An Example of a Hilbert Transform

An inequality for the hilbert transform.

Discrete Fractional Hilbert Transform

The Hilbert transform plays an important role in the theory and practice of signal processing. A generalization of the Hilbert transform, the fractional Hilbert transform, was recently proposed, and it presents physical interpretation in the definition. In this paper, we develop the discrete fractional Hilbert transform, and apply the proposed discrete fractional Hilbert transform to the edge d...

Hilbert Transform and Applications

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 ...

Complex Hilbert Transform Filter

Hilbert transform is a basic tool in constructing analytical signals for a various applications such as amplitude modulation, envelope and instantaneous frequency analysis, quadrature decoding, shift-invariant multi-rate signal processing and Hilbert-Huang decomposition. This work introduces a complex Hilbert transform (CHT) filter, where the real and imaginary parts are a Hilbert transform pai...

The Hilbert Transform of a Measure

Let e be a homogeneous subset of R in the sense of Carleson. Let μ be a finite positive measure on R and Hμ(x) its Hilbert transform. We prove that if limt→∞ t|e ∩ {x | |Hμ(x)| > t}| = 0, then μs(e) = 0, where μs is the singular part of μ.