General lattice structures of 2-D recursive digital filters

Abstract

This paper presents a general lattice structure for the realization of two-dimensional (2-D) recursive digital filters. We employ two basic lattice sections to realize 2-D recursive digital filters with general coefficient support regions like a nonsymmetric half-plane (NSHP) support region. 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. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive digital lattice filter.I. I NTRODUCTIONThe design and implementation of one-dimensional (1-D) lattice filters have been reported in the literature [1-3]. I-D lattice filter structure exhibits the attractive advantages of low pass-band sensitivity and robustness to quantization error. The corresponding all-pole and all-pass lattice filters can be directly obtained from the I-D all-zero lattice structure. Additionally, I-D digital lattice filter structure requires lower computational cost than I-D direct form digital filter with similar design specifications. The minimal realization of a 2-D system presented by [4] has been widely concerned because it results in the least hardware requirement and less computational complexity. The minimal delay realization for a 2-D lattice structure has been presented in [5]. The cascaded 2-D digital lattice filter has the minimal number of delay elements 2n when n basic lattice sections are employed. The resulting 2-D digital lattice filter exhibits all-pass characteristics with a quarter-plane (Q P ) support region for its filter coefficients.In this paper, we consider the extension of 2-D lattice filters with more general support regions. By using the matrix representations of the basic lattice sections, we can directly derive the transfer functions of the proposed 2-D digital lattice filters including 2-D all-zero, 2-D all-pole, and 2-D all-pass filters. The proposed 2-D digital all-pass lattice filter has the coefficient support region with a nonsymmetric half plane.

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

“…Notice in particular that, for the ladder network v M+N =1 and 𝑣 𝑖 = 0, i=0, 1, .M+N-1, we find the proposed structure in [11].…”

“…For 𝑣 2 = 1 and 𝑣 1 = 𝑣 0 = 0, the above transfer function (10) takes the form: It is obvious that the above transfer function ( 13) can provide filters having all-pass and all-pole characteristics as in [11].…”

“…This paper aims to propose a new lattice-ladder structure of 2-D digital filter, composed of a delay unit z 1 −1 and a basic lattice section z 1 z 2 −1 other than the one proposed in [7][8][9], which are two delay units z 1 −1 and z 2 −1 are used. Furthermore, we have considered the proposed lattice structure by using a state-space 2-D Givone-Roesser's form description presented in [9] and the implementations recommended by the authors in [10][11][12][13][14]. Using a matrix representation of the basic lattice sections and we derived transfer functions of the proposed 2-D digital ladder-lattice filters.…”