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Multivariate MIMO FIR inverses.

Ravikiran Rajagopal1, Lee C Potter

  • 1Dept. of Electr. Eng., Ohio State Univ., Columbus, OH 43210, USA. ravi@ee.eng.ohio-state.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 2, 2008
PubMed
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This study addresses computing exact finite impulse response (FIR) inverses for MIMO FIR systems. It provides conditions for invertibility and computes bounds on inverse filter orders for random and structured systems.

Area of Science:

  • Digital Signal Processing
  • Control Systems Engineering
  • Information Theory

Background:

  • Multivariate Multiple-Input Multiple-Output (MIMO) systems are crucial in modern signal processing.
  • Finite Impulse Response (FIR) filters are widely used due to their linear phase properties.
  • The invertibility of MIMO FIR systems is essential for various applications, including equalization and system identification.

Purpose of the Study:

  • To establish necessary and sufficient conditions for the exact invertibility of multivariate MIMO FIR systems.
  • To develop computational techniques for determining FIR inverses.
  • To analyze the invertibility of structured random MIMO FIR systems and bound the orders of their inverses.

Main Methods:

  • Derivation of theoretical conditions for system invertibility.

Related Experiment Videos

  • Development of algorithms for computing FIR inverse filters.
  • Definition and analysis of random and structured system models.
  • Computation of bounds on the orders of inverse filters.

    • Main Results:

    • Necessary and sufficient conditions for the invertibility of MIMO FIR systems are presented.
    • Techniques for computing exact FIR inverses are provided.
    • Conditions for the almost sure invertibility of structured random systems are derived.
    • Bounds on the orders of the computed inverse filters are established.

    Conclusions:

    • The study provides a comprehensive framework for understanding and computing FIR inverses in MIMO systems.
    • The derived conditions and methods are applicable to both theoretical analysis and practical implementation.
    • The findings contribute to the efficient design and analysis of complex signal processing systems.