{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/decomposition-of-higher-order-spectra-for","title":"Decomposition of Higher-Order Spectra for Blind Multiple-Input Deconvolution, Pattern Identification and Separation","arxiv_id":"1901.11395","date":"2019-01-28","proceeding":null,"authors":["Christopher K. Kovach","Matthew A. Howard III"],"abstract":"Like the ordinary power spectrum, higher-order spectra (HOS) describe signal\nproperties that are invariant under translations in time. Unlike the power\nspectrum, HOS retain phase information from which details of the signal\nwaveform can be recovered. Here we consider the problem of identifying multiple\nunknown transient waveforms which recur within an ensemble of records at\nmutually random delays. We develop a new technique for recovering filters from\nHOS whose performance in waveform detection approaches that of an optimal\nmatched filter, requiring no prior information about the waveforms. Unlike\nprevious techniques of signal identification through HOS, the method applies\nequally well to signals with deterministic and non-deterministic HOS. In the\nnon-deterministic case, it yields an additive decomposition, introducing a new\napproach to the separation of component processes within non-Gaussian signals\nhaving non-deterministic higher moments. We show a close relationship to\nminimum-entropy blind deconvolution (MED), which the present technique improves\nupon by avoiding the need for numerical optimization, while requiring only\nnumerically stable operations of time shift, element-wise multiplication and\naveraging, making it particularly suited for real-time applications. The\napplication of HOS decomposition to real-world signals is demonstrated with\nblind denoising, detection and classification of normal and abnormal heartbeats\nin electrocardiograms.","url_abs":"http://arxiv.org/abs/1901.11395v1","url_pdf":"http://arxiv.org/pdf/1901.11395v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"decomposition-of-higher-order-spectra-for","repo_url":"https://github.com/ckovach/HOSD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}