{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T02:10:50Z","timestamp":1771467050493,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T00:00:00Z","timestamp":1693440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"S\u00e3o Paulo Research Foundation (FAPESP)","award":["#2017\/08120-6"],"award-info":[{"award-number":["#2017\/08120-6"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Nowadays, sensors with built-in sigma\u2013delta modulators (\u03a3\u0394Ms) are widely used in consumer, industrial, automotive, and medical applications, as they have become a cost-effective and convenient way to deliver data to digital processors. This is the case for micro-electro-mechanical system (MEMS), digital microphones that convert analog audio to a pulse-density modulated (PDM) bitstream. However, as the \u03a3\u0394Ms output a PDM signal, sensors require either built-in or external high-order decimation filters to demodulate the PDM signal to a baseband multi-bit pulse-code modulated (PCM) signal. Because of this extra circuit requirement, the implementation of sensor array algorithms, such as beamforming in embedded systems (where the processing resources are critical) or in very large-scale integration (VLSI) circuits (where the power and area are crucial) becomes especially expensive as a large number of parallel decimation filters are required. This article proposes a novel architecture for beamforming algorithm implementation that fuses delay and decimation operations based on maximally flat (MAXFLAT) filters to make array processing more affordable. As proof of concept, we present an implementation example of a delay-and-sum (DAS) beamformer at given spatial and frequency requirements using this novel approach. Under these specifications, the proposed architecture requires 52% lower storage resources and 19% lower computational resources than the most efficient state-of-the-art architecture.<\/jats:p>","DOI":"10.3390\/s23177577","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T11:45:51Z","timestamp":1693482351000},"page":"7577","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Sigma\u2013Delta Sensor Array Beamforming"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4150-9044","authenticated-orcid":false,"given":"Sammy Johnatan","family":"Carbajal Ipenza","sequence":"first","affiliation":[{"name":"NXP Semiconductors N.V., 5656 Eindhoven, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2246-4450","authenticated-orcid":false,"given":"Bruno Sanches","family":"Masiero","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Universidade Estadual de Campinas, Campinas 13083-852, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. 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Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets, Wiley."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/17\/7577\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:44:14Z","timestamp":1760129054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/17\/7577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,31]]},"references-count":14,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["s23177577"],"URL":"https:\/\/doi.org\/10.3390\/s23177577","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,31]]}}}