Frequency-Domain Adaptive Filtering in Hypercomplex Systems

  • Francesca Ortolani
  • Danilo ComminielloEmail author
  • Michele Scarpiniti
  • Aurelio Uncini
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 54)


In recent years, linear and nonlinear signal processing applications required the development of new multidimensional algorithms. Higher-dimensional algorithms include quaternion-valued filters. One of the drawbacks filter designers have to cope with is the increasing computational cost due to multidimensional processing. A strategy to reduce the computational complexity of long adaptive filters is to implement block algorithms and update the filter coefficients periodically. More efficient techniques embed frequency-domain processing in block algorithms with the use of the Fast Fourier Transform (FFT). Transform-domain adaptive filters in the quaternion field require quaternion-valued transforms. In this paper we also suggest a simple method to obtain a quaternionic DFT/FFT from a complex DFT/FFT. As an example, we propose the Overlap-Save Quaternion Frequency Domain algorithm.


Adaptive filters Quaternion Hypercomplex Frequency domain Overlap-Save 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Francesca Ortolani
    • 1
  • Danilo Comminiello
    • 1
    Email author
  • Michele Scarpiniti
    • 1
  • Aurelio Uncini
    • 1
  1. 1.Department of Information Engineering Electronics and Telecommunications (DIET)“La Sapienza” University of RomeRomeItaly

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