More About Filters

  • Mads G. Christensen


By now, the reader is familiar with the concept of filters and has a basic understanding of what they are and what they do. We have seen that digital filters come in the form of difference equations involving delayed versions of the input and output signals that are multiplied by so-called filter coefficients and added up. In this chapter, we will go more into details about such filters. In particular, we will introduce the z-transform and discuss its properties, and we will use it as a tool to represent filters as rational function. By doing this, we can think of filters as polynomials and we can understand and analyze the behavior of filters this way. We will then explore the properties of filters, more specifically their linearity. Finally, we will present some basic filter types that are often encountered in practice.


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    S.J. Orfanidis, Introduction to Signal Processing (Prentice-Hall International, Englewood Cliffs, 1996)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mads G. Christensen
    • 1
  1. 1.Aalborg UniversityAalborgDenmark

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