Binary Sequences and Redundancy

The computational-complexity approach and entropy using nominal frequencies lead to different measures to characterize patterns in finite binary sequences. These have been compared to a measure obtained on taking integral transforms of the sequences. The transforms considered in this paper are the Walsh and the discrete Legendre. Pattern characterization through integral transforms turns out to be intuitively satisfying. In particular, Walsh transform characterization appears natural for binary sequences as does the use of discrete Legendre transforms for more general (nonbinary) sequences.