scholarly journals Non-decimated Wavelet Transform for a Shift-invariant Analysis

2018 ◽  
Vol 19 (1) ◽  
pp. 93 ◽  
Author(s):  
Gabriela De Oliveira Nascimento Brassarote ◽  
Eniuce Menezes de Souza ◽  
João Francisco Galera Monico
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Signal Analysis ◽  
Perfect Reconstruction ◽  
Discrete Wavelet ◽  
Continuous Version ◽  
Time Frequency ◽  
Application Potential ◽  
Invariant Analysis ◽  
Analysis Of Time Series

Due to the ability of time-frequency location, the wavelet transform hasbeen applied in several areas of research involving signal analysis and processing,often replacing the conventional Fourier transform. The discrete wavelet transformhas great application potential, being an important tool in signal compression,signal and image processing, smoothing and denoising data. It also presentsadvantages over the continuous version because of its easy implementation, goodcomputational performance and perfect reconstruction of the signal upon inversion.Nevertheless, the downsampling required in the discrete wavelet transformcalculous makes it shift variant and not appropriated to some applications, suchas for signals or time series analysis. On the other hand, the Non-Decimated DiscreteWavelet Transform is shift-invariant because it eliminates the downsamplingand, consequently, is more appropriate for identifying both stationary and nonstationarybehaviors in signals. However, the non-decimated wavelet transform hasbeen underused in the literature. This paper intends to show the advantages ofusing the non-decimated wavelet transform in signal analysis. The main theoricaland pratical aspects of the multiscale analysis of time series from non-decimatedwavelets in terms of its formulation using the same pyramidal algorithm of thedecimated wavelet transform was presented. Finally, applications with a simulatedand real time series compare the performance of the decimated and non-decimatedwavelet transform, demonstrating the superiority of non-decimated one, mainly dueto the shift-invariant analysis, patterns detection and more perfect reconstructionof a signal.

CWT × DWT × DTWT × SDTWT: Clarifying terminologies and roles of different types of wavelet transforms

2020 ◽  
Vol 18 (06) ◽  
pp. 2030001 ◽  
Author(s):  
Rodrigo Capobianco Guido ◽  
Fernando Pedroso ◽  
André Furlan ◽  
Rodrigo Colnago Contreras ◽  
Luiz Gustavo Caobianco ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Discrete Time ◽  
Wavelet Transforms ◽  
Signal Analysis ◽  
Applied Mathematics ◽  
Discrete Wavelet ◽  
Frequency Signal ◽  
Time Frequency ◽  
Subsequent Investigation ◽  
Different Types

Wavelets have been placed at the forefront of scientific researches involving signal processing, applied mathematics, pattern recognition and related fields. Nevertheless, as we have observed, students and young researchers still make mistakes when referring to one of the most relevant tools for time–frequency signal analysis. Thus, this correspondence clarifies the terminologies and specific roles of four types of wavelet transforms: the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the discrete-time wavelet transform (DTWT) and the stationary discrete-time wavelet transform (SDTWT). We believe that, after reading this correspondence, readers will be able to correctly refer to, and identify, the most appropriate type of wavelet transform for a certain application, selecting relevant and accurate material for subsequent investigation.

scholarly journals The Shift Invariant Discrete Wavelet Transform (SIDWT) with Inflation Time Series Application

2016 ◽  
Vol 8 (4) ◽  
pp. 14
Author(s):  
Suparti Suparti ◽  
Rezzy Eko Caraka ◽  
Budi Warsito ◽  
Hasbi Yasin
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Well Being ◽  
Discrete Wavelet ◽  
Time Series Modeling ◽  
The Government ◽  
Determining Factor ◽  
Analysis Of Time Series ◽  
Economic Well Being

<p>Analysis of time series used in many areas, one of which is in the field economy. In this research using time series on inflation using Shift Invariant Discrete Wavelet Transform (SIDWT).Time series decomposition using transformation wavelet namely SIDWT with Haar filter and D4. Results of the transformation, coefficient of drag coefficient wavelet and scale that is used for modeling time series. Modeling done by using Multiscale Autoregressive (MAR). In a certain area, inflation to it is an important that he had made the standard-bearer of economic well-being of society, the factors Directors investors in selecting a kind of investment, and the determining factor for the government to formulate policy fiscal, monetary, as well as non-monetary that will be applied. Inflation can be analyzed using methods Shift Invariant Discrete Wavelet Transform (SIDWT) which had been modeled for them to use Mulitiscale Autoregressive (MAR) with the R2 value 93.62%.</p>

scholarly journals Application of Discrete Wavelet Transform in Shapelet-Based Classification

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Lijuan Yan ◽  
Yanshen Liu ◽  
Yi Liu
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Weight Vector ◽  
Majority Voting ◽  
Discrete Wavelet ◽  
Time Series Classification ◽  
Original Time Series ◽  
Time Frequency ◽  
Original Time

Recently, several shapelet-based methods have been proposed for time series classification, which are accomplished by identifying the most discriminating subsequence. However, for time series datasets in some application domains, pattern recognition on the original time series cannot always obtain ideal results. To address this issue, we propose an ensemble algorithm by combining time frequency analysis and shape similarity recognition of time series. Discrete wavelet transform is used to decompose the time series into different components, and the shapelet features are identified for each component. According to the different correlations between each component and the original time series, an ensemble classifier is built by weighted majority voting, and the Monte Carlo method is used to search for optimal weight vector. The comparative experiments and sensitivity analysis are conducted on 25 datasets from UCR Time Series Classification Archive, which is an important open dataset resource in time series mining. The results show the proposed method has a better performance in terms of accuracy and stability than the compared classifiers.

Using multi-temporal analysis to classify monthly precipitation based on maximal overlap discrete wavelet transform

2019 ◽  
Vol 21 (4) ◽  
pp. 541-557 ◽  
Author(s):  
Kiyoumars Roushangar ◽  
Farhad Alizadeh
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Spatial Clustering ◽  
Superior Performance ◽  
Discrete Wavelet ◽  
Monthly Precipitation ◽  
Time Frequency ◽  
Clustering Model ◽  
Multi Temporal

AbstractIn the present study, a hybrid methodology was proposed in which temporal pre-processing and spatial classification approaches were used in a way to take advantage of multiscale properties of precipitation series. Monthly precipitation data (1960–2010) for 31 rain gauges were used in the proposed classification approaches. Maximal overlap discrete wavelet transform (MODWT) was used to capture the time–frequency attributes of the time series and multiscale regionalization was performed by using self-organizing maps (SOM) clustering model. Daubechies 2 function was selected as mother wavelet to decompose the precipitation time series. Also, proper boundary extensions and decomposition level were applied. Different combinations of the wavelet (W) and scaling (V) coefficients were used to determine the input dataset as a basis of spatial clustering. Four input combinations were determined as single-cycle and the remaining four combinations were determined with multi-temporal dataset. These combinations were determined in a way to cover all possible scales captured from MODWT. The proposed model's efficiency in spatial clustering stage was verified using Silhouette Coefficient index. Results demonstrated superior performance of MODWT-SOM in comparison to historical-based SOM approach. It was observed that the clusters captured by MODWT-SOM approach determined homogenous precipitation areas very well (based on physical analysis).

scholarly journals Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers

2021 ◽  
Vol 13 (2) ◽  
pp. 542
Author(s):  
Tarate Suryakant Bajirao ◽  
Pravendra Kumar ◽  
Manish Kumar ◽  
Ahmed Elbeltagi ◽  
Alban Kuriqi
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Suspended Sediment ◽  
River Basin ◽  
Time Series Data ◽  
Series Data ◽  
Discrete Wavelet ◽  
Original Time Series ◽  
Inference System ◽  
Original Time

Estimating sediment flow rate from a drainage area plays an essential role in better watershed planning and management. In this study, the validity of simple and wavelet-coupled Artificial Intelligence (AI) models was analyzed for daily Suspended Sediment (SSC) estimation of highly dynamic Koyna River basin of India. Simple AI models such as the Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were developed by supplying the original time series data as an input without pre-processing through a Wavelet (W) transform. The hybrid wavelet-coupled W-ANN and W-ANFIS models were developed by supplying the decomposed time series sub-signals using Discrete Wavelet Transform (DWT). In total, three mother wavelets, namely Haar, Daubechies, and Coiflets were employed to decompose original time series data into different multi-frequency sub-signals at an appropriate decomposition level. Quantitative and qualitative performance evaluation criteria were used to select the best model for daily SSC estimation. The reliability of the developed models was also assessed using uncertainty analysis. Finally, it was revealed that the data pre-processing using wavelet transform improves the model’s predictive efficiency and reliability significantly. In this study, it was observed that the performance of the Coiflet wavelet-coupled ANFIS model is superior to other models and can be applied for daily SSC estimation of the highly dynamic rivers. As per sensitivity analysis, previous one-day SSC (St-1) is the most crucial input variable for daily SSC estimation of the Koyna River basin.

scholarly journals An innovative image fusion algorithm based on wavelet transform and discrete fast curvelet transform

2011 ◽  
Vol 1 (3) ◽  
Author(s):  
T. Sumathi ◽  
M. Hemalatha
Keyword(s):  
Wavelet Transform ◽  
Image Fusion ◽  
Curvelet Transform ◽  
Relevant Information ◽  
Good Time ◽  
Discrete Wavelet ◽  
Fusion Algorithm ◽  
Time Frequency ◽  
Fused Image

AbstractImage fusion is the method of combining relevant information from two or more images into a single image resulting in an image that is more informative than the initial inputs. Methods for fusion include discrete wavelet transform, Laplacian pyramid based transform, curvelet based transform etc. These methods demonstrate the best performance in spatial and spectral quality of the fused image compared to other spatial methods of fusion. In particular, wavelet transform has good time-frequency characteristics. However, this characteristic cannot be extended easily to two or more dimensions with separable wavelet experiencing limited directivity when spanning a one-dimensional wavelet. This paper introduces the second generation curvelet transform and uses it to fuse images together. This method is compared against the others previously described to show that useful information can be extracted from source and fused images resulting in the production of fused images which offer clear, detailed information.

scholarly journals Discrete and Dual Tree Wavelet Features for Real-Time Speech/Music Discrimination

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Timur Düzenli ◽  
Nalan Özkurt
Keyword(s):  
Wavelet Transform ◽  
Real Time ◽  
Wavelet Transforms ◽  
Principal Component ◽  
Discrete Wavelet ◽  
Vanishing Moments ◽  
Zero Crossings ◽  
Time Frequency ◽  
Common Time ◽  
Classification Tool

The performance of wavelet transform-based features for the speech/music discrimination task has been investigated. In order to extract wavelet domain features, discrete and complex orthogonal wavelet transforms have been used. The performance of the proposed feature set has been compared with a feature set constructed from the most common time, frequency and cepstral domain features such as number of zero crossings, spectral centroid, spectral flux, and Mel cepstral coefficients. The artificial neural networks have been used as classification tool. The principal component analysis has been applied to eliminate the correlated features before the classification stage. For discrete wavelet transform, considering the number of vanishing moments and orthogonality, the best performance is obtained with Daubechies8 wavelet among the other members of the Daubechies family. The dual tree wavelet transform has also demonstrated a successful performance both in terms of accuracy and time consumption. Finally, a real-time discrimination system has been implemented using the Daubhecies8 wavelet which has the best accuracy.

scholarly journals A Hybrid Model Based on Wavelet Decomposition-Reconstruction in Track Irregularity State Forecasting

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Chaolong Jia ◽  
Lili Wei ◽  
Hanning Wang ◽  
Jiulin Yang
Keyword(s):  
Time Series ◽  
Signal Analysis ◽  
Wavelet Decomposition ◽  
Forecast Model ◽  
Practical Significance ◽  
Frequency Signal ◽  
Time Frequency ◽  
Simple Basis ◽  
Best Fitting ◽  
Track Irregularity

Wavelet is able to adapt to the requirements of time-frequency signal analysis automatically and can focus on any details of the signal and then decompose the function into the representation of a series of simple basis functions. It is of theoretical and practical significance. Therefore, this paper does subdivision on track irregularity time series based on the idea of wavelet decomposition-reconstruction and tries to find the best fitting forecast model of detail signal and approximate signal obtained through track irregularity time series wavelet decomposition, respectively. On this ideology, piecewise gray-ARMA recursive based on wavelet decomposition and reconstruction (PG-ARMARWDR) and piecewise ANN-ARMA recursive based on wavelet decomposition and reconstruction (PANN-ARMARWDR) models are proposed. Comparison and analysis of two models have shown that both these models can achieve higher accuracy.

COMPARISON BETWEEN DISCRETE AND PACKET WAVELET TRANSFORM ANALYSES IN THE STUDY OF HEARTBEAT CARDIAC SOUNDS

2007 ◽  
Vol 07 (02) ◽  
pp. 199-214 ◽  
Author(s):  
S. M. DEBBAL ◽  
F. BEREKSI-REGUIG
Keyword(s):  
Wavelet Transform ◽  
Heart Sound ◽  
Wavelet Packet ◽  
Extraction Methods ◽  
Heart Sounds ◽  
Discrete Wavelet ◽  
Clinical Tool ◽  
Prognostic Information ◽  
Transform Method ◽  
Time Frequency

This work investigates the study of heartbeat cardiac sounds through time–frequency analysis by using the wavelet transform method. Heart sounds can be utilized more efficiently by medical doctors when they are displayed visually rather through a conventional stethoscope. Heart sounds provide clinicians with valuable diagnostic and prognostic information. Although heart sound analysis by auscultation is convenient as a clinical tool, heart sound signals are so complex and nonstationary that they are very difficult to analyze in the time or frequency domain. We have studied the extraction of features from heart sounds in the time–frequency (TF) domain for the recognition of heart sounds through TF analysis. The application of wavelet transform (WT) for heart sounds is thus described. The performances of discrete wavelet transform (DWT) and wavelet packet transform (WP) are discussed in this paper. After these transformations, we can compare normal and abnormal heart sounds to verify the clinical usefulness of our extraction methods for the recognition of heart sounds.

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