On the energy leakage of discrete wavelet transform

Peng, Z.K.; Jackson, Michael R.; Rongong, J.A.; Chu, Fu Lei; Parkin, Robert M.

doi:10.1016/j.ymssp.2008.05.014

Cited by 72 publications

(31 citation statements)

References 22 publications

(15 reference statements)

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“…By doing so, the latter represented the original reflectance with a limited number of coefficients without causing significant errors for signal representations (loss of 0.01% of total energy). One of the important properties of DWT is that the energy of the Gaussian noise component of the signal will usually be dispersed as relatively small coefficients [54]. Hence, getting rid of the low coefficients might also have helped us eliminate the noise.…”

Section: Discussionmentioning

confidence: 99%

Investigating the Utility of Wavelet Transforms for Inverting a 3-D Radiative Transfer Model Using Hyperspectral Data to Retrieve Forest LAI

et al. 2013

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Abstract:The need for an efficient and standard technique for optimal spectral sampling of hyperspectral data during the inversion of canopy reflectance models has been the subject of many studies. The objective of this study was to investigate the utility of the discrete wavelet transform (DWT) for extracting useful features from hyperspectral data with which forest LAI can be estimated through inversion of a three dimensional radiative transfer model, the Discrete Anisotropy Radiative Transfer (DART) model. DART, coupled with the leaf optical properties model PROSPECT, was inverted with AVIRIS data using a look-up-table (LUT)-based inversion approach. We used AVIRIS data and in situ LAI measurements from two different hardwood forested sites in Wisconsin, USA. Prior to inversion, model-simulated and AVIRIS hyperspectral data were transformed into discrete wavelet coefficients using Haar wavelets. The LUT inversion was performed with three different datasets, the original reflectance bands, the full set of wavelet extracted features, and two wavelet subsets containing 99.99% and 99.0% of the cumulative energy The results indicate that the discrete wavelet transform can increase the accuracy of LAI estimates by improving the LUT-based inversion of DART (and, potentially, by implication, other terrestrial radiative transfer models) using hyperspectral data. The improvement in accuracy of LAI estimates is potentially due to different properties of wavelet analysis such as multi-scale representation, dimensionality reduction, and noise removal.

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Section: Discussionmentioning

confidence: 99%

Investigating the Utility of Wavelet Transforms for Inverting a 3-D Radiative Transfer Model Using Hyperspectral Data to Retrieve Forest LAI

et al. 2013

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“…In the j-th level, low-frequency components are limited in the interval . Note that the precise frequency spectrum partition is impractical, since the filters frequency responses should be ideal (Peng et al, 2009 As suggested by Peng et al (2009), the upper limit for the approximation coefficients is higher than 25 Hz, which is the frequency of interest. Therefore, setting the sampling rate at 125 Hz is suitable.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…Therefore, if s f is the sampling frequency, the frequency contents for approximation and detail coefficients, in the j -th decomposition level, are in the interval  , respectively. In practice, the ideal cut-off frequencies are not realizable (Peng et al, 2009 . Hence, there is a band overlap.…”

Section: Discrete Wavelet Transformmentioning

confidence: 99%

A wavelet-based method for power-line interference removal in ECG signals

et al. 2018

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Introduction: The analysis of electrocardiogram (ECG) signals allows the experts to diagnosis several cardiac disorders. However, the accuracy of such diagnostic depends on the signals quality. In this paper it is proposed a simple method for power-line interference (PLI) removal based on the wavelet decomposition, without the use of thresholding techniques. Methods: This method consists in identifying the ECG and noise frequency range for further zeroing wavelet detail coefficients in the subbands with no ECG coefficients in the frequency content. Afterward, the enhanced ECG signal is obtained by the inverse discrete wavelet transform (IDWT

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“…The differences in the wavelet spectrum observed at time scales near the annual cycle (Fig. 4c) likely result from the ''leakage of the energy'' (in this case toward the strong annual and semiannual cycles) commonly associated with discrete wavelet transforms (Peng et al 2009). The wavelet power spectrum of CEOF-2 was obtained using the Morlet wavelet base function [see Torrence and Compo (1998) for details on the wavelet transform].…”

Section: A Definitionmentioning

confidence: 98%

Intraseasonal-to-Interannual Variability of the Indian Monsoon Identified with the Large-Scale Index for the Indian Monsoon System (LIMS)

et al. 2016

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The Indian monsoon system (IMS) is among the most complex and important climatic features on land. This study proposes a simple and robust method to investigate large-scale variations and changes in the IMS that accounts for fluctuations in amplitude, onset, and duration of the summer monsoon, including active and break phases, and the postmonsoon season. This study uses 35 years of daily data from the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR) at 18 resolution and indicates great potential for application to other reanalyses and climate model datasets. The method is based on combined EOF (CEOF) analysis of variables associated with the IMS's seasonal cycle (precipitation, circulation at 10 m, and temperature and specific humidity at 2 m). The first CEOF (CEOF-1) explains ;40% of the total variance and represents the continental-scale Asian monsoon. The second CEOF (CEOF-2) explains 11% of the variance and characterizes the Indian monsoon variability, including increased precipitation over western, central, and northern parts of India and the monsoon onset and demise over those regions. Thus, CEOF-2 is referred to as the large-scale index for the Indian monsoon system (LIMS). It is shown that LIMS's amplitude is strongly correlated with the total June-September precipitation over India. LIMS is continuous in time and can be used to evaluate significant postmonsoon rainfall events that often affect the Indian subcontinent. Moreover, LIMS exhibits spectral variance on intraseasonal time scales that are associated with active and break phases of the monsoon during summer and enhanced rainfall in the postmonsoon period.

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On the energy leakage of discrete wavelet transform

Cited by 72 publications

References 22 publications

Investigating the Utility of Wavelet Transforms for Inverting a 3-D Radiative Transfer Model Using Hyperspectral Data to Retrieve Forest LAI

Investigating the Utility of Wavelet Transforms for Inverting a 3-D Radiative Transfer Model Using Hyperspectral Data to Retrieve Forest LAI

A wavelet-based method for power-line interference removal in ECG signals

Intraseasonal-to-Interannual Variability of the Indian Monsoon Identified with the Large-Scale Index for the Indian Monsoon System (LIMS)

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