Abstract
A linear system or filter is a linear, homogeneous function of time which transforms an input signal (un)n ∈ ℤ to an output signal (yn)n ∈ ℤ thus it may be represented by the convolution
(6.1.1) where S ≔ (sk)k ∈ ℤ is the impulse response of the system. To avoid convergence problems, we shall assume in this paragraph that the entries (un) are almost always zero, which means that they are zero except for a finite number of instants n.
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© 1990 Springer-Verlag Berlin Heidelberg
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Benveniste, A., Métivier, M., Priouret, P. (1990). Appendices to Part I. In: Adaptive Algorithms and Stochastic Approximations. Applications of Mathematics, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75894-2_7
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DOI: https://doi.org/10.1007/978-3-642-75894-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-75896-6
Online ISBN: 978-3-642-75894-2
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