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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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A bound on null functions for digital imaging systems with positivity constraints.

E Clarkson, H Barrett

    Optics Letters
    |June 1, 1997
    PubMed
    Summary

    This study establishes an upper limit for the L(1) norm difference between two nonnegative object functions in digital imaging systems that produce identical data. This bound is attainable under specific system conditions and for any nonnegative object.

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    Area of Science:

    • Digital imaging
    • Image processing
    • Mathematical analysis

    Background:

    • Nonnegative object functions are fundamental in digital imaging.
    • Understanding the difference between object functions is crucial for system analysis.
    • Previous research has explored various norms for function differences.

    Purpose of the Study:

    • To determine the existence and nature of bounds for the L(1) and L(2) norms of the difference between two nonnegative object functions.
    • To investigate conditions under which these bounds are achieved in digital imaging systems.
    • To analyze the behavior of these norms for identical data output.

    Main Methods:

    • Theoretical analysis of function norms.
    • Investigation of digital imaging system properties.
    • Mathematical derivation of bounds for L(1) and L(2) norms.

    Main Results:

    • An upper bound exists for the L(1) norm of the difference between two nonnegative object functions producing the same digital image data.
    • This L(1) norm bound is achievable for specific digital imaging systems and any nonnegative object.
    • No upper bound was found for the L(2) norm of the difference under the same conditions.

    Conclusions:

    • The L(1) norm provides a bounded measure for differences in object functions under specific digital imaging constraints.
    • The L(2) norm is unbounded, indicating greater potential variability in function differences.
    • These findings have implications for understanding information limits and system performance in digital imaging.