{"id":433,"date":"2020-06-19T23:07:29","date_gmt":"2020-06-19T21:07:29","guid":{"rendered":"https:\/\/www.wolter.tech\/?p=433"},"modified":"2021-07-30T15:48:38","modified_gmt":"2021-07-30T13:48:38","slug":"jaxlets-fast-wavelet-transformations-in-jax","status":"publish","type":"post","link":"https:\/\/www.wolter.tech\/?p=433","title":{"rendered":"Jaxlets &#8211; Fast Wavelet Transformations in JAX"},"content":{"rendered":"\n<p>The fast wavelet transform is an important signal processing algorithm. Jet a differentiable implementation in <a href=\"https:\/\/github.com\/google\/jax\" target=\"_blank\" rel=\"noreferrer noopener\">JAX<\/a> has been missing so far, I have therefore opened <a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/v0lta\/jaxlets\" target=\"_blank\">my implementation<\/a> . It supports the one and two dimensional analysis and synthesis transforms. As well as an implementation of the forward wavelet packet transform. The plot below shows an analysis of a linear chirp signal using a Daubechies wavelet.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"798\" src=\"https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2020\/06\/wavelet_packet_analysis-1024x798.png\" alt=\"\" class=\"wp-image-434\" srcset=\"https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2020\/06\/wavelet_packet_analysis-1024x798.png 1024w, https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2020\/06\/wavelet_packet_analysis-300x234.png 300w, https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2020\/06\/wavelet_packet_analysis-768x598.png 768w, https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2020\/06\/wavelet_packet_analysis-1200x935.png 1200w, https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2020\/06\/wavelet_packet_analysis.png 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Wavelet analysis of a linear chirp signal.<\/figcaption><\/figure>\n\n\n\n<p>As the chirps&#8217; frequency increases we see that the wavelet coefficients rise as well.<\/p>\n\n\n\n<p>Source code is available at<a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/v0lta\/jaxlets\" target=\"_blank\"> https:\/\/github.com\/v0lta\/jaxlets<\/a> .<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The fast wavelet transform is an important signal processing algorithm. Jet a differentiable implementation in JAX has been missing so far, I have therefore opened my implementation . It supports the one and two dimensional analysis and synthesis transforms. As well as an implementation of the forward wavelet packet transform. The plot below shows an &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.wolter.tech\/?p=433\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Jaxlets &#8211; Fast Wavelet Transformations in JAX&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[25,28],"class_list":["post-433","post","type-post","status-publish","format-standard","hentry","category-all","tag-frequency-domain","tag-wavelets","entry"],"_links":{"self":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts\/433","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=433"}],"version-history":[{"count":4,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts\/433\/revisions"}],"predecessor-version":[{"id":438,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts\/433\/revisions\/438"}],"wp:attachment":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}