Sampling pattern conversion with 2-D FIR filters

The problem of conversion between different periodic sampling structures is of importance in a number of applications related to multidimensional signal processing. For instance in areas of image processing, as multiresolution representations or high definition television, one has to modify sampling structures. For these types of processing finite impulse response (FIR) digital filters offer two main advantages, firstly a strictly linear phase, or a zero-phase, characteristic can be easily obtained, secondly they avoid the stability problem inherent to infinite impulse response (IIR) digital filters. In this paper, the design problem is stated for two-dimensional (2-D FIR) digital filters in the context of a transformation, defined by two integer parameters, which allows the conversion, in both directions, from an orthogonal to a quincunx sampling structure, which will be called (L,K) structure. The filter coefficients are obtained after a minimisation of the maximum error in the frequency domain where some constraints, depending on the parameters L and K, are added. Finally, a test picture is used to illustrate two conversion schemes