Fig. 4

Results of (1)–(6) for A the DNA sequence with the accession number FJ807392.1 and B a totally random synthetic DNA sequence. The identity matrix is used as the similarity matrix for computing these functions. In each figure: a The symmetry function from (3). b The ambiguity function from (6) showing the stationarity and spectral color of the sequence. c The instantaneous auto-correlation using (1) representing the similarity of the sequence with its time lag nucleotides. d The auto-correlation function of the sequence using (2), with a maximum peak at τ=0. e The WV transform using (5), indicating the time-frequency properties of the sequence. f The spectrum using (4), which shows the global spectral properties for the sequence