 17. 2004.

T. B. Welch, G. W. C., H., and G. M. M. Real-Time Digital Signal Processing -From Matlab to C with the TMS320C6x DSK. Taylor and Francis, 2006



  • There are currently no refbacks.

Copyright (c) 2023 G Vinu Priya, R Jothilakshmi

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.