Synthesis of the parameters of multi-dimensional multi-rate systems. Multidimensional fractional delay filters

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.