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Related Experiment Videos

Temporal impulse responses from flicker sensitivities: causality, linearity, and amplitude data do not determine

J D Victor1

  • 1Department of Neurology, Cornell University Medical College, New York, New York 10021.

Journal of the Optical Society of America. A, Optics and Image Science
|September 1, 1989
PubMed
Summary

A recent study challenges a method for determining impulse response from amplitude spectra. The paper argues that assuming the logarithm of a transfer function is analytic and causal is an unjustified minimum phase assumption, leading to multiple possible phase spectra.

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Area of Science:

  • Optics
  • Signal Processing
  • System Identification

Background:

  • A prior publication proposed a method to determine impulse response using amplitude spectrum data.
  • This method relies on the assumption that the logarithm of an analytic and causal transfer function is also analytic and causal.

Purpose of the Study:

  • To critically evaluate the assumption of minimum phase in the context of determining impulse response from amplitude spectra.
  • To demonstrate the theoretical and practical limitations of this assumption.

Main Methods:

  • Analysis of the mathematical relationship between transfer functions, their logarithms, and causality.
  • Examination of the implications of the minimum phase assumption on phase spectrum determination.

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Main Results:

  • The assumption that the logarithm of an analytic and causal transfer function is also analytic and causal is not mathematically justified.
  • This unjustified assumption is equivalent to a minimum phase assumption, which may not hold true.
  • An amplitude spectrum alone is insufficient to uniquely determine a phase spectrum.

Conclusions:

  • The method for impulse response determination, as advanced in the cited paper, is fundamentally flawed due to an unjustified minimum phase assumption.
  • Without additional constraints or information, a given amplitude spectrum is consistent with numerous possible phase spectra.
  • This highlights the importance of considering phase information or making explicit, justifiable assumptions in system identification problems.