Phase and the Hilbert transform
نویسندگان
چکیده
منابع مشابه
Hilbert Transform and Gain/Phase Error Bounds for Rational Functions
It is well known that a function analytic in the right half plane can be constructed from its real part alone, or (modulo an additive constant) from its imaginary part alone via the Hilbert transform. It is also known that a stable minimum phase transfer function can be reconstructed from its gain alone, or (modulo a multiplicative constant) from its phase alone, via the Bode gain/phase relatio...
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When x(t) is narrow-banded, |z(t)| can be regarded as a slow-varying envelope of x(t) while the phase derivative ∂t[tan −1(y/x)] is an instantaneous frequency. Thus, Hilbert transform can be interpreted as a way to represent a narrow-band signal in terms of amplitude and frequency modulation. The transform is therefore useful for diverse purposes such as latency analysis in neuro-physiological ...
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A phase resetting curve (PRC) measures the transient change in the phase of a neural oscillator subject to an external perturbation. The PRC encapsulates the dynamical response of a neural oscillator and, as a result, it is often used for predicting phase-locked modes in neural networks. While phase is a fundamental concept, it has multiple definitions that may lead to contradictory results. We...
متن کاملThe Number Theoretic Hilbert Transform
Abstract This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being zero and non-zero. Specific examples for 4point, 6-point, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cry...
متن کامل-boundedness of the Hilbert transform
The Hilbert transform is essentially the only singular operator in dimension 1. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on several theoretical and physical problems across a wide range of disciplines; this includes problems in Fourier convergence, complex analysis, potential theory, modulatio...
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ژورنال
عنوان ژورنال: The Leading Edge
سال: 2014
ISSN: 1070-485X,1938-3789
DOI: 10.1190/tle33101164.1