{"_id":"11735","user_id":"40767","language":[{"iso":"eng"}],"date_created":"2019-07-12T05:27:15Z","main_file_link":[{"url":"https://groups.uni-paderborn.de/nt/pubs/2017/ArXiv_2017_BoeddekerHanebrinkHaeb_Article.pdf","open_access":"1"}],"date_updated":"2022-01-06T06:51:08Z","year":"2017","type":"report","abstract":[{"lang":"eng","text":"This report describes the computation of gradients by algorithmic differentiation for statistically optimum beamforming operations. Especially the derivation of complex-valued functions is a key component of this approach. Therefore the real-valued algorithmic differentiation is extended via the complex-valued chain rule. In addition to the basic mathematic operations the derivative of the eigenvalue problem with complex-valued eigenvectors is one of the key results of this report. The potential of this approach is shown with experimental results on the CHiME-3 challenge database. There, the beamforming task is used as a front-end for an ASR system. With the developed derivatives a joint optimization of a speech enhancement and speech recognition system w.r.t. the recognition optimization criterion is possible."}],"department":[{"_id":"54"}],"oa":"1","citation":{"short":"C. Boeddeker, P. Hanebrink, L. Drude, J. Heymann, R. Haeb-Umbach, On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming, 2017.","apa":"Boeddeker, C., Hanebrink, P., Drude, L., Heymann, J., &#38; Haeb-Umbach, R. (2017). <i>On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming</i>.","mla":"Boeddeker, Christoph, et al. <i>On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming</i>. 2017.","ama":"Boeddeker C, Hanebrink P, Drude L, Heymann J, Haeb-Umbach R. <i>On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming</i>.; 2017.","bibtex":"@book{Boeddeker_Hanebrink_Drude_Heymann_Haeb-Umbach_2017, title={On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming}, author={Boeddeker, Christoph and Hanebrink, Patrick and Drude, Lukas and Heymann, Jahn and Haeb-Umbach, Reinhold}, year={2017} }","ieee":"C. Boeddeker, P. Hanebrink, L. Drude, J. Heymann, and R. Haeb-Umbach, <i>On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming</i>. 2017.","chicago":"Boeddeker, Christoph, Patrick Hanebrink, Lukas Drude, Jahn Heymann, and Reinhold Haeb-Umbach. <i>On the Computation of Complex-Valued Gradients with Application to Statistically Optimum Beamforming</i>, 2017."},"status":"public","author":[{"first_name":"Christoph","last_name":"Boeddeker","id":"40767","full_name":"Boeddeker, Christoph"},{"last_name":"Hanebrink","full_name":"Hanebrink, Patrick","first_name":"Patrick"},{"full_name":"Drude, Lukas","id":"11213","last_name":"Drude","first_name":"Lukas"},{"full_name":"Heymann, Jahn","id":"9168","last_name":"Heymann","first_name":"Jahn"},{"last_name":"Haeb-Umbach","id":"242","full_name":"Haeb-Umbach, Reinhold","first_name":"Reinhold"}],"title":"On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamforming"}