A Two-Stage Approach to the Establishment of State-Space Formulation of 2-D Frequency Transformation

Frequency Transformation for Linear State-Space Systems and Its Application to High-Performance Analog/Digital Filters

“…One of them is the state-space formulation of 2-D frequency transformation [36], which presents an explicit state-space-based frequency transformation for 2-D digital filters. Also, Yan et al [37,38] extended this work to Another interesting topic is the transformations based on "lossy" functions. In both the cases of analog frequency transformation and digital frequency transformation, the required transformation functions have the lossless property.…”

2-D zero-phase IIR notch filters design based on state-space representation of 2-D frequency transformation

“…However, it has been noted that the state-space representation has its particular advantages for the roundoff noise analysis and optimal design of the required filter. There are two ways to establish a state-space representation of the filter obtained by the frequency transformation, or simply the transformed filter: one is to find a state-space model realization from the transfer function of the transformed filter by using the approaches in, e.g., [12][13][14][15], and the other one is to get it by utilizing the state-space representation or formulation for the 2-D frequency transformation in either Roesser model or Fornasini-Marchesini second (FM II) model proposed by the authors recently in [16][17][18]. An attractive This work was partly supported by the National Natural Science Foundation of China (No.61104122) and the Fundamental Research Funds for the Central Universities (lzujbky-2014-51).…”

State-space formulation of 2-D frequency transformation base on Fornasini-Marchesini second model

“…It is just based on such a formulation, the invariance of the minimum attainable roundoff noise of digital filters under 1-D and 2-D frequency transformation is clarified by [4,5]. In recent years, the statespace formulation has been extended to the cases of both the 1-D and 2-D frequency transformation for 2-D digital filters by [6][7][8][9][10] based on Roesser state-space model [11]. However, to the best of authors' knowledge, state-space formulation of frequency transformation is not yet developed based on the Fornasini-Marchesini second (FM II) model [12] though a special case of this problem has been stated as a possible extension work of [6,7].…”

“…where 1 and 2 denote unit backward-shift (delay) operators here (see, e.g., [9,10,15]). Let ( 1 , 2 ) be a 2-D prototype digital filter which has an FM II state-space representation ( 1 , 2 , 1 , 2 , , ) and satisfies (2).…”

“…Let ( 1 , 2 ) be a 2-D prototype digital filter which has an FM II state-space representation ( 1 , 2 , 1 , 2 , , ) and satisfies (2). Then a new 2-D digital filter ( 1 , 2 ) with a desired frequency characteristic can be obtained by the 2-D frequency transformation [2,9,10] (…”