Open AccessResolution limits of analyzers and oscillatory systems
Author(s) -
Edith L. R. Corliss
Publication year - 1963
Publication title -
journal of research of the national bureau of standards. section a. physics and chemistry
Language(s) - English
Resource type - Journals
eISSN - 2376-5704
pISSN - 0022-4332
DOI - 10.6028/jres.067a.048
Subject(s) - signal (programming language) , computation , resolution (logic) , energy (signal processing) , limit (mathematics) , noise (video) , observable , transient (computer programming) , state (computer science) , product (mathematics) , physics , computer science , mathematical analysis , control theory (sociology) , mathematics , algorithm , quantum mechanics , geometry , control (management) , artificial intelligence , image (mathematics) , programming language , operating system
This paper considers the resolution limits of those analyzers and oscillatory systems whose performance may be represented by a second-order differential equation. The "signal uncertainty" product Δ f ·Δ t is shown to be controlled by the ability of a system to indicate changes in energy content. The discussion refers the functioning of the system to a signal space whose coordinates are energy, frequency, and time. In this signal space, the product of the resolution limits, U = (Δ E / E 0 ) (Δ f / f 0 ) (Δ t / T 0 ) is the volume of a region within which no change of state in the system may be observed. Whereas the area element Δ f ·Δ t is freely deformable, no operations upon either Δ f or Δ t can further the reduction of the energy resolution limit. Thus U is irreducibly fixed by the limiting value of Δ E / E 0 . By considering the effects of noise upon Δ E / E 0 , and thus upon U , the paper demonstrates the rise of statistical features as signal-to-noise ratios decrease. Functional relationships derived from Δ E / E 0 and U are tabulated. These equations facilitate computation of the limits of observable changes of state in a system, and they provide guidance for the design of experiments to apportion the uncertainties of measurement of transient phenomena as advantageously as possible. A reference bibliography and appendices giving somewhat detailed proofs are included.