{"id":340649,"date":"2017-07-05T05:19:26","date_gmt":"2017-07-05T09:19:26","guid":{"rendered":"https:\/\/ntrs.nasa.gov\/search.jsp?R=20170005773"},"modified":"2017-07-05T05:19:26","modified_gmt":"2017-07-05T09:19:26","slug":"feature-detection-and-curve-fitting-using-fast-walsh-transforms-for-shock-tracking-applications","status":"publish","type":"post","link":"https:\/\/spaceweekly.com\/?p=340649","title":{"rendered":"Feature Detection and Curve Fitting Using Fast Walsh Transforms for Shock Tracking: Applications"},"content":{"rendered":"<p>Abstract: Walsh functions form an orthonormal basis set consisting of square waves. Square waves make the system well suited for detecting and representing functions with discontinuities. Given a uniform distribution of 2p cells on a one-dimensional element, it has been proven that the inner product of the Walsh Root function for group p with every polynomial of degree < or = (p - 1) across the element is identically zero. It has also been proven that the magnitude and location of a discontinuous jump,...\n<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Abstract: Walsh functions form an orthonormal basis set consisting of square waves. Square waves make the system well suited for detecting and representing functions with discontinuities. Given a uniform distribution of 2p cells on a one-dimensional element, it has been proven that the inner product of the Walsh Root function for group p with every polynomial of degree <\/p>\n","protected":false},"author":60,"featured_media":615444,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-340649","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/spaceweekly.com\/index.php?rest_route=\/wp\/v2\/posts\/340649","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/spaceweekly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/spaceweekly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/spaceweekly.com\/index.php?rest_route=\/wp\/v2\/users\/60"}],"replies":[{"embeddable":true,"href":"https:\/\/spaceweekly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=340649"}],"version-history":[{"count":1,"href":"https:\/\/spaceweekly.com\/index.php?rest_route=\/wp\/v2\/posts\/340649\/revisions"}],"predecessor-version":[{"id":340650,"href":"https:\/\/spaceweekly.com\/index.php?rest_route=\/wp\/v2\/posts\/340649\/revisions\/340650"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/spaceweekly.com\/index.php?rest_route=\/wp\/v2\/media\/615444"}],"wp:attachment":[{"href":"https:\/\/spaceweekly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=340649"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/spaceweekly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=340649"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/spaceweekly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=340649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}