Compression and Filtering of Random Signals under Constraint of Variable Memory
We study a new technique for optimal data compression
subject to conditions of causality and different types of memory. The
technique is based on the assumption that some information about
compressed data can be obtained from a solution of the associated
problem without constraints of causality and memory. This allows
us to consider two separate problem related to compression and decompression
subject to those constraints. Their solutions are given
and the analysis of the associated errors is provided.
[1] I.T. Jolliffe, Principal Component Analysis, Springer Verlag, New York,
1986.
[2] Y. Hua and M. Nikpour, Computing the reduced rank Wiener filter by
IQMD, IEEE Signal Processing Letters, No. 9, Vol. 6, pp. 240-242, 1999.
[3] L. L. Scharf, The SVD and reduced rank signal processing, Signal
Processing, vol. 25, 113 - 133, 1991.
[4] Y. Hua and W. Q. Liu, Generalized Karhunen-Lo`eve transform, IEEE
Signal Processing Letters, vol. 5, pp. 141-143, 1998.
[5] A. Torokhti and P. Howlett, Computational Methods for Modelling of
Nonlinear Systems, Elsevier, 2007.
[6] A. Torokhti, P. Howlett, IEEE Trans. Circuits & Syst., II, Analog & Digit.
Signal Processing, 48, 2001.
[7] S. Friedland, A. Niknejad, M. Kaveh, H. Zare, Fast Monte-Carlo low
rank approximations for matrices, 10 pp. submited.
[8] T. Zhang, G. Golub, Rank-One Approximation to High Order Tensors,
SIAM J. Matrix Anal. Appl., 23, 2001.
[9] P. Common, G.H. Golub, Tracking a few extreme singular values and
vectors in signal processing, Proc. IEEE, 78, 1990.
[10] E. D. Sontag, Lecture Notes in Control and Information Sciences, 13
1979.
[11] R. M. De Santis, Causality Theory in Systems Analysis, Proc. of IEEE,
64, pp. 36-44, 1976.
[12] G. H. Golub and C. F. Van Loan, Matrix Computations, Baltimore, MD:
Johns Hopkins University Press, 1996.
[13] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and
Applications, John Wiley & Sons, New York, 1974.
[14] V. Gimeno, Obtaining the EEG envelope in real time: a practical method
based on homomorphic filtering, Neuropsychobiology, 18, (1987) pp 110-
112.
[15] H. Kim, G.H. Golub, H. Park, Missing value estimation for DNA
microarray gene expression data: local least squares imputation, Bioinformatics,
21, 2005.
[1] I.T. Jolliffe, Principal Component Analysis, Springer Verlag, New York,
1986.
[2] Y. Hua and M. Nikpour, Computing the reduced rank Wiener filter by
IQMD, IEEE Signal Processing Letters, No. 9, Vol. 6, pp. 240-242, 1999.
[3] L. L. Scharf, The SVD and reduced rank signal processing, Signal
Processing, vol. 25, 113 - 133, 1991.
[4] Y. Hua and W. Q. Liu, Generalized Karhunen-Lo`eve transform, IEEE
Signal Processing Letters, vol. 5, pp. 141-143, 1998.
[5] A. Torokhti and P. Howlett, Computational Methods for Modelling of
Nonlinear Systems, Elsevier, 2007.
[6] A. Torokhti, P. Howlett, IEEE Trans. Circuits & Syst., II, Analog & Digit.
Signal Processing, 48, 2001.
[7] S. Friedland, A. Niknejad, M. Kaveh, H. Zare, Fast Monte-Carlo low
rank approximations for matrices, 10 pp. submited.
[8] T. Zhang, G. Golub, Rank-One Approximation to High Order Tensors,
SIAM J. Matrix Anal. Appl., 23, 2001.
[9] P. Common, G.H. Golub, Tracking a few extreme singular values and
vectors in signal processing, Proc. IEEE, 78, 1990.
[10] E. D. Sontag, Lecture Notes in Control and Information Sciences, 13
1979.
[11] R. M. De Santis, Causality Theory in Systems Analysis, Proc. of IEEE,
64, pp. 36-44, 1976.
[12] G. H. Golub and C. F. Van Loan, Matrix Computations, Baltimore, MD:
Johns Hopkins University Press, 1996.
[13] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and
Applications, John Wiley & Sons, New York, 1974.
[14] V. Gimeno, Obtaining the EEG envelope in real time: a practical method
based on homomorphic filtering, Neuropsychobiology, 18, (1987) pp 110-
112.
[15] H. Kim, G.H. Golub, H. Park, Missing value estimation for DNA
microarray gene expression data: local least squares imputation, Bioinformatics,
21, 2005.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51936", author = "Anatoli Torokhti and Stan Miklavcic", title = "Compression and Filtering of Random Signals under Constraint of Variable Memory", abstract = "We study a new technique for optimal data compression
subject to conditions of causality and different types of memory. The
technique is based on the assumption that some information about
compressed data can be obtained from a solution of the associated
problem without constraints of causality and memory. This allows
us to consider two separate problem related to compression and decompression
subject to those constraints. Their solutions are given
and the analysis of the associated errors is provided.", keywords = "stochastic signals, optimization problems in signal
processing.", volume = "2", number = "11", pages = "787-6", }