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)

Abstract

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,
$$\sum\limits_{k = 0}^q {{b_k}} {g^{(k)}} = \sum\limits_{j = 0}^p {{a_j}} {f^{(j)}},{a_p} \cdot {b_q} \ne 0,$$
(24.1)
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).

Keywords

Convolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations