In this talk, we explore sequences and their autocorrelation functions. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform.\u00a0 Resolving the lack of phase information is called the phase problem.\u00a0 We say that two sequences are equicorrelational to mean that they have the same aperiodic autocorrelation function.\u00a0 We investigate the necessary and sufficient conditions for two sequences to be equicorrelational, where
\nwe take into consideration the alphabet from which their terms are drawn.\u00a0 There are trivial forms of equicorrelationality arising from modifications that predictably preserve the autocorrelation, for example, negating the sequence or writing the sequence in reverse order and then complex conjugating every term.\u00a0 By an exhaustive search of binary sequences up to length $44$, we find that nontrivial equicorrelationality among binary sequences does occur, but is rare.\u00a0 We say that a positive integer $n$ is {\\it unequivocal} to mean that there is no pair of nontrivially equicorrelational binary sequences of length $n$; otherwise $n$ is {\\it equivocal}.\u00a0 For integers $n \\leq 44$, we found that the unequivocal ones are $1$–$8$, $10$, $11$, $13$, $14$, $19$, $22$, $23$, $26$, $29$, $37$, and $38$.\u00a0 We prove that any multiple of a equivocal number is also equivocal, and pose open questions as to whether there are finitely or infinitely many unequivocal numbers and whether the probability of nontrivial equicorrelationality occurring tends to zero as the sequence length tends to infinity.\u00a0 (This is joint work with Adeebur Rahman and Michael J Ward.)<\/p>\n","protected":false},"excerpt":{"rendered":"
In this talk, we explore sequences and their autocorrelation functions. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform.\u00a0 Resolving the lack […]<\/p>\n","protected":false},"author":73,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":""},"tags":[],"tribe_events_cat":[13],"class_list":["post-3487","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"\n