# Two-Dimensional IFIR Structures Using Generalized Factorable Filters

### Roberto Manduchi

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-93-785

October 1994

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/CSD-93-785.pdf

The extension of the idea of Interpolated FIR filters to the two-dimensional case is presented. Such systems allow for lower computational weight, in terms of number of elementary operations per input sample. In the 1-D case, the justification to such a performance advantage rests upon the relationship between filter order, transition bandwidth and minimax errors for equiripple linear-phase filters. Even though no similar relation is known for minimax optimal multidimensional filters, a qualitatively parallel behaviour is shared by a class of suboptimal filters recently developed by Chen and Vaidyanathan. Such filters are particularly suitable for the sampling structure conversion of video signals. In particular, they belong to the class of Generalized Factorable filters, for which an efficient implementation exists.

We examine in detail the design procedure of Generalized Factorable filters, and devise some properties that have not been described before in the literature. Then, we apply such filter in the 2-D IFIR scheme.

An interesting problem peculiar to the multidimensional case is the choice of the sublattice which represents the definition support of the first-stage filter. We present a strategy to choose (given the spectral support of the desired frequency response) the optimal sublattice, and to design the second-stage (interpolator) filter in order to achieve low overall computational complexity.

BibTeX citation:

@techreport{Manduchi:CSD-93-785, Author = {Manduchi, Roberto}, Title = {Two-Dimensional IFIR Structures Using Generalized Factorable Filters}, Institution = {EECS Department, University of California, Berkeley}, Year = {1994}, Month = {Oct}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/6323.html}, Number = {UCB/CSD-93-785}, Abstract = {The extension of the idea of Interpolated FIR filters to the two-dimensional case is presented. Such systems allow for lower computational weight, in terms of number of elementary operations per input sample. In the 1-D case, the justification to such a performance advantage rests upon the relationship between filter order, transition bandwidth and minimax errors for equiripple linear-phase filters. Even though no similar relation is known for minimax optimal multidimensional filters, a qualitatively parallel behaviour is shared by a class of suboptimal filters recently developed by Chen and Vaidyanathan. Such filters are particularly suitable for the sampling structure conversion of video signals. In particular, they belong to the class of Generalized Factorable filters, for which an efficient implementation exists. <p>We examine in detail the design procedure of Generalized Factorable filters, and devise some properties that have not been described before in the literature. Then, we apply such filter in the 2-D IFIR scheme. <p>An interesting problem peculiar to the multidimensional case is the choice of the sublattice which represents the definition support of the first-stage filter. We present a strategy to choose (given the spectral support of the desired frequency response) the optimal sublattice, and to design the second-stage (interpolator) filter in order to achieve low overall computational complexity.} }

EndNote citation:

%0 Report %A Manduchi, Roberto %T Two-Dimensional IFIR Structures Using Generalized Factorable Filters %I EECS Department, University of California, Berkeley %D 1994 %@ UCB/CSD-93-785 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/6323.html %F Manduchi:CSD-93-785