Bias errors in estimating frequency response and coherence functions from truncated transient signals

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    An estimation bias error is known to exist when spectra are estimated from truncated responses to transient signals. Expressions for this bias error are developed for zeroth, first and second order systems excited by a burst of white noise, with varying degrees of truncation of the response signal. A series of experiments confirms the theoretical results. For the zeroth order system the effects of truncation are identical for both the frequency response and coherence functions, with a bias error proportional to the fraction of output signal truncation. For first and second order systems, it is shown that the frequency response functions can be accurately estimated with 5% provided that one and three time constants, respectively, of the response signal are captured after the excitation has ceased. On the other hand, the bias of the output autospectrum and the coherence function are much more sensitive to the degree of truncation. Estimating these functions within 5% may require capturing seven or more time constants after the excitation has ceased. Upper bound error limits are developed from the bias functions to help establish data capture requirements when analyzing real systems under varying degrees of signal truncation. It is shown that transient excitation requires significantly shorter capture time per record than continuous excitation to provide the same degree of estimation accuracy.

    Original languageEnglish (US)
    Pages (from-to)1-16
    Number of pages16
    JournalJournal of Sound and Vibration
    Volume145
    Issue number1
    DOIs
    StatePublished - Feb 22 1991

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    frequency response
    Frequency response
    estimating
    approximation
    time constant
    excitation
    output
    White noise
    white noise
    bursts
    Data acquisition
    requirements
    Experiments

    All Science Journal Classification (ASJC) codes

    • Engineering(all)
    • Mechanical Engineering

    Cite this

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    title = "Bias errors in estimating frequency response and coherence functions from truncated transient signals",
    abstract = "An estimation bias error is known to exist when spectra are estimated from truncated responses to transient signals. Expressions for this bias error are developed for zeroth, first and second order systems excited by a burst of white noise, with varying degrees of truncation of the response signal. A series of experiments confirms the theoretical results. For the zeroth order system the effects of truncation are identical for both the frequency response and coherence functions, with a bias error proportional to the fraction of output signal truncation. For first and second order systems, it is shown that the frequency response functions can be accurately estimated with 5{\%} provided that one and three time constants, respectively, of the response signal are captured after the excitation has ceased. On the other hand, the bias of the output autospectrum and the coherence function are much more sensitive to the degree of truncation. Estimating these functions within 5{\%} may require capturing seven or more time constants after the excitation has ceased. Upper bound error limits are developed from the bias functions to help establish data capture requirements when analyzing real systems under varying degrees of signal truncation. It is shown that transient excitation requires significantly shorter capture time per record than continuous excitation to provide the same degree of estimation accuracy.",
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    Bias errors in estimating frequency response and coherence functions from truncated transient signals. / Evensen, H. A.; Trethewey, Martin Wesley.

    In: Journal of Sound and Vibration, Vol. 145, No. 1, 22.02.1991, p. 1-16.

    Research output: Contribution to journalArticle

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    AB - An estimation bias error is known to exist when spectra are estimated from truncated responses to transient signals. Expressions for this bias error are developed for zeroth, first and second order systems excited by a burst of white noise, with varying degrees of truncation of the response signal. A series of experiments confirms the theoretical results. For the zeroth order system the effects of truncation are identical for both the frequency response and coherence functions, with a bias error proportional to the fraction of output signal truncation. For first and second order systems, it is shown that the frequency response functions can be accurately estimated with 5% provided that one and three time constants, respectively, of the response signal are captured after the excitation has ceased. On the other hand, the bias of the output autospectrum and the coherence function are much more sensitive to the degree of truncation. Estimating these functions within 5% may require capturing seven or more time constants after the excitation has ceased. Upper bound error limits are developed from the bias functions to help establish data capture requirements when analyzing real systems under varying degrees of signal truncation. It is shown that transient excitation requires significantly shorter capture time per record than continuous excitation to provide the same degree of estimation accuracy.

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