<i>Wavelet Basics</i>

Chan, C. T.; Bates, Bruce J.

doi:10.1121/1.414569

Cited by 7 publications

(3 citation statements)

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“…Wavelets [12,13] are mathematical functions that decompose the data into different frequency components and study each component with a resolution matched to its scale. This is a fast, linear, and invertible orthogonal transform with the basic idea of defining a time-scale representation of a signal by decomposing it onto a set of basic functions, called wavelets.…”

Section: Prameters Extraction Using a Discrete Wavelet Transformmentioning

confidence: 99%

Fire Detection in Video Using Genetic-Based Neural Networks

Truong

Kim

2011

2011 International Conference on Information Science and Applications

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In this paper, we propose an effective four-stage approach that detects fire automatically. The proposed algorithm is composed of four stages. In the first stage, an approximate median method is used to detect moving regions. In the second stage, a fuzzy c-means (FCM) algorithm based on the color of fire is used to select candidate fire regions from these moving regions. In the third stage, a discrete wavelet transform (DWT) is used to derive the approximated and detailed wavelet coefficients of subimage. In the final stage, a generic-based back-propagation neural network (BPNN) is utilized to distinguish between fire and non-fire. Experimental results indicate that the proposed method outperforms other fire detection algorithms, providing high reliability and low false alarm rate.

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Section: Prameters Extraction Using a Discrete Wavelet Transformmentioning

confidence: 99%

Fire Detection in Video Using Genetic-Based Neural Networks

Truong

Kim

2011

2011 International Conference on Information Science and Applications

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“…Every 1‐D signal f ∈ L 2 ( R ) can be represented using wavelet base functions as (Chan 1995): where and d m n are detailing coefficients, ψ m , n is the wavelet function generated from the original mother wavelet function ψ∈ L 2 (ℜ), λ m 0 is the scale space parameter, t m 0 is the translation space parameter, m is the scale or level of decomposition integer and n is the shifting or translation integer.…”

Section: Wavelet Transform Fundamentalsmentioning

confidence: 99%

A wavelet thresholding technique for local geoid and deflection of the vertical determination using a planar approximation

Habiby¹,

Sideris²

2007

Geophysical Journal International

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S U M M A R YA computational scheme using the wavelet transform is employed for local geoid determination, where wavelet multiresolution analysis (MRA) is introduced as an alternative approach to the well-established fast Fourier transform (FFT). The Stokes and Vening Meinesz integrals are approximated in finite MRA subspaces. The algorithm is built using an orthogonal wavelet base function. The characteristics of the base function and its effect on the final result are investigated. Hard and soft thresholding are tested in the compression of the kernel as well as global thresholding is compared to level-wise thresholding to optimize the compression level with an acceptable accuracy. Both global and level-wise thresholding are combined in order to achieve the maximum compression level, with acceptable geoid accuracy. The compression rate depends on the degree of singularity of the kernel. In the case of Stokes, a 94 per cent compression level is achieved with 1 cm (rms) accuracy in comparison to FFT and numerical integration approaches. Due to its stronger singularity, in the case of the Vening Meinesz kernel, 97 per cent compression rate is achieved with a 0.07 arc-second (rms) accuracy. The compression percentages achieved in this study are higher than those reported in pervious studies, which shows that this algorithm is very suitable for use in local geoid determination.

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“…The occurrence of GICs involves with the nonlinear processes of energy transmission, conversion, and dissipation in the solar‐terrestrial coupling system during magnetic storms, in which the magnetosphere is in nonequilibrium state responding to the solar wind changes [ Consolini et al , ]. In consequence, neither spectrogram [ Oppenheim and Schafer , 1989] nor wavelet [ Chan , ] is optimal to deal with storm data because of the spurious harmonic components caused by nonstationarity and nonlinearity. The former is a limited window‐width Fourier spectral analysis, and the latter is essentially an adjustable window Fourier spectral analysis, while the Fourier spectra only give meaningful interpretation to linear and stationary processes in principle.…”

Section: Introductionmentioning

confidence: 99%

The response of local power grid at low-latitude to geomagnetic storm: An application of the Hilbert Huang transform

et al. 2016

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The Hilbert-Huang transform (HHT) is an adaptive data analysis method that can accommodate the variety of data generated by nonlinear and nonstationary processes in nature. In this paper, we focus on the small geomagnetically induced current (GIC) at the local substations in low-latitude power grid of China, responding to a moderate storm on 14-18 July 2012. The HHT is applied to analyze the neutral point currents (NPCs) of transformers measured at different substations, and the GIC indices converted from local geomagnetic field measurements. The original data are decomposed into intrinsic mode functions (IMFs) using the ensemble empirical mode decomposition. After removal of the quasi-diurnal components related with the solar quiet variation, the IMFs representing storm disturbances are transformed into Hilbert energy spectra. The results show that some transformers have more or less responses to the moderate storm in the form of Hilbert energy spectra with the frequency around 2-3 mHz. A comparison on the amplitude changes of the spectra total energy of NPCs' perturbation during storm time intervals at different sites suggests that a shell type of three-phase single transformer group seems to be more vulnerable in the storm. Although the low-latitude power grids usually show very small GIC, these can be used to investigate the potential risk of space weather to the system.

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Wavelet Basics

Cited by 7 publications

References 0 publications

Fire Detection in Video Using Genetic-Based Neural Networks

Fire Detection in Video Using Genetic-Based Neural Networks

A wavelet thresholding technique for local geoid and deflection of the vertical determination using a planar approximation

The response of local power grid at low-latitude to geomagnetic storm: An application of the Hilbert Huang transform

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