A bidimensional model of line-shuffling

TLDR: Owing to the time dependence, the line-shuffling is a three-dimensional operation; the paper develops a bidimensional approximation where the operation is confined to a fixed constellation.

Abstract: This paper deals with a theoretical formulation of line-shuffling, which is a standard technique proposed for compatible HDTV systems to halve the number of lines, e.g. from a 1250/2:1/50 format to a 625/2:1/50 format. An HD-MAC system is taken as reference where, starting from the 1250/2:1/50 format, the subsampling reduces the number of pixels by four. The resulting pixel constellation has a quincunx structure for each field with a periodicity of four fields. Finally, pixels of odd columns are vertically shifted to halve the number of lines. Owing to the time dependence, the line-shuffling is a three-dimensional operation; the paper develops a bidimensional approximation where the operation is confined to a fixed constellation. An equivalent scheme for the shuffling operation is derived, consisting of two vertical filters and one horizontal modulator, which is useful for shuffling frequency domain analysis. A similar model is derived for the deshuffling operation at the receiver. As an example of application of the theory scheme, the spectral analysis of the line-shuffling error in MAC compatible systems and its application to real test images are carried out.