The aim of the article is to present non-clasical copyrighted algorithm for prediction of time series, presenting macroeconomic indicators and stock market indices. The algorithm is based on artificial neural networks...The aim of the article is to present non-clasical copyrighted algorithm for prediction of time series, presenting macroeconomic indicators and stock market indices. The algorithm is based on artificial neural networks and multi-resolution analysis （the algorithm is based on Daubechies wavelet）. However, the main feature of the algorithm, which gives a good quality of the forecasts, is all included in the series analysis division into, a few partial under-series and prediction dependence on a number of other economic series. The algorithm used for the prediction, is copyrighted algorithm, labeled M.H-D in this article. Application of the algorithm was performed on a series presenting WIG 20. The forecast of WIG 20 was conditional on trading the Dow Jones, DAX, Nikkei, Hang Seng, taking into account the sliding time window. As an example application of copyrighted model, the forecast of WIG 20 for a period of two years, one year, six month was appointed. An empirical example is described. It shows that the proposed model can predict index with the scale of two years, one year, a half year and other intervals. Precision of prediction is satisfactory. An average absolute percentage error of each forecast was： 0.0099%---for two-year forecasts WIG 20; 0.0552%--for the annual forecast WIG 20; and 0.1788%---for the six-month forecasts WIG 20.展开更多
In this paper, we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form. We prove that the general non-separab...In this paper, we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form. We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form. This helps us to explicate the difficulty of constructing the non-separable variate wavlet basis and to hint how to construct non-separable variate wavlet basis.展开更多
Brain signal analysis plays a significant role in attaining data related to motor activities.The parietal region of the brain plays a vital role in muscular movements.This approach aims to demonstrate a unique techniq...Brain signal analysis plays a significant role in attaining data related to motor activities.The parietal region of the brain plays a vital role in muscular movements.This approach aims to demonstrate a unique technique to identify an ideal region of the human brain that generates signals responsible for muscular movements;perform statistical analysis to provide an absolute characterization of the signal and validate the obtained results using a prototype arm.This can enhance the practical implementation of these frequency extractions for future neuro-prosthetic applications and the characterization of neurological diseases like Parkinson’s disease(PD).To play out this handling method,electroencepha-logram(EEG)signals are gained while the subject is performing different wrist and elbow movements.Then,the frontal brain signals and just the parietal signals are separated from the obtained EEG signal by utilizing a band pass filter.Then,feature extraction is carried out using Fast Fourier Transform(FFT).Subse-quently,the extraction process is done by Daubechies(db4)and Haar wavelet(db1)in MATLAB and classified using the Levenberg-Marquardt Algorithm.The results of the frequency changes that occurred during various wrist move-ments in the parietal region are compared with the frequency changes that occurred in frontal EEG signals.This proposed algorithm also uses the deep learn-ing pattern analysis network to evaluate the matching sequence for each action that takes place.Maximum accuracy of 97.2%and maximum error range of 0.6684%are achieved during the analysis.Results of this research confirm that the Levenberg-Marquardt algorithm,along with the newly developed deep learn-ing hybrid PatternNet,provides a more accurate range of frequency changes than any other classifier used in previous works of literature.Based on the analysis,the peak-to-peak value is used to define the threshold for the prototype arm,which performs all the intended degrees of freedom(DOF),verifying the results.These results would aid the speci展开更多
A 1-D and 2-D Daubechies 5 (db5) discrete wavelet shrinkage methods using a 10 level decomposition was applied to white light lidar data particularly at 350 nm and 550 nm backscattered signal. At 350 nm, the backscatt...A 1-D and 2-D Daubechies 5 (db5) discrete wavelet shrinkage methods using a 10 level decomposition was applied to white light lidar data particularly at 350 nm and 550 nm backscattered signal. At 350 nm, the backscattered signal is very weak as compared to 550 nm backscattered signal because of the spectral intensity distribution of the generated white light. The 1-D and 2-D wavelet shrinkage method gave a much better result as compared with the moving average method. However, the 2-D wavelet shrinkage method produced a much better denoised lidar signal compared with the 1-D wavelet shrinkage method. This is indicated by the 142% increase in correlation coefficient between the 2-D denoised lidar signal and the 800 nm original lidar signal as compared with only 12% increase in correlation coefficient for the 1-D denoised lidar signal. The 2-D wavelet shrinkage method also gave a much higher SNR value of 65.9 compared to 1-D which is 38.8.展开更多
In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the c...In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.展开更多
This paper presents an algorithm based on the wavelet decomposition, for feature extraction from the Electrocardiogram (ECG) signal and recognition of three types of Ventricular Arrhythmias using neural networks. A se...This paper presents an algorithm based on the wavelet decomposition, for feature extraction from the Electrocardiogram (ECG) signal and recognition of three types of Ventricular Arrhythmias using neural networks. A set of Discrete Wavelet Transform (DWT) coefficients, which contain the maximum information about the arrhythmias, is selected from the wavelet decomposition. These coefficients are fed to the feed forward neural network which classifies the arrhythmias. The algorithm is applied on the ECG registrations from the MIT-BIH arrhythmia and malignant ventricular arrhythmia databases. We applied Daubechies 4 wavelet in our algorithm. The wavelet decomposition enabled us to perform the task efficiently and produced reliable results.展开更多
In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes...In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes. Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations. Furthermore, they have high-order accuracy in smooth regions and good resolution of singularities.展开更多
The aim of this study is to recognize the best and suitable wavelet family for analyzing cognitive memory using Electroencephalograph (EEG) signal. The participant was given some visual stimuli during the study phase,...The aim of this study is to recognize the best and suitable wavelet family for analyzing cognitive memory using Electroencephalograph (EEG) signal. The participant was given some visual stimuli during the study phase, which were a sequence of pictures that had to be remembered to acquire the EEG signal. The Neurofax EEG 9200 was used to record the acquisition of cognitive memory at channel Fz. The raw EEG signals were analyzed using Wavelet Transform. A lot of mother wavelets can be used for analyzing the signal, but do not lose any information on the wavelet, some predictions must be made beforehand. The criteria of the EEG signal were narrowed down to the Daubechies, Symlets and Coiflets, and it is the final selection depending on their Mean Square Error (MSE). The best solution would have the least difference between the original and constructed signal. Results indicated that the Daubechies wavelet at a level of decomposition of 4 (db4) was the most suitable wavelet for pre-processing the raw EEG signal of cognitive memory. To conclude, choosing the suitable wavelet family is more important than relying on the MSE value alone to successfully perform a wavelet transformation.展开更多
In this paper, collocation method based on Bernoulli and Galerkin method based on wavelet are proposed for solving nonhomogeneous heat and wave equations. The two methods have the linear systems solved by suitable sol...In this paper, collocation method based on Bernoulli and Galerkin method based on wavelet are proposed for solving nonhomogeneous heat and wave equations. The two methods have the linear systems solved by suitable solvers. Several examples are given to examine the performance of these methods and a comparison is made.展开更多
Fatigue has a tremendously adverse impact on pilot performance.This study aims to explore the Biceps Brachii(BB),Rectus Femoris(RF),Flexor Carpi Radialis(FCR),and Tibialis Anterior(TA)activities of fighter pilots in t...Fatigue has a tremendously adverse impact on pilot performance.This study aims to explore the Biceps Brachii(BB),Rectus Femoris(RF),Flexor Carpi Radialis(FCR),and Tibialis Anterior(TA)activities of fighter pilots in the early and late combat stages,and the target hitting time.A total of 13 volunteers were recruited to conduct simulated combats inside a real fighter cockpit.The surface Electromyography(sEMG)was collected from all volunteers in the initial and final 20s of flight,and the target hitting time during three simulated combats was recorded.The root mean square(RMS)values of right BB and TA were significantly higher than the left side values(p<0.001),while insignificant differences were found in the RMS values between the bilateral RF and FCR.Compared to the early flight period,the median frequency(MF)values of BB and TA were significantly lower during the late flight period,and the RMS values were significantly higher(p<0.047).Contrastively,the RMS values of FCR and RF differed insignificantly during the late flight period.Regarding the target hitting time,a significant difference was noted between task 1 and rask3.Subjects exhibit varying levels of muscle fatigue for different muscle groups before and after the flight.The muscle fatigue levels are asymmetrical on the left and right sides.Muscle fatigue might reduce the pilots'operational ability.This study provides a reference for fighter pilot fatigue protection and treatment.展开更多
Watermarking is an effective approach to the copyright protection of digital media such as audio, image, and video. By inspiration from cryptography and considering the immensity of the set of all possible wavelets, i...Watermarking is an effective approach to the copyright protection of digital media such as audio, image, and video. By inspiration from cryptography and considering the immensity of the set of all possible wavelets, it is presented that in wavelet domain watermarking, the associated wavelet can be considered as the private key for encrypting the watermark so as to enhance the security of the embedded mark. This idea is partly supported by the fact that from computational complexity viewpoint, it is very time-consuming to search over the immense set of all candidate wavelets for the right one if no a priori knowledge is known about it. To verify our proposal, the standard image 'Lena' is first watermarked in a specific wavelet domain, the watermark recovery experiments are then conducted in the wavelet domain for a set of wavelets with the one used for mark embedded in it,separately. It follows from the experimental results that the mark can be recovered only in the right wavelet domain, which justifies the suggestion.展开更多
This paper gives a kind of series represeotation of the scaling functions φNand the associated wavelets . constructed by Daubechies. Based on Poission sununation formula, the functions gh. φN(x+N-1), φN (x+N),'...This paper gives a kind of series represeotation of the scaling functions φNand the associated wavelets . constructed by Daubechies. Based on Poission sununation formula, the functions gh. φN(x+N-1), φN (x+N),'''' φN (x+2N-2)(Ox 1) are linearly represented by φN(x), φN(x + 1),''', φN(x + 2N - 2) and some polynomials of order less than N, and φ0(x):= (φN (x), φN (x + 1),''', φN (x + N -2))t is translated into a solution of a nonhomogeneous vectorvalued functional equationwhere A0, A1 are (N - 1) x (N - 1)-dimensional matrices, the components of P0(x), P1 (x) are polynomials of order less than N. By iteration, .φ0(x) is eventualy represented as an (N - 1)-dimensional vector series with vector norm where and展开更多
文摘The aim of the article is to present non-clasical copyrighted algorithm for prediction of time series, presenting macroeconomic indicators and stock market indices. The algorithm is based on artificial neural networks and multi-resolution analysis （the algorithm is based on Daubechies wavelet）. However, the main feature of the algorithm, which gives a good quality of the forecasts, is all included in the series analysis division into, a few partial under-series and prediction dependence on a number of other economic series. The algorithm used for the prediction, is copyrighted algorithm, labeled M.H-D in this article. Application of the algorithm was performed on a series presenting WIG 20. The forecast of WIG 20 was conditional on trading the Dow Jones, DAX, Nikkei, Hang Seng, taking into account the sliding time window. As an example application of copyrighted model, the forecast of WIG 20 for a period of two years, one year, six month was appointed. An empirical example is described. It shows that the proposed model can predict index with the scale of two years, one year, a half year and other intervals. Precision of prediction is satisfactory. An average absolute percentage error of each forecast was： 0.0099%---for two-year forecasts WIG 20; 0.0552%--for the annual forecast WIG 20; and 0.1788%---for the six-month forecasts WIG 20.
基金the National Natural Science Foundation of China (No.69982002) and theOpening Foundation of National Mobile Communications Res
文摘In this paper, we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form. We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form. This helps us to explicate the difficulty of constructing the non-separable variate wavlet basis and to hint how to construct non-separable variate wavlet basis.
文摘Brain signal analysis plays a significant role in attaining data related to motor activities.The parietal region of the brain plays a vital role in muscular movements.This approach aims to demonstrate a unique technique to identify an ideal region of the human brain that generates signals responsible for muscular movements;perform statistical analysis to provide an absolute characterization of the signal and validate the obtained results using a prototype arm.This can enhance the practical implementation of these frequency extractions for future neuro-prosthetic applications and the characterization of neurological diseases like Parkinson’s disease(PD).To play out this handling method,electroencepha-logram(EEG)signals are gained while the subject is performing different wrist and elbow movements.Then,the frontal brain signals and just the parietal signals are separated from the obtained EEG signal by utilizing a band pass filter.Then,feature extraction is carried out using Fast Fourier Transform(FFT).Subse-quently,the extraction process is done by Daubechies(db4)and Haar wavelet(db1)in MATLAB and classified using the Levenberg-Marquardt Algorithm.The results of the frequency changes that occurred during various wrist move-ments in the parietal region are compared with the frequency changes that occurred in frontal EEG signals.This proposed algorithm also uses the deep learn-ing pattern analysis network to evaluate the matching sequence for each action that takes place.Maximum accuracy of 97.2%and maximum error range of 0.6684%are achieved during the analysis.Results of this research confirm that the Levenberg-Marquardt algorithm,along with the newly developed deep learn-ing hybrid PatternNet,provides a more accurate range of frequency changes than any other classifier used in previous works of literature.Based on the analysis,the peak-to-peak value is used to define the threshold for the prototype arm,which performs all the intended degrees of freedom(DOF),verifying the results.These results would aid the speci
文摘A 1-D and 2-D Daubechies 5 (db5) discrete wavelet shrinkage methods using a 10 level decomposition was applied to white light lidar data particularly at 350 nm and 550 nm backscattered signal. At 350 nm, the backscattered signal is very weak as compared to 550 nm backscattered signal because of the spectral intensity distribution of the generated white light. The 1-D and 2-D wavelet shrinkage method gave a much better result as compared with the moving average method. However, the 2-D wavelet shrinkage method produced a much better denoised lidar signal compared with the 1-D wavelet shrinkage method. This is indicated by the 142% increase in correlation coefficient between the 2-D denoised lidar signal and the 800 nm original lidar signal as compared with only 12% increase in correlation coefficient for the 1-D denoised lidar signal. The 2-D wavelet shrinkage method also gave a much higher SNR value of 65.9 compared to 1-D which is 38.8.
基金Supported by the Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities(ZZQ10010)Supported by the Fund for the Doctoral Program of Higher Education(20090141120010)
文摘In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.
文摘This paper presents an algorithm based on the wavelet decomposition, for feature extraction from the Electrocardiogram (ECG) signal and recognition of three types of Ventricular Arrhythmias using neural networks. A set of Discrete Wavelet Transform (DWT) coefficients, which contain the maximum information about the arrhythmias, is selected from the wavelet decomposition. These coefficients are fed to the feed forward neural network which classifies the arrhythmias. The algorithm is applied on the ECG registrations from the MIT-BIH arrhythmia and malignant ventricular arrhythmia databases. We applied Daubechies 4 wavelet in our algorithm. The wavelet decomposition enabled us to perform the task efficiently and produced reliable results.
基金the National Natural Science Foundation of China(No.10571178)
文摘In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes. Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations. Furthermore, they have high-order accuracy in smooth regions and good resolution of singularities.
文摘The aim of this study is to recognize the best and suitable wavelet family for analyzing cognitive memory using Electroencephalograph (EEG) signal. The participant was given some visual stimuli during the study phase, which were a sequence of pictures that had to be remembered to acquire the EEG signal. The Neurofax EEG 9200 was used to record the acquisition of cognitive memory at channel Fz. The raw EEG signals were analyzed using Wavelet Transform. A lot of mother wavelets can be used for analyzing the signal, but do not lose any information on the wavelet, some predictions must be made beforehand. The criteria of the EEG signal were narrowed down to the Daubechies, Symlets and Coiflets, and it is the final selection depending on their Mean Square Error (MSE). The best solution would have the least difference between the original and constructed signal. Results indicated that the Daubechies wavelet at a level of decomposition of 4 (db4) was the most suitable wavelet for pre-processing the raw EEG signal of cognitive memory. To conclude, choosing the suitable wavelet family is more important than relying on the MSE value alone to successfully perform a wavelet transformation.
文摘In this paper, collocation method based on Bernoulli and Galerkin method based on wavelet are proposed for solving nonhomogeneous heat and wave equations. The two methods have the linear systems solved by suitable solvers. Several examples are given to examine the performance of these methods and a comparison is made.
基金the National Military Commission Logistics Department[Grant number:BZZ18J004].
文摘Fatigue has a tremendously adverse impact on pilot performance.This study aims to explore the Biceps Brachii(BB),Rectus Femoris(RF),Flexor Carpi Radialis(FCR),and Tibialis Anterior(TA)activities of fighter pilots in the early and late combat stages,and the target hitting time.A total of 13 volunteers were recruited to conduct simulated combats inside a real fighter cockpit.The surface Electromyography(sEMG)was collected from all volunteers in the initial and final 20s of flight,and the target hitting time during three simulated combats was recorded.The root mean square(RMS)values of right BB and TA were significantly higher than the left side values(p<0.001),while insignificant differences were found in the RMS values between the bilateral RF and FCR.Compared to the early flight period,the median frequency(MF)values of BB and TA were significantly lower during the late flight period,and the RMS values were significantly higher(p<0.047).Contrastively,the RMS values of FCR and RF differed insignificantly during the late flight period.Regarding the target hitting time,a significant difference was noted between task 1 and rask3.Subjects exhibit varying levels of muscle fatigue for different muscle groups before and after the flight.The muscle fatigue levels are asymmetrical on the left and right sides.Muscle fatigue might reduce the pilots'operational ability.This study provides a reference for fighter pilot fatigue protection and treatment.
基金Funded by the visit scholar Foundation of the Electrooptical Technique & System key Lab of Chinese Ministry of Education in Chongqing.
文摘Watermarking is an effective approach to the copyright protection of digital media such as audio, image, and video. By inspiration from cryptography and considering the immensity of the set of all possible wavelets, it is presented that in wavelet domain watermarking, the associated wavelet can be considered as the private key for encrypting the watermark so as to enhance the security of the embedded mark. This idea is partly supported by the fact that from computational complexity viewpoint, it is very time-consuming to search over the immense set of all candidate wavelets for the right one if no a priori knowledge is known about it. To verify our proposal, the standard image 'Lena' is first watermarked in a specific wavelet domain, the watermark recovery experiments are then conducted in the wavelet domain for a set of wavelets with the one used for mark embedded in it,separately. It follows from the experimental results that the mark can be recovered only in the right wavelet domain, which justifies the suggestion.
文摘This paper gives a kind of series represeotation of the scaling functions φNand the associated wavelets . constructed by Daubechies. Based on Poission sununation formula, the functions gh. φN(x+N-1), φN (x+N),'''' φN (x+2N-2)(Ox 1) are linearly represented by φN(x), φN(x + 1),''', φN(x + 2N - 2) and some polynomials of order less than N, and φ0(x):= (φN (x), φN (x + 1),''', φN (x + N -2))t is translated into a solution of a nonhomogeneous vectorvalued functional equationwhere A0, A1 are (N - 1) x (N - 1)-dimensional matrices, the components of P0(x), P1 (x) are polynomials of order less than N. By iteration, .φ0(x) is eventualy represented as an (N - 1)-dimensional vector series with vector norm where and
