Geodesic
Synthesis of the parameters of multi-dimensional multi-rate systems. Multidimensional fractional delay filters
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 219-238

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The problem of multi-dimensional multi-rate systems design by application of a lifting technique is considered. In order to solve it, it is proposed to apply the design method of multidimensional digital filters with a fractional delay. A symmetric structure is given for $\tau=(1/2,1/2)$, as well as a new structure based on application of the multidimensional Taylor series. The impulse and the frequency responses are given for the filters with a fractional space delay, their $L_2$ norm being found. 
@article{SJVM_2008_11_2_a7,
     author = {M. K. Tchobanou},
     title = {Synthesis of the parameters of multi-dimensional multi-rate systems. {Multidimensional} fractional delay filters},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {219--238},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a7/}
}
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M. K. Tchobanou. Synthesis of the parameters of multi-dimensional multi-rate systems. Multidimensional fractional delay filters. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 219-238. http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a7/