Filters, Differential Equations, and Distributions

  • Claude Gasquet
  • Patrick Witomski
Part of the Texts in Applied Mathematics book series (TAM, volume 30)


Filters for functions have been studied in Lessons 1, 2, 24, and 25. We are going to recast and complete this analysis in the light of what we now know about distributions. We will see that the basic tools developed so far, namely, convolution and the Fourier transform, play an essential role in the study of generalized filters, in the same way they did in the study of filters for functions.


Impulse Response Imaginary Axis Linear Differential Equation Inverse Fourier Transform Step Response 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Claude Gasquet
    • 1
  • Patrick Witomski
    • 2
  1. 1.Université Joseph Fourier (Grenoble I)France
  2. 2.Laboratoire LMCIMAGTour IRMAGrenoble, Cedex 09France

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