1/fα signal synthesis with precision control

  • Authors:

  • Michel Guglielmi

  • Affiliations:

  • Institute of Communications and Cybernetics of Nantes, IRRCyN, Ecole Centrale de Nantes, Université de Nantes, Ecole des Mines de Nantes, Nantes Cedex, France

  • Venue:
  • Signal Processing - Fractional calculus applications in signals and systems
  • Year:
  • 2006

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Abstract

This paper deals with the synthesis of signals which have a power spectral density (PSD) equal to 1/fα. It is well known that a linear infinite line of RC cells can generate such signals. For a finite number of cells, the spectrum is not perfect. Here, we propose a novel method which enables the control of the precision within a frequency bandwidth. The algorithm proposed in the paper is based on a geometric approach. A cluster of elementary cells is designed. Each cell is defined by two parameters (the two cut off frequencies) which are easily computed through recursive formulae. The digital conversion requires the analog to digital open loop design method. Finally, sample paths are generated and their PSD compared to 1/fα