The spectral envelope, a frequency based technique for analyzing categorical time series, is applied to amino acid sequences to examine their periodicity. The periodic signatures of such sequences is related to the secondary structure of the folding patterns in the gene. For a pair of sequences, we define a spectral envelope covariance which emphasizes the common periodicities in the two sequences. This is used to give a similarity measure for the two sequences which can then be used in a neighbour joining algorithm to construct a phylogeny. We apply the spectral methods to myoglobin sequences from primates and cetaceans. The spectral envelope reflects the structure of this protein and the tree constructed using spectral methods shows strong agreement with published trees.The spectral envelope can be used to explore similarities between and within different protein families. Since we do not require aligned sequences, the spectral methods can be used to create phylogenies across different protein families. We apply the method to 11 protein families from PANDIT obtaining a tree where the families are separated and the relationship among the families is given.
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