Complementary sets of sequences: a filter bank approach

The relationship between orthogonal finite impulse response filter bank structures, and orthonormal bases of compactly supported wavelets is a well-developed theory. In this paper, we identify further relationships between the design and construction of complementary pairs of sequences, filter banks satisfying the condition for perfect reconstruction and the property of losslessness. We then develop a construction method which enables a new class of complementary sequences to be formulated. Finally, we generalise these new sequences to form complementary sets, thus increasing the number of possible application areas for this class of sequences.