Novel 2-D cascade ladder-lattice structure recursive digital filters


  • Mohamed Zitouni
  • Thameur Obeidi
  • Mohamed Elbar
  • Ahmed Chinoun



2-D recursive digital filters, basic lattice section, lattice-ladder filters, Givone-Roesser’s state space


We present in this paper a novel cascade ladder-lattice structure of two-dimensional (2-D) recursive digital filters; this cascade based on two delay units M and N and a basic lattice section. Our new realization has a minimal number of basic lattice sections. Using a transfer function representation; the matrix representations for the basic lattice sections are proposed and used to derive the transfer functions of the realized 2-D digital lattice filters. The theory and transfer functions of the realized 2-D lattice Digital filter are derived. We use the 2-D Givone–Roesser’s state space model to verify the minimal realization of the proposed 2-D recursive digital filte; this later gives matrix-vectors A, b, c and a scalar d which are derived. As result, the dimension of the 2-D generalized state space model is minimal. Finally, several design examples are provided for conducting illustration.


Bose, N.K. Applied Multidimensional Systems Theory, Springer, Cham,.

Krzysztof Galkowski and Jeff David Woo, Multidimensional signals, circuits and systems,280 pages, Taylor & Francis, May 10 (2001).

Kaczorek. T., (1999). Two-Dimensional Linear Systems. In: Frank P.M. (eds) Advances in Control. Springer, London, pp.1-406. .( 2017).

Konrad. R, D. Dansereau. G., Masood. A., and etzstein. G., SpinVR: Towards live–streaming 3D virtual reality video,ACM Transactions on Graphics (TOG), SIGGRAPH ASIA, Vol. 36, No. 6,. 3130800.3130836 (2017).

Bose N. K. – Multidimensional systems and signal processing: Good theory for good practice, IEEE Circuits and Systems Magazine 7 (4) 20 – 41. DOI: 10.1109/MCAS.2007.910028 (2007).

Antoniou. G. E., Varoufakis S. J. and Paraskevopoulos P. N. State space realization of 2D systems via continued fraction expansion, IEEE Trans. Circuits Syst. CAS-33 ,926-930 DOI: 10.1109/TCS.1986.1086014 (1986).

Antoniou. G, On The Realization Of 2D Lattice-Ladder. Discrete Filters, Journal of Circuits System and Computers (2004) 1079-1083. DOI: 10.1109/LASCAS.2019.8667598.

Kousoulis. M. T. and Coutras C. A. and Antoniou G. E. 4D Bidirectional Lattice Digital Filters, IEEE 10th Latin American Symposium on Circuits Systems (LASCAS), 205-208 (2019).

Givone D.D., Roesser. R. P. (1973). Minimization of multidimensional linear iterative circuits,IEEE Transactions on Computers C-22 (7673-678. DOI: 10.1109/TC.1973.5009134.

Lee J. H., Du. J. S. Lattice structure realization for the design of 2-D digital allpass filters with general causality, IEEE Transactions on Circuits and Systems I: Regular Papers PP (99) 1-13. DOI: 10.1109/TCSI.2016.2604678 (2016).

Lee. J. H. and Yang. Y. H. General lattice structures of 2-D recursive digital filters, 2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS) 1-4. DOI: 10.1109/MWSCAS.2011.6026633 (2011).

G. E. Antoniou, Generalized one. Multiplier lattice discrete 2-D filters: minimal circuit and state-space realization, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48 (2) ,215-218. DOI: 10.1109/81.904886 (2001).

Chang. P and Cheng.C; Tseng. Two dimensional IIR digital notch filter design, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing (IEEE) 227-231. DOI:10.1109/82.279208 .(1994).

Regalia. P. and Mitra.S. Tunable digital frequency response equalization, IEEE Transactions on Acoustics, Speech, and Signal Processing 118-120.January DOI:10.1109/TASSP.1987. 1165037.( 1987).

M.T. Kousoulis, C.A. Coutras, G.E. Antoniou, “Minimum multiplier– delay 4D digital filter”, 9th IEEE Latin-American Symposium on Circuits and Systems (IEEE LASCAS’2018), Puerto Vallarta, Mexico, 2018.

Mohamed, ELBAR; Ahmed Zohair, DJEDDI; Hafaifa, Ahmed; Naas, CHARRAK; Iratni, Abdelhamid; and colak, ilhami (2023) "Evaluation of Reliability Indices for Gas Turbines Based on the Johnson SB Distribution: Towards Practical Development," Emirates Journal for Engineering Research: Vol. 28: Iss. 2, Article 5, .

M.T. Kousoulis, C.A. Coutras, G.E. Antoniou, “4D reverberator-based digital filters”, 8th IEEE Latin-American Symposium on Circuits and Systems (IEEE LASCAS’2017), Bariloche, Argentina, 2017.




How to Cite

Zitouni, M., Obeidi, T., Elbar, M., & Chinoun, A. (2024). Novel 2-D cascade ladder-lattice structure recursive digital filters. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 403–417.