DISCRETE WAVELET TRANSFORM · Performing the Continues Wavelet Transform (CWT) on a signal will...

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DISCRETE WAVELET TRANSFORM DEDY RAHMAN WIJAYA [email protected]

Transcript of DISCRETE WAVELET TRANSFORM · Performing the Continues Wavelet Transform (CWT) on a signal will...

Page 1: DISCRETE WAVELET TRANSFORM · Performing the Continues Wavelet Transform (CWT) on a signal will lead to the generation of redundant information. ... Daubechies wavelet of order 9

DISCRETE WAVELETTRANSFORM

DEDY RAHMAN [email protected]

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INTROPerforming the Continues Wavelet Transform (CWT) on asignal will lead to the generation of redundant information.Continues data lead to high computational , memory, andstorage cost.

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DISCRETIZATION OF SCALE ANDTRANSLATION PARAMETERS

Generally, the values of s0=2 and τ0=1

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PROCEDURE OF A FOUR LEVEL SIGNALDECOMPOSITION USING DWT

Decompositionlevelcorrespond towaveletscales:j=121=2j=222=4j=323=8j=424=16

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HAAR WAVELETSOrthogonal, symmetric,The simplest base waveletwith the highest timeresolution given by acompact support.The best signal compressionperformance (Chompusri,2012)

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DAUBECHIES WAVELETOrthogonal & Asymmetric.Large phase distortion, Itmeans that it cannot be usedin applications where asignal’s phase informationneeds to be kept.

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COIFLET WAVELETOrthogonal, nearsymmetric.Near linear phase

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SYMLET WAVELETOrthogonal and nearsymmetric.This property ensures minimalphase distortion.Similar to the Daubechieswavelet, except for bettersymmetry

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BIORTHOGONAL AND REVERSEBIORTHOGONAL WAVELETS

Biorthogonal and symmetric.The property of symmetryensures that they have linearphase characteristics.

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MEYER WAVELETOrthogonal andsymmetric

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BASE WAVELET COMPARISON

J. Saraswathy, 2014

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WAVELET FAMILIES INMATLABdaubechies (daubechies1 daubechies10),symlet (symlet2 - symlet8),coiflet(coiflet1- coiflet5),biorthogonal (bior1.1, bior1.3, bior1.5, bior2.2, bior2.4,bior2.6, bior2.8, bior3.1, bior3.3, bior3.5, bior3.7, bior3.9,bior4.4, bior5.5, bior6.8),and dmey

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MOTHER WAVELETSELECTION

MWT

Qualitative

Quantitative

Properties

Visual observation

W.K.Ngui et.al, 2013

MSE

etc

Corr Coef

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MOTHER WAVELET SELECTING METHOD FORSELECTIVE MAPPING TECHNIQUE ECG

COMPRESSION (YOTAKA CHOMPUSRI, 2012)

Description:The most appropriate mother wavelet for Electrocardiogram (ECG) signals. The size ofrecorded ECG data are very large because it recorded in a long term. This work focus oncompression performance and evaluates for regular and irregular period of ECG signals. Ituses four types of mother wavelet to be competitors, ‘db1’, ‘db2’, ‘db9’ and ‘bior2.4’.

Parameters:Percent Root Mean Square Difference and Compression Ratio.Results:Db1 mother wavelet gives good compression performance from more than 50 percent of alltested ECG signals and also makes the maximum compression ratio for some ECG signals.

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SELECTION OF AN OPTIMAL MOTHER WAVELET BASISFUNCTION FOR ECG SIGNAL DENOISING (USMAN SELJUQ,2014)

Description:Wavelet based technique is preferred as it has shown improved detection accuracy. Theobjective of this study is to compare the performance of mother wavelet basis functions and toselect the most suitable mother wavelet so that it retains the desired diagnostics information inthe ECG signal. Simulations are performed over ECG signal corrupted by White GaussianNoise (WGN).

Parameters:mean square error (MSE), signal to noise ratio (SNR) and correlationResults:Daubechies wavelet of order 9 (db9) is best suited in preserving the features of denoisedsignal

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SELECTION OF MOTHER WAVELETS THRESHOLDING METHODS INDENOISING MULTI-CHANNEL EEG SIGNALS DURING WORKING

MEMORY TASK (NOOR KAMAL AL-QAZZAZ ET.AL, 2014)

Description:This is a pilot research which aims to find the most suitable base wavelet for EEG signals. 19electrodes were placed on the scalp of post-stroke patients. The selection of mother waveletfunctions like Daubechies (db1-db20), symlet (sym1-sym20) and coiflet (coif1-coif5) and thethresholding methods these are sqtwolog, rigrsure, heursure and minimax are to check motherwavelet functions similarity with the recorded EEG signals during working memory task.

Parameters:signal to noise ratio (SNR), peak signal to noise ratio (PSNR), mean square error (MSE) andcross corelation method (xcorr)Results:Symlet mother wavelet of order 9 is the most similar function for both EEG datasets which wasrecording during a working memory task using Rigrsure thresholding method.

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SELECTION OF MOTHER WAVELET FUNCTIONS FOR MULTI-CHANNEL EEG SIGNAL ANALYSIS DURING A WORKINGMEMORY TASK (NOOR KAMAL AL-QAZZAZ ET.AL, 2015)

Description:This is a comparative study to select the efficient mother wavelet (MWT) basis functions forEEG . These functions included Daubechies (db1–db20), Symlets (sym1–sym20), and Coiflets(coif1–coif5). ANOVA was employed to determine the MWT with the most significantdifferences in the ability of the five scalp regions to maximize their cross-correlation with theEEG signals. The similarities of these MWT functions to be matched to the recorded EEGdataset were also analyzed using a cross-correlation method (XCorr)

Parameters:Xcorr, ANOVAResults:Sym9 exhibits the highest similarities and compatibilities with the recorded EEG signals in allof the five scalp regions

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A COMPARATIVE STUDY OF WAVELET FAMILIESFOR EEG SIGNAL CLASSIFICATION (TAPANGANDHI ET.AL, 2011)

Description:This paper attemps to determine the most suitable wavelet family for electroencephalogram(EEG) signal. The wavelet families such as—Haar, Daubechies (orders 2–10), Coiflets(orders 1–10), and Biorthogonal (orders 1.1, 2.4,3.5, and 4.4) are computed base on energy,entropy and standard deviation. The choice of wavelet has significant impact on the quality ofresults with regard to the classifier. This study employed PNN and SVM as classifiers.

Parameters:Accuracy, computational timeResults:Coiflets 1 is the most suitable candidate among the wavelet families considered in this studyfor accurate classification of the EEG signals. It was observed that there is no significantchange in classification accuracy after 6th level of decomposition

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WAVELET BASIS FUNCTIONS IN BIOMEDICALSIGNAL PROCESSING (J. RAFIEE ET.AL, 2011)

Description:Three-hundred and twenty four potential mother wavelet functions were selected andinvestigated in the search for the most similar function. The algorithms were validated by threecategories of biological signals: forearm electromyographic (EMG), electroencephalographic(EEG), and vaginal pulse amplitude (VPA).

Parameters:Correlation coefficientResults:db44 appears to be the most similar function to EMG, EEG, and VPA signals among 324mother wavelet functions.

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A COMPARATIVE STUDY ON MOTHER WAVELET SELECTIONIN ULTRASOUND IMAGE DENOISING (FRANCESCO ADAMO

ET.AL, 2013)

Description:The aim of this work is to evaluate how the choice of mother wavelet function affectsultrasound image denoising. The mother wavelet included db1-db5, sym1-sym5, coif1-coif5,and bior1.1-bior6.8. The effect of choosing different mother wavelets each with its ownpeculiar properties of orthogonality, filter orders, symmetry and compact support has beeninvestigated.

Parameters:peak signal to noise ratio (PSNR), edges preservation measureResults:(i) the orthogonal families generally outperform biorthogonal functions, (ii) Coiflet functionsprovide worstresults because of the high filter length, (iii) Daubechies and Symlet provide very similarresults and (iv) to de-noise very noisy images (PSNR < 15 dB) a first filter order is preferredwhereas as the noise level increases the wavelet functions with higher filter order (3rd–4thorder) are more effective.

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SELECTION OF A SUITABLE MOTHER WAVELET FORMICROEMBOLI CLASSIFICATION USING SVM AND RF

SIGNALS (K. FERROUDJI,2012)

Description:Many mother wavelets have been used for this analysis such as Biorthogonal, Coiflet,Daubechies, and Symlet. In this study, all of the method of standard deviation, root meansquare, energy, and Shannon entropy were used as the features extractors.

Parameters:SVM Classification rate (%)Results:db6 appears to be the most appropriate wavelet function for this application

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COMPARATIVE STUDY OF DIFFERENT WAVELETSFOR HYDROLOGIC FORECASTING (R.MAHESWARAN, 2012)

Description:this paper presents a comparative evaluation of different wavelet forms when employed forforecasting future states of various kinds of time series. Type of wavelet families used in thisstudy are db1(haar), db2,db3,db4,sym4,spline-B3.

Parameters:Mean absolute error (MAE), Root mean square error (RMSE), Nash Sutcliffe criteria (NSC)

Results:(i) For time series having short memory and transient features, wavelets with compact supportand reduced vanishing moments such as the Haar wavelet (db1) is recommended. (ii)Wavelets with wider support and higher vanishing moments such as the db2 and spline-Bwavelets are recommended for time series having long term memory and nonlinear featuresas seen from the obtained prediction accuracy. Overall, the results show that there is nouniversal wavelet function which suits all type of time series.

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SELECTION OF A SUITABLE MOTHER WAVELET FORANALYZING POWER SYSTEM FAULT TRANSIENTS (A.I.MEGAHED, 2008)

Description:In this paper, wavelet techniques are proposed for the analysis of power system transients.Mother wavelets have been used for this analysis such as Haar, Daubechies (db), Symlets,and Coiflets. It also shows the deviation between Matlab and theoretical (mathematicallycalculated) db-wavelets when they are used for the analysis of power system transient. Thesimulation study is carried out using PSCAD simulation program and Matlab wavelet toolbox.

Parameters:root mean square error (RMSE)Results:The results show that thdb4 (theoretical db4) is more suitable for voltage signals while thdb5(theoretical db5) for current signals

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OPTIMAL SELECTION OF MOTHER WAVELET FORACCURATE INFANT CRY CLASSIfiCATION (J.SARASWATHY ET.AL, 2014)

Description:Optimal wavelet is found using three different criteria namely the degree of similarity of motherwavelets, regularity of mother wavelets and accuracy of correct recognition duringclassification processes. Recorded normal and pathological infant cry signals are decomposedinto five levels using wavelet packet transform. Energy and entropy features are extracted atdifferent sub bands of cry signals and their effectiveness are tested with four supervisedneural network architectures.

Parameters:similarity (Cross correlation), regularity (decomposed wavelet coefficients ), classification rate

Results:Meyer’s wavelet (‘dmey’) is the best candidate among other mother wavelets (haar,daubechies, symlet, coiflet, biorthogonal and reverse biorthogonal) for the accurate neonatescry signal classification

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BEST BASIS-BASED WAVELET PACKET ENTROPY FEATUREEXTRACTION AND HIERARCHICAL EEG CLASSIFICATION FOREPILEPTIC DETECTION (DENG WANG,2011)

Description:

In this study, a hierarchical electroencephalogram (EEG) classification system for epileptic seizure detec- tion isproposed. The system includes the following three stages: (i) original EEG signals representation by wavelet packetcoefficients and feature extraction using the best basis-based wavelet packet entropy method, (ii) cross-validation (CV)method together with k-Nearest Neighbor (k-NN) classifier used in the training stage to hierarchical knowledge base(HKB) construction, and (iii) in the testing stage, computing classification accuracy and rejection rate using the top-ranked discriminative rules from the HKB. In this present work, five wavelet functions (represented in the MATLABWavelet toolbox) in common use, such as Daubechies, Coiflets, Symlets, Discrete Meyer Wavelet, Biorthogonal and itsre- verse version, were examined and compared with decomposition level of 3.

Parameters:

accuracy, reject rate

Results:

(1) in Daubechies family of wavelets, the Db1 type of wavelet provided the best classification results; (2) Coiflet withorder 4 (coif4) and the Symlet with or- der 7 (sym7) showed best results among the Coiflet and Symlet families oforthogonal wavelets, respectively; (3) in case of bior- thogonal types of wavelets, bior1.1 and bior 2.6 provided bestcom- pression results where as in case of reverse type of biorthogonal wavelets rbio3.1 provided better compressionresults; (4)

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COMPARATIVE STUDY OF DIFFERENT WAVELET BASEDNEURAL NETWORK MODELS FOR RAINFALL–RUNOFFMODELING (MUHAMMAD SHOAIB, 2014)

Description:The present study is therefore conducted to evaluate the effects of 23 mother waveletfunctions on the performance of the hybrid wavelet based artificial neural network rain- fall–runoff models. The hybrid Multilayer Perceptron Neural Network (MLPNN) and the RadialBasis Function Neural Network (RBFNN) models are developed in this study using both thecontinuous wavelet and the discrete wavelet transformation types. The performances of the 92developed wavelet based neu- ral network models with all the 23 mother wavelet functions arecompared with the neural network models developed without wavelet transformations.

Parameters:Root Mean Squared Error (RMSE) and the Nash– Sutcliffe Efficiency (NSE) coefficient

Results:It is found that among all the models tested, the discrete wavelet transform multilayerperceptron neural network (DWTMLPNN) and the discrete wavelet transform radial basis

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