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Building IIR and FIR filters for signal recovery

Developed for: OOO “GeoPhysTechnika”, Saratov, Russia

Purpose: restoration of the signal distorted during transmission to its initial condition with available physical line indicators

The given development is dedicated to building IIR and FIR filters that allow recovering the initial signal from the received one based on frequency and phase response of the channel.
It is the Levy method that is used to build the filters. It enables generation of an analog filter minimizing an external environment error. A signal is restored with the use of an inverse IIR filter produced from the previously calculated analog one. Direct methods of inverse filters generation yielded an unstable result, and therefore we used the reflection of roots leading to destabilization to stabilize IIR filter; the given method does not alter the frequency response filter but makes it stable.


Client: OOO “GeoPhysTechnika” , Saratov, Russia
Area of use: geophysical researches, signal processing
Type (platform): .NET-classes library
Technologies and algorithms in use: .NET, C#, IIR-filter recovery using frequency response/phase response (Levy method), polynomial roots-finding procedure, eigenproblems
More information:


  1. Cuthbert T. R. Circuit design using personal computers. — John Wiley & Sons. — 1983
  2. Mitra S. K. Digital Signal Processing: A Computer Base Approach (2nd Edition). — McGraw-Hill. — 2001
  3. Clinton J. Lectures on Geophysical Data Processing. — ETH Zürich Department of Geophysics. — 2007. — http://www.seismo2009.ethz.ch/staff/jclinton/GDP07/lectures/6.pdf
  4. Evans B. L. Stabilization and Stability Testing of Multidimensional Recursive Digital Filters. — http://www.ece.utexas.edu/bevans/courses/ee381k/lectures/15_Stability/lecture15
  5. Rational substitution. — dsplib.ru. — http://www.dsplib.ru/content/subst/subst.html
  6. Williams P. M. Solving Polynomial equations using linear algebra. — John Hopkins Apl Technical Digest. — V 28. — N. 4. — 2010. — http://www.jhuapl.edu/techdigest/TD/td2804/Williams.pdf

Other materials:

  • Author’s review on IIR-filters reconstruction and inversion 

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