Showing papers by "John Bechhoefer published in 2011"
TL;DR: In this article, Bode derived a similar relation between the magnitude (response gain) and the phase of a linear response function, which is an inequality between the Kramers-Kronig relations between real and imaginary parts of a response function.
Abstract: The implications of causality are captured by the Kramers–Kronig relations between the real and imaginary parts of a linear response function. In 1937, Bode derived a similar relation between the magnitude (response gain) and the phase. Although the Kramers–Kronig relations are an equality, the Bode’s relation is effectively an inequality. This difference is explained using elementary examples and is traced back to delays in the flow of information within the system formed by the physical object and the measurement apparatus.
64 citations
TL;DR: In this paper, the Kramers-Kronig relation between the real and imaginary parts of a linear response function is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.
Abstract: The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.
63 citations
Journal Article•
2 citations