FUNDAMENTALS OF MULTIDIMENSIONAL TIME-SERIES ANALYSIS

This paper presents a survey of recent research in multi-dimensional signal processing. As a means of illustrating the fundamental principals, the presentation focuses on two-dimensional (2-D) results. A tutorial section in the paper addresses the basic subjects of 2-D systems representations (convolution and difference equations), 2-D Z-transforms, stability theorems/tests, and modeling. Both deterministic and random formalisms are described. To give some flavor for on-going research in this field, two new results are also described. The first deals with the extension of Wiener’s realizable filtering technique to 2-D and the second with the concept of autoregressive models of 2-D random fields.

[1]  D.E. Dudgeon,et al.  Two-dimensional digital filtering , 1975, Proceedings of the IEEE.

[2]  M. Ekstrom,et al.  Multidimensional spectral factorization and unilateral autoregressive models , 1980 .

[3]  Gary A. Shaw,et al.  An algorithm for testing stability of two-dimensional digital recursive filters , 1978, ICASSP.

[4]  M. Ekstrom,et al.  Two-dimensional recursive filter design--A spectral factorization approach , 1980 .

[5]  W. Rudin.  Function theory in polydiscs , 1969 .

[6]  D. Siljak.  Stability criteria for two-variable polynomials , 1975 .

[7]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[8]  T. Marzetta.  Two-dimensional linear prediction: Autocorrelation arrays, minimum-phase prediction error filters, and reflection coefficient arrays , 1980 .

[9]  M. Fahmy,et al.  On the stability of two-dimensional digital filters , 1973 .

[10]  J. Shanks,et al.  Stability criterion for N -dimensional digital filters , 1973 .

[11]  Brian D. O. Anderson,et al.  Stability test for two-dimensional recursive filters , 1973 .

[12]  B. Dickinson,et al.  Two-dimensional Markov spectrum estimates need not exist , 1980, IEEE Trans. Inf. Theory.

[13]  R. T. Lacoss,et al.  ESTIMATION OF SEISMIC NOISE STRUCTURE USING ARRAYS , 1969 .

[14]  Michael M. Fitelson,et al.  Notes on maximum-entropy processing (Corresp.) , 1973, IEEE Trans. Inf. Theory.

[15]  R.E. Dubroff.  The effective autocorrelation function of maximum entropy spectra , 1975, Proceedings of the IEEE.

[16]  H. Helson,et al.  Prediction theory and Fourier Series in several variables , 1958 .

[17]  P. Whittle.  ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[18]  Douglas R. Goodman,et al.  Some stability properties of two-dimensional linear shift-invariant digital filters , 1977 .

[19]  Thomas L. Marzetta.  A linear prediction approach to two-dimensional spectral factorization and spectral estimation , 1978 .

[20]  Michael G. Strintzis,et al.  Tests of stability of multidimensional filters , 1977 .

[21]  J. Makhoul,et al.  Linear prediction: A tutorial review , 1975, Proceedings of the IEEE.

[22]  Herbert Freeman,et al.  Discrete-Time Systems , 1980 .

[23]  T. Huang,et al.  Stability of general two-dimensional recursive digital filters , 1978 .

[24]  D. Chan.  The structure of recursible multidimensional discrete systems , 1980 .

[25]  John W. Woods,et al.  Two-dimensional discrete Markovian fields , 1972, IEEE Trans. Inf. Theory.

[26]  M. Ekstrom,et al.  Two-dimensional spectral factorization with applications in recursive digital filtering , 1976 .

[27]  J. Aggarwal,et al.  Design of two-dimensional semicasual recursive filters , 1978 .

[28]  John W. Woods,et al.  Two-dimensional Markov spectral estimation , 1976, IEEE Trans. Inf. Theory.

[29]  Thomas S. Huang,et al.  Stability of two-dimensional recursive filters , 1972 .

[30]  S. Treitel,et al.  Stability and synthesis of two-dimensional recursive filters , 1972 .

[31]  R. Saeks,et al.  Multivariable Nyquist theory , 1977 .

[32]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[33]  J. P. Burg,et al.  Maximum entropy spectral analysis. , 1967 .

[34]  R. Lacoss.  DATA ADAPTIVE SPECTRAL ANALYSIS METHODS , 1971 .

[35]  A. Gray,et al.  On autocorrelation equations as applied to speech analysis , 1973 .

[36]  Thomas L. Marzetta.  The design of 2-D recursive filters in the 2-D reflection coefficient domain , 1979, ICASSP.

[37]  Y. Kamp,et al.  Counterexample in the least-squares inverse stabilisation of 2D recursive filters , 1975 .

[38]  T. Ulrych,et al.  Time series modeling and maximum entropy , 1976 .