An improved Hilbert Vibration Decomposition method for analysis of low frequency oscillations

Ramos, Juan; Reyes, J. I.; Barocio, E.

doi:10.1109/tdc-la.2014.6955216

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…Using

ω_{1} false(t false)

, the IA of the highest component in the decomposition, i.e.

A_{1} false(t false)

is determined using synchronous demodulation procedure [43]. Finally, the highest energy component is generated with

A_{1} false(t false)

and

ω_{1} false(t false)

, and a new signal is obtained by subtracting the highest component from the original signal and the process is repeated iteratively.…”

Section: Review Of Hvd Methodsmentioning

confidence: 99%

“…This is done using the analytical signal representation of a given real signal [43]. The analytical signal Z ( t ) of a real signal H ( t ) is a complex signal as given by [43]

Z false(t false) = H false(t false) + H_{normalH} false(t false) = A false(t false) {normale}^{i ϕ false(t false)}

where the real part corresponds to the original signal

H false(t false)

and the imaginary part

H_{normalH} false(t false)

is the Hilbert transform of

H false(t false)

.…”

Section: Review Of Hvd Methodsmentioning

confidence: 99%

“…This is done using the analytical signal representation of a given real signal [43]. The analytical signal Z ( t ) of a real signal H ( t ) is a complex signal as given by [43]

Z false(t false) = H false(t false) + H_{normalH} false(t false) = A false(t false) {normale}^{i ϕ false(t false)}

where the real part corresponds to the original signal

H false(t false)

and the imaginary part

H_{normalH} false(t false)

is the Hilbert transform of

H false(t false)

. From (1), the IA

A false(t false)

and instantaneous phase

ϕ false(t false)

are obtained as

A false(t false) = \sqrt{H {(t)}^{2} + H_{H} {(t)}^{2}}

ϕ false(t false) = \tan^{- 1} ()(, \frac{H_{normalH} false(t false)}{H false(t false)})

The IF

ω false(t false)

is the derivative of

ϕ false(t false)

in (3) expressed as

ω false(t false) = \frac{normald}{d t} ϕ (t) = H (t) {\dot{H}}_{H} (t) - \dot{H} (t

…”

Section: Review Of Hvd Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Pansharpening approach using Hilbert vibration decomposition

Saxena

Sharma

2017

IET image process

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In this study, a new approach for pansharpening of multispectral and panchromatic (PAN) images is proposed. The proposed technique is based on recently developed signal decomposition technique known as Hilbert vibration decomposition (HVD). In the proposed method, the histogram equalised PAN image is decomposed into many instantaneous amplitude (IA) and frequency components in the decreasing order of energy using the HVD. The IA of the first component (having highest energy) in the decomposition of the PAN image is used to generate the pansharpened image using appropriate pansharpening model. The tuning factor associated with the pansharpening model is optimised by single‐objective particle swarm optimization algorithm. This method is also extended for the hyperspectral images. Experimental results of the proposed technique are compared with existing pansharpening methods in terms of both visual perception and objective metrics. It is observed that the proposed pansharpening scheme has improved spectral and spatial qualities as compared with the existing schemes. The effects of aliasing and misregistration errors in the proposed method are also investigated and it is observed that the proposed method is robust against aliasing and misregistration errors as compared with other existing methods.

show abstract

“…Using

ω_{1} false(t false)

, the IA of the highest component in the decomposition, i.e.

A_{1} false(t false)

is determined using synchronous demodulation procedure [43]. Finally, the highest energy component is generated with

A_{1} false(t false)

and

ω_{1} false(t false)

, and a new signal is obtained by subtracting the highest component from the original signal and the process is repeated iteratively.…”

Section: Review Of Hvd Methodsmentioning

confidence: 99%

“…This is done using the analytical signal representation of a given real signal [43]. The analytical signal Z ( t ) of a real signal H ( t ) is a complex signal as given by [43]

Z false(t false) = H false(t false) + H_{normalH} false(t false) = A false(t false) {normale}^{i ϕ false(t false)}

where the real part corresponds to the original signal

H false(t false)

and the imaginary part

H_{normalH} false(t false)

is the Hilbert transform of

H false(t false)

.…”

Section: Review Of Hvd Methodsmentioning

confidence: 99%

“…This is done using the analytical signal representation of a given real signal [43]. The analytical signal Z ( t ) of a real signal H ( t ) is a complex signal as given by [43]