Limit cycle oscillations in first-order two-dimensional digital filters

In first-order two-dimensional digital filters, limit cycles can occur as a result of rounding off after multiplication. Such limit cycles are discussed for the case of fixed point arithmetic. The period and bounds for the amplitude of the limit cycles existing in the rows, columns, and diagonals are obtained. It is proved here that the bound obtained is the tightest possible bound for the amplitude of the limit cycles. Several (sufficient or necessary) conditions for the existence of the limit cycles in the rows, columns, and diagonals are also given.