Lattice valued vector systems have taken an important role in packing, coding, cryptography, and signal processing problems.\u00a0 In compressed sensing, improvements in sparse recovery methods can be reached with an additional\u00a0 assumption that the signal of\u00a0 interest is lattice\u00a0 valued, as demonstrated by A.\u00a0 Flinth\u00a0 and G. Kutyniok. Equiangular\u00a0 tight\u00a0 frames are\u00a0 particular systems\u00a0 of unit\u00a0 vectors\u00a0 with minimal\u00a0 coherence,\u00a0 a measure of how well distributed the vectors are, and have provable guarantees for recovery of sparse vectors in standard methods.\u00a0 The determination whether real equiangular tight frames have integer span on a lattice has been given a characterization within two papers by A. Bottcher, L. Fukshansky, one with S. R. Garcia, H. Maharaj and D. Needell.\u00a0 Here the corresponding question is considered for the complex case and several families are demonstrated to have either integer span on a lattice or not.\u00a0 In addition, it is demonstrated that a real Parseval tight frame can have integer span on a lattice if and only if the inner products appearing in the system are rational.\u00a0 (Collaboration with L. Fukshansky, D. Needell, and Y. Xin)<\/p>\n","protected":false},"excerpt":{"rendered":"
Lattice valued vector systems have taken an important role in packing, coding, cryptography, and signal processing problems.\u00a0 In compressed sensing, improvements in sparse recovery methods can be reached with an […]<\/p>\n","protected":false},"author":73,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":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":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[13],"class_list":["post-961","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"\n