Applications to Analog Filters Governed by a Differential Equation

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


The tools we have just developed (convolution and the Fourier transform for functions) are going to be used to study analog filters that are governed by a linear differential equation with constant coefficients,
$$\sum\limits_{k = 0}^q {{b_k}} {g^{(k)}} = \sum\limits_{j = 0}^p {{a_j}} {f^{(j)}},{a_p} \cdot {b_q} \ne 0,$$
where f is the input and g = A(f) is the output. Other conditions must be given to eliminate ambiguity among the possible solutions of (24.1).


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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