A frequency-domain approach to frequency-weighted balanced realization

Jeffrey Harrison

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    The Ho-Kalman/Kung algorithm for balanced realization by singular-value decomposition of the Hankel operator has a natural frequency-domain equivalent. The controllability operator and observability operator are represented by intermediate transfer functions, called the gain to states and noise gain respectively. The product of these, the Hankel operator, can be expressed in terms of the input-output transfer function using an identity which the author refers to as the dynamic-range limitation. This frequency-domain theory extends naturally to the frequency-weighted case, and further to non-integrator-based linear fractional systems. It also provides additional design insight into the filter dynamic-range problem.
    Original languageEnglish
    Pages (from-to)655-662
    Number of pages8
    JournalIEEE Transactions on Circuits and Systems Part 1: Regular Papers
    Issue number5
    Publication statusPublished - 2003


    • Frequency domain
    • Frequency-weighted balanced realization
    • Hankel operator
    • Ho-Kalman realization
    • Laplace transformation
    • Singular-value decomposition (SVD)


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