Publication: Automatic Differentiation of Computer Programs in the Time and Frequency Domain
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Automatic Differentiation of Computer Programs in the Time and Frequency Domain

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Author(s)
H. M. Bücker , D. Walther

Published in
Proceedings of the 2017 European Conference on Electrical Engineering and Computer Science EECS, Bern, Switzerland, November 17--19, 2017

Year
2017

Publisher
IEEE Computer Society

Abstract
Automatic differentiation of computer programs has been successfully used in a wide variety of application areas. However, in this set of techniques, the differentiation is not carried out on the level of an abstract mathematical representation of some function, but on the level of an actual implementation of this mathematical representation. We consider the resulting subtle differences when automatic differentiation is used to transform functions from the area of digital signal processing. To this end, we apply the software tool ADiMat, implementing automatic differentiation for programs written in Matlab, to an implementation of a simple sinusoidal function in both, the time and the frequency domain. This comparison illustrates that the mechanical process of applying automatic differentiation is currently not capable of recognizing and exploiting the known mathematical connection between derivatives in the time and in the frequency domain.

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BibTeX
@INPROCEEDINGS{
         Bucker2017ADo,
       author = "H. M. B{\"u}cker and D. Walther",
       title = "Automatic Differentiation of Computer Programs in the Time and Frequency Domain",
       booktitle = "Proceedings of the 2017 European Conference on Electrical Engineering and Computer
         Science EECS, Bern, Switzerland, November 17--19, 2017",
       pages = "335--340",
       url = "https://doi.org/10.1109/EECS.2017.69",
       doi = "10.1109/EECS.2017.69",
       year = "2017",
       address = "Los Alamitos, CA, USA",
       publisher = "IEEE Computer Society",
       abstract = "Automatic differentiation of computer programs has been successfully used in a wide
         variety of application areas. However, in this set of techniques, the differentiation is not carried
         out on the level of an abstract mathematical representation of some function, but on the level of an
         actual implementation of this mathematical representation. We consider the resulting subtle
         differences when automatic differentiation is used to transform functions from the area of digital
         signal processing. To this end, we apply the software tool ADiMat, implementing automatic
         differentiation for programs written in Matlab, to an implementation of a simple sinusoidal function
         in both, the time and the frequency domain. This comparison illustrates that the mechanical process
         of applying automatic differentiation is currently not capable of recognizing and exploiting the
         known mathematical connection between derivatives in the time and in the frequency domain.",
       ad_tools = "ADiMat",
       ad_theotech = "Teaching"
}


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