Discrete Meyer Wavelet Research Articles

Performance analysis of a nonlinear energy harvester with subharmonic responses based on discrete Meyer wavelet filtering scheme

Performance analysis of a nonlinear energy harvester with subharmonic responses based on discrete Meyer wavelet filtering scheme

Filtered-orthogonal wavelet division multiplexing (F-OWDM) technique for 5G and beyond communication systems.

Filtered-orthogonal frequency division multiplexing (F-OFDM) is one of the most protruding multicarrier modulation (MCM) techniques for fifth-generation and beyond wireless communication. However, it possesses a high peak-to-average power ratio (PAPR), which results in its poor performance. Thus, a novel wavelet based MCM technique, namely filtered orthogonal wavelet division multiplexing (F-OWDM), is proposed as an efficient alternative to conventional F-OFDM (C-F-OFDM) to reduce the PAPR. In this model, the traditional Fourier transforms (FT) as used in C-F-OFDM was replaced with Wavelet Transforms. The proposed F-OWDM system does not require a cyclic prefix because of the overlapping sub-carriers in the time and frequency domains. Thus, the F-OWDM system exhibits higher bandwidth efficiency. In this paper, the performance of the F-OWDM system with various wavelets from different wavelet families under an additive white Gaussian noise and flat fading channel is investigated. The PAPR and bit error rate (BER) of the F-OWDM system using Haar, discrete Meyer, bi-orthogonal, symlet, and Daubechies wavelets are analyzed. A comparative study between F-OWDM and C-F-OFDM is also presented. From the results, it is able to prove that F-OWDM has the advantage of lower PAPR and lower bit error rate than the C-F-OFDM system.

Source Localization of EEG Brainwaves Activities via Mother Wavelets Families for SWT Decomposition.

A Brain-Computer Interface (BCI) is a system used to communicate with an external world through the brain activity. The brain activity is measured by electroencephalography (EEG) signal and then processed by a BCI system. EEG source reconstruction could be a way to improve the accuracy of EEG classification in EEG based brain-computer interface (BCI). The source localization of the human brain activities can be an important resource for the recognition of the cognitive state, medical disorders, and a better understanding of the brain in general. In this study, we have compared 51 mother wavelets taken from 7 different wavelet families, which are applied to a Stationary Wavelet Transform (SWT) decomposition of an EEG signal. This process includes Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal wavelet families in extracting five different brainwave subbands for source localization. For this process, we used the Independent Component Analysis (ICA) for feature extraction followed by the Boundary Element Model (BEM) and the Equivalent Current Dipole (ECD) for the forward and inverse problem solutions. The evaluation results in investigating the optimal mother wavelet for source localization eventually identified the sym20 mother wavelet as the best choice followed by bior6.8 and coif5.

Nowcasting prediction of wind speed using computational intelligence and wavelet in Brazil

This work presents a novel investigation on the nowcasting prediction of wind speed for three sites in Bahia, Brazil. For this, it was applied the computational intelligence by supervised machine learning using different artificial neural network technique, which was trained, validated, and tested using time series are derived from measurements that are acquired in towers equipped with anemometers at heights of 100.0, 120.0 and 150.0 m. To define the most efficient ANN, different topologies were tested using MLP and RNN, applying Wavelet packet decomposition (bior, coif, db, dmey, rbior, sym). The best statistical analysis was RNN + discrete Meyer wavelet. Highlights A new methodology for improving forecast accuracy of wind speed using artificial neural network (ANN) and Wavelet packet decomposition. Using machine learning and Wavelet packet decomposition to nowcast wind speed (m/s). To predict the wind speed at 100.0 m, 120.0 m and 150.0 m height in tropical region. Performance evaluation of Wavelet packet decomposition applying 48 different mother Wavelet functions. ANN approach for the estimation of nine types of wind speed time series. The proposed hybrid model (ANN + Wavelet packet decomposition) is capable of wind speed forecasting efficiently.

Performance of Discrete Meyer wavelet Transform on Encoding Levels using Computed Tomography Lung Image

The image transmits and storage capability could be a broad appliance in compression. Image compression techniques engage the appropriate and successful transforms and encoding methods to attain the aim. In this work, discrete Meyer transform based image compression algorithm is used for decomposing the image. The effects of different Encoder loops are described based on the values of peak signal to noise ratio (PSNR), compression ratio (CR), means square error (MSE) and bits per pixel (BPP). The finest encoding loop level for compression is also found based on the results.

Selection of Optimum Mother Wavelet Function for Turkish Phonemes

In this paper, we propose the selection of most suitable mother wavelet function for Turkish phonemes using discrete wavelet transform. The determination of most similar mother wavelet function to the signal has been a challenge in speech processing. The optimum mother wavelet function for Turkish phonemes have been determined by using quantitative measures which are energy and Shannon entropy, information theoretic measures which are joint entropy, conditional entropy, mutual information, and relative entropy from wavelet coefficients of the phonemes. In this study, 101 potential functions were investigated to determine the most appropriate mother wavelet. Experimental results show that the most appropriate wavelet functions for /ç/ and /ş/ phonemes which are unvoiced fricatives have been found as Bi-orthogonal 3.9 and Bi-orthogonal 5.5, respectively. By considering all the results, it is seen that the Bi-orthogonal 3.1 and Discrete Meyer wavelet functions are the most suitable mother wavelets for all other phonemes.

웨이블릿 변환 기반의 Wavelet-OFDM 시스템과 푸리에 변환 기반의 OFDM 시스템의 성능 비교

Orthogonal frequency division multiplexing(OFDM) is a multicarrier modulation(MCM) system that enables high-speed communications using multiple carriers and has advantages of power and spectral efficiency. Therefore, this study aims to complement the existing shortcomings and to design an efficient MCM system. The proposed system uses the inverse discrete wavelet transform(IDWT) operation instead of the inverse fast Fourier transform(IFFT) operation. The bit error rate(BER), spectral efficiency, and peak-to-average power ratio(PAPR) performance were compared with the conventional OFDM system through the OFDM system design based on wavelet transform. Our results showed that the conventional OFDM and Wavelet-OFDM exhibited the same BER performance, and that the Wavelet-OFDM using the discrete Meyer wavelet had the same spectral efficiency as the conventional OFDM. In addition, all systems of Wavelet-OFDM based on various wavelets confirm a PAPR performance lower than that of conventional OFDM.

Individual Identification Using ECG SignalsW

The electrocardiogram (ECG) signal used for diagnosis and patient monitoring, has recently emerged as a biometric recognition tool. Indeed, ECG signal changes from one person to another according to health status, heart geometry and anatomy among other factors. This paper forms a comparative study between different identification techniques and their performances. Previous works in this field referred to methodologies implementing either set of fiducial or set non-fiducial features. In this study we show a comparison of the same data using a fiducial feature set and a non-fiducial feature set based on statistical calculation of wavelet coefficient. High identification rates were measured in both cases, non-fiducial using Discrete Meyer (dmey) wavelet outperformed the rest at 98.65.

Forecasting the Electric Energy Supply in Duhok Province using Proposed Methods Based on Wavelet Analysis and Sarima Methods

Many applications have been done in the field of using wavelet analysis for time series analysis. In this study, we used the quarterly data of Electric Energy Supply in Duhok Province-Iraq in Megawatt which represents a sample size (46) observations during the period 2004 and 2015.we aim to describe how wavelet de-noising can be used in time series forecasting and improve the forecasting quality through presenting some proposed methods based on wavelet analysis and SARIMA method and applying on real data and make comparison between methods depending on some statistical criteria.Results from the analysis showed the superiority of the three proposed methods and showed that we can get more information from a series when using Wavelet-SARIMA method and this leads to enhance the classical SARIMA model in forecasting. Furthermore, after many empirical experiments with many wavelet families, it has been found that Daubechies, Coiflets, Discrete Meyer(dmey) and Symlet wavelets are very suitable when denoising the data and out of these four wavelet families, the Daubechies and Discrete Meyer performed better.

PAPR analysis of wavelet based multitaper GFDM system

To guarantee a reliable, accurate communication with reduced latency and increased throughput, one of the 5G candidates Generalized Frequency Division Multiplexing (GFDM) has emerged out. Due to the non-orthogonal nature of GFDM inherent Inter Symbol Interference (ISI), Inter Carrier Interference (ICI) and high Peak to Average Power Ratio (PAPR) may occur. In order to combat such effects prolate windows are incorporated as a prototype filter to design an improved orthogonal system which provides a robust multitaper GFDM (MGFDM) carrier technique for next generation wireless networks, which outperforms conventional GFDM in terms of PAPR. In this paper, we propose a novel wavelet based MGFDM (WM-GFDM) to further reduce the PAPR by considering various wavelet transforms such as Haar, Daubechies, symlets, coiflets, Biorthogonal, Reverse Biorthogonal and Discrete Meyer Wavelets. Here, the conventional Fourier Transforms as used in traditional systems was replaced with Wavelet Transforms. The results show that PAPR performance with wavelet implementation outperformed both conventional GFDM and MGFDM by several dB. In addition, symbol error rate (SER) of WM-GFDM in comparison with conventional GFDM, MGFDM and Orthogonal FDM (OFDM) is analyzed along with spectral comparison where the results suggest that WM-GFDM follows the steps of GFDM and MGFDM.

Chemometrics-assisted spectrophotometric method for simultaneous determination of Pb2+ and Cu2+ ions in different foodstuffs, soil and water samples using 2-benzylspiro [isoindoline-1,5′-oxazolidine]-2′,3,4′-trione using continuous wavelet transformation and partial least squares – Calculation of pKf of complexes with rank annihilation factor analysis

A new multi-component analysis method based on zero-crossing point-continuous wavelet transformation (CWT) was developed for simultaneous spectrophotometric determination of Cu2+ and Pb2+ ions based on the complex formation with 2-benzyl espiro[isoindoline-1,5oxasolidine]-2,3,4 trione (BSIIOT). The absorption spectra were evaluated with respect to synthetic ligand concentration, time of complexation and pH. Therefore according the absorbance values, 0.015mmolL−1 BSIIOT, 10min after mixing and pH 8.0 were used as optimum values. The complex formation between BSIIOT ligand and the cations Cu2+ and Pb2+ by application of rank annihilation factor analysis (RAFA) were investigated. Daubechies-4 (db4), discrete Meyer (dmey), Morlet (morl) and Symlet-8 (sym8) continuous wavelet transforms for signal treatments were found to be suitable among the wavelet families. The applicability of new synthetic ligand and selected mother wavelets were used for the simultaneous determination of strongly overlapped spectra of species without using any pre-chemical treatment. Therefore, CWT signals together with zero crossing technique were directly applied to the overlapping absorption spectra of Cu2+ and Pb2+. The calibration graphs for estimation of Pb2+ and Cu 2+were obtained by measuring the CWT amplitudes at zero crossing points for Cu2+ and Pb2+ at the wavelet domain, respectively. The proposed method was validated by simultaneous determination of Cu2+ and Pb2+ ions in red beans, walnut, rice, tea and soil samples. The obtained results of samples with proposed method have been compared with those predicted by partial least squares (PLS) and flame atomic absorption spectrophotometry (FAAS).

Passive Image-Splicing Detection by a 2-D Noncausal Markov Model

In this paper, a 2-D noncausal Markov model is proposed for passive digital image-splicing detection. Different from the traditional Markov model, the proposed approach models an image as a 2-D noncausal signal and captures the underlying dependencies between the current node and its neighbors. The model parameters are treated as the discriminative features to differentiate the spliced images from the natural ones. We apply the model in the block discrete cosine transformation domain and the discrete Meyer wavelet transform domain, and the cross-domain features are treated as the final discriminative features for classification. The support vector machine which is the most popular classifier used in the image-splicing detection is exploited in our paper for classification. To evaluate the performance of the proposed method, all the experiments are conducted on public image-splicing detection evaluation data sets, and the experimental results have shown that the proposed approach outperforms some state-of-the-art methods.

Flow Measurement Wavelet Filtering for Ultrasonic Flow Meter

This paper introduces the wavelet filtering to the digital signal processing of ultrasonic flow meter. The noise sources in ultrasonic flow meter are analyzed, and they are divided into three groups: power input, integrated circuit, and other acoustic ways. Some of the noise is not white noise, so traditional noise reduction filter is not effective. Original signal from ultrasonic flow meter is sampled, and four wavelet filters (Haar wavlet, Daubechies wavelet, Symlets wavlet, and discrete Meyer wavelet) with three threshold methods (SURE threshold, Universal threshold, and Minimax threshold) on the signal is compared through experiment. The result shows Haar wavelet with Universal threshold has the best filtering ability for ultrasonic flow meter.

Multi-scale topographic analysis of Merbabu and Merapi volcanoes using wavelet decomposition

With the increasing availability of data, geo-sciences have experienced deep changes in handling and processing it. One of the presently explored research directions concerns the systematic decomposition and understanding of topographical features, without the subjective interactions of humans. This can eventually lead to fully automated algorithms for topographic analysis and understanding. This paper aims at being a contribution to this broad research area for the specific cases of stratovolcanoes, whose general geometry are very similar to a perfect cone. More specifically, this paper addresses two issues: (1) is it possible to separate erosion features (local variations) from structural features (large variations) on stratovolcanoes, through mathematical expression; (2) can information on volcanic activity—intensity, age, etc.—be retrieved from a topographic analysis? The study has been conducted from two volcanoes in Central Java (Indonesia): the Merapi and the Merbabu. The DEM of these volcanoes has been sampled using concentric circles with a radius ranging from 500 to 5,000 m (horizontal distance) to the summit. The data conversion and sampling was performed in ArcMap®, while the data analysis was carried out with Matlab®, using Discrete Meyer wavelet decomposition. Results provide an insight on large-scale topographic variations (long-wave wavelet) that have been separated from rapidly varying topographic features such as lahar channels (short-wave wavelets). Observations proved that flanks where the most recent volcanic activity occur—like at Merapi Volcano on the S-SE flank—present a very low variability of long-wave variations, whereas short-wave variations are important. The author argues that this feature is due to highly erosive lahars that dig the valleys combined with a recent production of material and volcanic growth keeping the overall structure regular. Flanks with lesser activity are characterized at the two volcanoes by important long-wave variations—most certainly due to long-term differential erosion—and different level of short-waves variations. Comparing the two volcanoes, results show that the valleys of Merapi and Merbabu volcanoes are deeply incised, indicating recent periods of high activity, with reworkable material eroded by lahars and other channels deepening processes. The topography of the summit area of Merapi Volcano is smoother than at Merbabu Volcano, where deep erosion features extend up to the summit area. This difference is most certainly due by the material production at the summit of Merapi Volcano. Developing such classification is important for automated mapping and computer recognition of volcanic past activities and their impacts on landscapes. It is the based for the development of decision trees that assist computer assisted and automated computer vision.

Phase retrieval from fringe pattern with 1-D discrete wavelet transform

This paper proposes a novel method to obtain frequency modulation (FM) signals from a single fringe pattern for phase retrieval. First, a 1D discrete Meyer wavelet is employed to decompose the pattern image signal row by row and the soft-thresholding approach is applied to remove noise. The low frequency coefficients of the wavelet decomposition are then set to 0, and the signal is reconstructed. Moreover, the optimal wavelet decomposition level is adaptively determined using a cost function-based method. The reconstructed signal, which no longer contains a background component, is normalized using a nonlinear and piecewise normalization method. The proposed method is faster and more accurate than some other phase retrieval approaches, which is illustrated with two test cases.

THE APPLICATION OF WAVELET ANALYSIS FOR INTERNAL WAVE DETECTION IN SAR AND OPTICAL IMAGES DATA OVER TSUSHIMA STRAIT

On this paper, wavelet analysis has been used for internal wave detection in ERS SAR and ASTER images data over Tsushima strait, southwest of Japan, during 1993-2004 period. Various wavelet transforms, such as Haar wavelet, Symlet wavelet, Coif wavelet, Daubechies wavelet, and Discreet Meyer wavelet, are tested comparably with different level of synthesize image on horizontal, diagonal, and vertical detail, and approximation to study the internal wave characteristic in image. Internal wave features were detected as elongated pattern in image with higher wavelet coefficient (>36) than sea surface (litlle than 10) on horizontal and vertical detail coefficient of image transforms at level 2-5. The decomposition image shows the tendency that the decomposition of internal wave feature using wavelet transform tends to follow the wavelet function. This may reduced the height of leading wave. Smoother result of internal wave shape can be formed using higher scale resolution of image and higher number of vanishing moments such as Daubechies waveletdb5, Symlet wavelet-sym5, and Discrete Meyer wavelet. The compactly supported wavelet function with orthogonal basis with scale function and FIR filter, such as discrete Meyer function is proposed for smoothness of feature, space save coding, and to avoid depashing in image. So far, the detection processes were performed well on the internal waves data that occurred at north coast off Kitakyushu and NW/W/SW/E coast off Tsushima Island on June to September period whose lengths were detected between 6-28 km and wavelength between 120m-1.28km. The directions of internal wave propagation were varied between NW-SW at eastern channel and N-SW at western channel of Tsushima Strait. Keywords: wavelet analysis, SAR image, optical image, internal wave.

Gas film formation time and gas film life time during electrochemical discharge phenomenon

The formation of a gas film around an electrode is at the origin of the electrochemical discharges in aqueous solutions and in molten salts. The study of the electrochemical discharge phenomenon from the current signal point of view is conducted to identify the gas film formations and the following discharges. This is performed using the wavelet analysis as a denoising tool with the discrete Meyer wavelet as base function. The proposed algorithm allows to measure experimentally the gas film life time and its necessary building time prior to each series of discharges. The accuracy of the algorithm is evaluated using generated signals and its application to real data is demonstrated. From the experimental data, it is concluded that the gas film is more stable at high terminal voltages whereas its formation time decreases with it. Electrochemical and thermal interpretations for the measured statistics are proposed.

Application of continuous wavelet transformation to the simultaneous kinetic determination of binary mixtures

Wavelet transformation of kinetic profiles as a new and simple method was developed for the simultaneous determination of binary mixtures without prior separation steps. The mathematical explanation of the procedure is illustrated. Daubechies (db), symlet (sym) and discrete meyer wavelet (meyr) from the family of wavelet transforms were selected and applied under the optimal conditions for the resolution of binary mixtures. A model data as well as experimental data were tested. The results from the experimental data relating to the simultaneous spectrophotometric determination of phosphate and silicate based on the formation of phospho- and silico-molybdenum blue complexes in the presence of ascorbic acid, and also simultaneous determination of Co 2+ and Ni 2+ based on their complexation reactions with 1-(2-pyridylazo)-2-naphthol (PAN) in micellar media at pH 6.0 were presented as real models. The proposed method was validated by simultaneous determination of phosphate and silicate in detergent and tap water and also Co 2+ and Ni 2+ in tap water samples.

Construction and application of a novel library: Fourier transform infrared wavelet coefficients library

This article aims at designing a wavelet alternative to Fourier transform infrared spectra (FTIR). In order to select the most suitable wavelet parameters to perform, several decomposition levels and 53 wavelets were tested by trial and error approach, respectively. The result indicated that discrete meyer wavelet (dmey) associated with its third decomposition level was very efficient for this purpose. On the base of it, a novel library named as Fourier transform infrared wavelet coefficients library (FTIR-WC) has been constructed. Finally, two tools such as library search and structure elucidation were developed to evaluate the capability of the new library system. The results obtained were also compared with those from FTIR library by a variety of indices. The results suggested that the new library performed better but with less volume. This work is expected to propose a novel and practical strategy in infrared spectroscopic analysis.

MULTIRESOLUTION ANALYSIS FOR SEPARATING CLOSELY SPACED FREQUENCIES WITH AN APPLICATION TO INDIAN MONSOON RAINFALL DATA

In this paper we make use of the multiresolution properties of discrete wavelets, including their ability to remove interference, to reveal closely spaced spectral peaks. We propose a procedure which we first verify on two test signals, and then apply it to the time series of homogeneous Indian monsoon rainfall annual data. We show that, compared to empirical mode decomposition, discrete wavelet analysis is more effective in identifying closely spaced frequencies if used in combination with classical power spectral analysis of wavelet-based partially reconstructed time series. An effective criterion based on better localization of specific frequency components and accurate estimation of their amplitudes is used to select an appropriate wavelet. It is shown here that the discrete Meyer wavelet has the best frequency properties among the wavelet families considered (Haar, Daubechies, Coiflet and Symlet). In rainfall data, the present analysis reveals two additional spectral peaks besides the fifteen found by classical spectral analysis. Moreover, these two new peaks have been found to be statistically significant, although a detailed discussion of testing for significance is being presented elsewhere.