tric Properties of 2 - D Sequences and Their uadrantally Symmetric Linear - Phase

Conventionally, the design of linear-phase 2-D FIR digital filters is concentrated on the class of quadrantally symmetric filters, such as circular filters, fan-type filters etc [l]. A 2-D sequence, which is symmetric in both directions, is required to realize such quadrantally symmetric filters. In this paper, we will start from the discussion of the symmetric properties of 2-D sequences to disclose their applications for designing quadrantally symmetric/antisymmetric linear-phase 2D FIR digital filters by the eigenfilter approach, which has been used successfully t o design linearphase 1-D filters [2][3] and 2-D quadrantally symmetric filters [4]. It is shown that there are sixteen types cases to be considered according t o the symmetry/antisymmztry of 2-D sequences in both directions and their filter lengths ( even or odd ). The corresponding types of amplitude responses are tabulated into a complete table if these 2-D sequences are used to realize 2-D FIR filters. Also, the definitions of quadrantal-plane, half-plane and full-plane filters are described.