Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-t...Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.展开更多
The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was...The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was used to decompose two blasting seismic signals with the continuous wavelet transforms (CWT). The resultshows that wavelet analysis is the better method to help us determine the essential factors which create damage effectsthan Fourier analysis.展开更多
Continuous improvements in very-large-scale integration(VLSI)technology and design software have significantly broadened the scope of digital signal processing(DSP)applications.The use of application-specific integrat...Continuous improvements in very-large-scale integration(VLSI)technology and design software have significantly broadened the scope of digital signal processing(DSP)applications.The use of application-specific integrated circuits(ASICs)and programmable digital signal processors for many DSP applications have changed,even though new system implementations based on reconfigurable computing are becoming more complex.Adaptable platforms that combine hardware and software programmability efficiency are rapidly maturing with discrete wavelet transformation(DWT)and sophisticated computerized design techniques,which are much needed in today’s modern world.New research and commercial efforts to sustain power optimization,cost savings,and improved runtime effectiveness have been initiated as initial reconfigurable technologies have emerged.Hence,in this paper,it is proposed that theDWTmethod can be implemented on a fieldprogrammable gate array in a digital architecture(FPGA-DA).We examined the effects of quantization on DWTperformance in classification problems to demonstrate its reliability concerning fixed-point math implementations.The Advanced Encryption Standard(AES)algorithm for DWT learning used in this architecture is less responsive to resampling errors than the previously proposed solution in the literature using the artificial neural networks(ANN)method.By reducing hardware area by 57%,the proposed system has a higher throughput rate of 88.72%,reliability analysis of 95.5%compared to the other standard methods.展开更多
Based on the characteristics of surface acoustic wave(SAW) devices, the theory for realizing wavelet transform (WT) by SAW is deduced. Simulated experiment shows that the method of implementing WT using SAW devices ha...Based on the characteristics of surface acoustic wave(SAW) devices, the theory for realizing wavelet transform (WT) by SAW is deduced. Simulated experiment shows that the method of implementing WT using SAW devices has virtues of high speed and utility and is compatible with digital technique. It is important to implement wavelet transform.展开更多
A new method of resolving overlapped peak, Fourier self-deconvolution （FSD） using approximation CN obtained from frequency domain wavelet transform of F（ω） yielded by Fourier transform of overlapped peak signals ...A new method of resolving overlapped peak, Fourier self-deconvolution （FSD） using approximation CN obtained from frequency domain wavelet transform of F（ω） yielded by Fourier transform of overlapped peak signals f（t） as the linear function, was presented in this paper. Compared with classical FSD, the new method exhibits excellent resolution for different overlapped peak signals such as HPLC signals, and have some characteristics such as an extensive applicability for any overlapped peak shape signals and a simple operation because of no selection procedure of the linear function. Its excellent resolution for those different overlapped peak signals is mainly because F（ω） obtained from Fourier transform of f（t） and CN obtained from wavelet transform of F（ω） have the similar linearity and peak width. The effect of those fake peaks can be eliminated by the algorithm proposed by authors. This method has good potential in the process of different overlapped peak signals.展开更多
This paper presents a novel method for radar emitter signal recognition. First, wavelet packet transform （WPT） is introduced to extract features from radar emitter signals. Then, rough set theory is used to select t...This paper presents a novel method for radar emitter signal recognition. First, wavelet packet transform （WPT） is introduced to extract features from radar emitter signals. Then, rough set theory is used to select the optimal feature subset with good discriminability from original feature set, and support vector machines （SVMs） are employed to design classifiers. A large number of experimental results show that the proposed method achieves very high recognition rates for 9 radar emitter signals in a wide range of signal-to-noise rates, and proves a feasible and valid method.展开更多
In this paper, the Raman spectrum signal de-noising based on stationary wavelet transform is discussed. Haar wavelet is selected to decompose the Raman spectrum signal for several levels based on stationary wavelet tr...In this paper, the Raman spectrum signal de-noising based on stationary wavelet transform is discussed. Haar wavelet is selected to decompose the Raman spectrum signal for several levels based on stationary wavelet transform. The noise mean square j is estimated by the wavelet details at every level, and the wavelet details toward 0 by a threshold , where n is length of the detail, then recovery signal is reconstructed. Experimental results show this method not only suppresses noise effectively, but also preserves as many target characteristics of original signal as possible. This de-noising method offers a very attractive alternative to Raman spectrum signal noise suppress.展开更多
Investigating characteristics of spline wavelet, we found that if the two-order spline function, the derivative function of the three-order B spline function, is used as the wavelet base function, the spline wavelet t...Investigating characteristics of spline wavelet, we found that if the two-order spline function, the derivative function of the three-order B spline function, is used as the wavelet base function, the spline wavelet transform has both the property of denoising and that of differential. As a result, the relation between the spline wavelet transform and the differential was studied in theory. Experimental results show that the spline wavelet transform can well be applied to the differential of the electroanalytical signal. Compared with other kinds of wavelet transform, the spline wavelet transform has a characteristic of differential. Compared with the digital differentia] and simulative differential with electronic circuit, the spline wavelet transform not only can carry out denoising and differential for a signal, but also has the advantages of simple operation and small quantity of calculation, because step length, RC constant and other kinds of parameters need not be selected. Compared with展开更多
It is well known that the Orthogonal Frequency Division Multiplexing （ OFDM ） system has a high ability to overcome the effect of multipath and can obtain high spectral efficiency in the wireless communication chann...It is well known that the Orthogonal Frequency Division Multiplexing （ OFDM ） system has a high ability to overcome the effect of multipath and can obtain high spectral efficiency in the wireless communication channel. However, avoid Interchannel Interference （ICI） and Intersymbol Interference （ISI） in wireless channel, a guard interval longer than channel delay is used in conventional OFDM system, which cause the efficiency of bandwidth usage reduced. Due to the superior spectral containment of wavelets, this paper proposed a new OFDM system based on Lifting Wavelet Transform （LWT-OFDM）, which adopts lifting wavelet transform to replace the conventional Fourier transform. This new OFDM system doesn＇t need the Cyclic Prefix （CP） so its structure is more simply than FFT-OFDM and its algorithm is as simply as FFT-OFDM. The new LWT-OFDM system can mitigates some disadvantages of FFT-OFDM system, such as a relatively large peak-to-average power ratio, more sensitive to carrier frequency offset and phase noise. Simulations show that the LWT-OFDM system is more effective and attractive than conversional FFT-OFDM in wireless channel.展开更多
An analysis of the received signal of array antennas shows that the received signal has multi-resolution characteristics, and hence the wavelet packet theory can be used to detect the signal. By emplying wavelet packe...An analysis of the received signal of array antennas shows that the received signal has multi-resolution characteristics, and hence the wavelet packet theory can be used to detect the signal. By emplying wavelet packet theory to adaptive beamforming, a wavelet packet transform-based adaptive beamforming algorithm (WP-ABF) is proposed . This WP-ABF algorithm uses wavelet packet transform as the preprocessing, and the wavelet packet transformed signal uses least mean square algorithm to implement the ~adaptive beamforming. White noise can be wiped off under wavelet packet transform according to the different characteristics of signal and white under the wavelet packet transform. Theoretical analysis and simulations demonstrate that the proposed WP-ABF algorithm converges faster than the conventional adaptive beamforming algorithm and the wavelet transform-based beamforming algorithm. Simulation results also reveal that the convergence of the algorithm relates closely to the wavelet base and series; that is, the algorithm convergence gets better with the increasing of series, and for the same series of wavelet base the convergence gets better with the increasing of regularity.展开更多
Piezoelectric sensor array-based spatial filter technology is a new promising method presented in research area of structural health monitoring （SHM） in the recent years. To apply this method to composite structures...Piezoelectric sensor array-based spatial filter technology is a new promising method presented in research area of structural health monitoring （SHM） in the recent years. To apply this method to composite structures and give the actual position of damage, this paper proposes a spatial filter-based damage imaging method improved by complex Shannon wavelet transform. The basic principle of spatial filter is analyzed first. Then, this paper proposes a method of using complex Shannon wavelet transform to construct analytic signals of time domain signals of PZT sensors array. The analytic signals are synthesized depending on the principle of the spatial filter to give a damage imaging in the form of angle-time. A method of converting the damage imaging to the form of angle-distance is discussed. Finally, an aircraft composite oil tank is adopted to validate the damage imaging method. The validating results show that this method can recognize angle and distance of damage successfully.展开更多
Because muzzle impulse noise could cause damage to or have an intluence on the operator, tiae ettecnve protecnve measures should be taken. Therefore, correct analysis of impulse noise characteristics is very significa...Because muzzle impulse noise could cause damage to or have an intluence on the operator, tiae ettecnve protecnve measures should be taken. Therefore, correct analysis of impulse noise characteristics is very significant. Considering the shortcomings of fast Fourier transform method （FFT） in analysis of muzzle impulse noise frequency characteristics, wavelet energy spectrum method is put forward. Based on specific experiment data, the frequency characteristics and spectral energy dis tribution can be obtained. The experiment results show that wavelet energy spectrum method is applicable in muzzle impulse noise characteristic analysis.展开更多
With the development of human-computer interaction technology,brain-computer interface(BCI)has been widely used in medical,entertainment,military,and other fields.Imagined speech is the latest paradigm of BCI and repr...With the development of human-computer interaction technology,brain-computer interface(BCI)has been widely used in medical,entertainment,military,and other fields.Imagined speech is the latest paradigm of BCI and represents the mental process of imagining a word without making a sound or making clear facial movements.Imagined speech allows patients with physical disabilities to communicate with the outside world and use smart devices through imagination.Imagined speech can meet the needs of more complex manipulative tasks considering its more intuitive features.This study proposes a classification method of imagined speech Electroencephalogram(EEG)signals with discrete wavelet transform(DWT)and support vector machine(SVM).An open dataset that consists of 15 subjects imagining speaking six different words,namely,up,down,left,right,backward,and forward,is used.The objective is to improve the classification accuracy of imagined speech BCI system.The features of EEG signals are first extracted by DWT,and the imagined words are clas-sified by SVM with the above features.Experimental results show that the proposed method achieves an average accuracy of 61.69%,which is better than those of existing methods for classifying imagined speech tasks.展开更多
It is desirable to develop new signal processing techniques for effectively extracting reflected waves under the strong interferences of borehole guided waves. We presented a multi-scale semblance method for the separ...It is desirable to develop new signal processing techniques for effectively extracting reflected waves under the strong interferences of borehole guided waves. We presented a multi-scale semblance method for the separation and velocity （slowness） analysis of the reflected waves and guided waves in borehole acoustic logging. It was specially designed for the newly developed tools with ultra-long source- receiver spacing for acoustic reflection survey. This new method was a combination of the dual tree com- plex wavelets transform （DT-CWT） and the slowness travel time coherence （STC） method. Applications to the 3D finite difference （FD） modeling simulated data and to the field array sonic waveform signals have demonstrated the ability of this method to appropriately extract the reflected waves under severe interference from the guided waves and to suppress noise in the time-frequency domain.展开更多
In this paper, a new feature space for PD （partial discharge） signal separation is presented. Three typical PD defects were experimentally reproduced in a laboratory for obtaining independent PD sources. Signals wer...In this paper, a new feature space for PD （partial discharge） signal separation is presented. Three typical PD defects were experimentally reproduced in a laboratory for obtaining independent PD sources. Signals were acquired with a digital storage oscilloscope and then post-processed with DWT （discrete Wavelet transform） for de-noising. The new feature space for PD source separation was constructed with the variance of each Wavelet coefficient vector and was compared with an established feature space for PD source separation; based on the energy of DWT coefficient vectors. After a space reduction by mean of PCA （principal components analysis）, the separation capability among them was measured by comparing the final classification error after training a neural network Results showed that with this new feature space it is possible to separate different sources of PD signals. Later, the feature space proposed was used to separate two PD sources from a real equipment tested. Further analysis on the reduced feature space has shown the band location of PD signals information for separating purpose.展开更多
基金The National High Technology Research and Devel-opment Program of China (863Program) (No2002AA812038)
文摘Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.
文摘The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was used to decompose two blasting seismic signals with the continuous wavelet transforms (CWT). The resultshows that wavelet analysis is the better method to help us determine the essential factors which create damage effectsthan Fourier analysis.
基金This work was supported by King Saud University for funding this work through Researchers Supporting Project number(RSP-2021/387),King Saud University,Riyadh,Saudi Arabia。
文摘Continuous improvements in very-large-scale integration(VLSI)technology and design software have significantly broadened the scope of digital signal processing(DSP)applications.The use of application-specific integrated circuits(ASICs)and programmable digital signal processors for many DSP applications have changed,even though new system implementations based on reconfigurable computing are becoming more complex.Adaptable platforms that combine hardware and software programmability efficiency are rapidly maturing with discrete wavelet transformation(DWT)and sophisticated computerized design techniques,which are much needed in today’s modern world.New research and commercial efforts to sustain power optimization,cost savings,and improved runtime effectiveness have been initiated as initial reconfigurable technologies have emerged.Hence,in this paper,it is proposed that theDWTmethod can be implemented on a fieldprogrammable gate array in a digital architecture(FPGA-DA).We examined the effects of quantization on DWTperformance in classification problems to demonstrate its reliability concerning fixed-point math implementations.The Advanced Encryption Standard(AES)algorithm for DWT learning used in this architecture is less responsive to resampling errors than the previously proposed solution in the literature using the artificial neural networks(ANN)method.By reducing hardware area by 57%,the proposed system has a higher throughput rate of 88.72%,reliability analysis of 95.5%compared to the other standard methods.
文摘Based on the characteristics of surface acoustic wave(SAW) devices, the theory for realizing wavelet transform (WT) by SAW is deduced. Simulated experiment shows that the method of implementing WT using SAW devices has virtues of high speed and utility and is compatible with digital technique. It is important to implement wavelet transform.
基金the National Natural Science Foundation of China （No. 20275030） the Natural Science Foundation of Shaanxi Province in China （No. 2004B20）.
文摘A new method of resolving overlapped peak, Fourier self-deconvolution （FSD） using approximation CN obtained from frequency domain wavelet transform of F（ω） yielded by Fourier transform of overlapped peak signals f（t） as the linear function, was presented in this paper. Compared with classical FSD, the new method exhibits excellent resolution for different overlapped peak signals such as HPLC signals, and have some characteristics such as an extensive applicability for any overlapped peak shape signals and a simple operation because of no selection procedure of the linear function. Its excellent resolution for those different overlapped peak signals is mainly because F（ω） obtained from Fourier transform of f（t） and CN obtained from wavelet transform of F（ω） have the similar linearity and peak width. The effect of those fake peaks can be eliminated by the algorithm proposed by authors. This method has good potential in the process of different overlapped peak signals.
文摘This paper presents a novel method for radar emitter signal recognition. First, wavelet packet transform （WPT） is introduced to extract features from radar emitter signals. Then, rough set theory is used to select the optimal feature subset with good discriminability from original feature set, and support vector machines （SVMs） are employed to design classifiers. A large number of experimental results show that the proposed method achieves very high recognition rates for 9 radar emitter signals in a wide range of signal-to-noise rates, and proves a feasible and valid method.
基金This work was supported by the NationalN Natu-ral Science Foundation of China(No.59972001)and the Natural Science Foundation of Anhui Province,P.R.China(No.01044901).
文摘In this paper, the Raman spectrum signal de-noising based on stationary wavelet transform is discussed. Haar wavelet is selected to decompose the Raman spectrum signal for several levels based on stationary wavelet transform. The noise mean square j is estimated by the wavelet details at every level, and the wavelet details toward 0 by a threshold , where n is length of the detail, then recovery signal is reconstructed. Experimental results show this method not only suppresses noise effectively, but also preserves as many target characteristics of original signal as possible. This de-noising method offers a very attractive alternative to Raman spectrum signal noise suppress.
基金the National NaturalScience Foundation of China (Grant No. 29775018) the Natural Science Foundation of Shaanxi Province (Grant No. 98H07) the Special Foundation of the Provincial Education Commission of Shaanxi and the Postdoctoral Foundation of Ch
文摘Investigating characteristics of spline wavelet, we found that if the two-order spline function, the derivative function of the three-order B spline function, is used as the wavelet base function, the spline wavelet transform has both the property of denoising and that of differential. As a result, the relation between the spline wavelet transform and the differential was studied in theory. Experimental results show that the spline wavelet transform can well be applied to the differential of the electroanalytical signal. Compared with other kinds of wavelet transform, the spline wavelet transform has a characteristic of differential. Compared with the digital differentia] and simulative differential with electronic circuit, the spline wavelet transform not only can carry out denoising and differential for a signal, but also has the advantages of simple operation and small quantity of calculation, because step length, RC constant and other kinds of parameters need not be selected. Compared with
文摘It is well known that the Orthogonal Frequency Division Multiplexing （ OFDM ） system has a high ability to overcome the effect of multipath and can obtain high spectral efficiency in the wireless communication channel. However, avoid Interchannel Interference （ICI） and Intersymbol Interference （ISI） in wireless channel, a guard interval longer than channel delay is used in conventional OFDM system, which cause the efficiency of bandwidth usage reduced. Due to the superior spectral containment of wavelets, this paper proposed a new OFDM system based on Lifting Wavelet Transform （LWT-OFDM）, which adopts lifting wavelet transform to replace the conventional Fourier transform. This new OFDM system doesn＇t need the Cyclic Prefix （CP） so its structure is more simply than FFT-OFDM and its algorithm is as simply as FFT-OFDM. The new LWT-OFDM system can mitigates some disadvantages of FFT-OFDM system, such as a relatively large peak-to-average power ratio, more sensitive to carrier frequency offset and phase noise. Simulations show that the LWT-OFDM system is more effective and attractive than conversional FFT-OFDM in wireless channel.
文摘An analysis of the received signal of array antennas shows that the received signal has multi-resolution characteristics, and hence the wavelet packet theory can be used to detect the signal. By emplying wavelet packet theory to adaptive beamforming, a wavelet packet transform-based adaptive beamforming algorithm (WP-ABF) is proposed . This WP-ABF algorithm uses wavelet packet transform as the preprocessing, and the wavelet packet transformed signal uses least mean square algorithm to implement the ~adaptive beamforming. White noise can be wiped off under wavelet packet transform according to the different characteristics of signal and white under the wavelet packet transform. Theoretical analysis and simulations demonstrate that the proposed WP-ABF algorithm converges faster than the conventional adaptive beamforming algorithm and the wavelet transform-based beamforming algorithm. Simulation results also reveal that the convergence of the algorithm relates closely to the wavelet base and series; that is, the algorithm convergence gets better with the increasing of series, and for the same series of wavelet base the convergence gets better with the increasing of regularity.
基金National Natural Science Foundation of China (50830201,10872217)Aeronautical Science Foundation of China (20090952015)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(20103218110005)National Science Foundation of the General Program of Jiangsu Higher Education Institutions (09KJD520005)
文摘Piezoelectric sensor array-based spatial filter technology is a new promising method presented in research area of structural health monitoring （SHM） in the recent years. To apply this method to composite structures and give the actual position of damage, this paper proposes a spatial filter-based damage imaging method improved by complex Shannon wavelet transform. The basic principle of spatial filter is analyzed first. Then, this paper proposes a method of using complex Shannon wavelet transform to construct analytic signals of time domain signals of PZT sensors array. The analytic signals are synthesized depending on the principle of the spatial filter to give a damage imaging in the form of angle-time. A method of converting the damage imaging to the form of angle-distance is discussed. Finally, an aircraft composite oil tank is adopted to validate the damage imaging method. The validating results show that this method can recognize angle and distance of damage successfully.
文摘Because muzzle impulse noise could cause damage to or have an intluence on the operator, tiae ettecnve protecnve measures should be taken. Therefore, correct analysis of impulse noise characteristics is very significant. Considering the shortcomings of fast Fourier transform method （FFT） in analysis of muzzle impulse noise frequency characteristics, wavelet energy spectrum method is put forward. Based on specific experiment data, the frequency characteristics and spectral energy dis tribution can be obtained. The experiment results show that wavelet energy spectrum method is applicable in muzzle impulse noise characteristic analysis.
基金supported in part by the Fundamental Research Funds for the Central Universities(xcxjh20210104).
文摘With the development of human-computer interaction technology,brain-computer interface(BCI)has been widely used in medical,entertainment,military,and other fields.Imagined speech is the latest paradigm of BCI and represents the mental process of imagining a word without making a sound or making clear facial movements.Imagined speech allows patients with physical disabilities to communicate with the outside world and use smart devices through imagination.Imagined speech can meet the needs of more complex manipulative tasks considering its more intuitive features.This study proposes a classification method of imagined speech Electroencephalogram(EEG)signals with discrete wavelet transform(DWT)and support vector machine(SVM).An open dataset that consists of 15 subjects imagining speaking six different words,namely,up,down,left,right,backward,and forward,is used.The objective is to improve the classification accuracy of imagined speech BCI system.The features of EEG signals are first extracted by DWT,and the imagined words are clas-sified by SVM with the above features.Experimental results show that the proposed method achieves an average accuracy of 61.69%,which is better than those of existing methods for classifying imagined speech tasks.
基金National Natural Science Foundation of China (the project No.is 50674098)the National 863 Project of China (Grant 2006AA06Z207)theNational Basic Research Program of China (973 Program,2007CB209601).
文摘It is desirable to develop new signal processing techniques for effectively extracting reflected waves under the strong interferences of borehole guided waves. We presented a multi-scale semblance method for the separation and velocity （slowness） analysis of the reflected waves and guided waves in borehole acoustic logging. It was specially designed for the newly developed tools with ultra-long source- receiver spacing for acoustic reflection survey. This new method was a combination of the dual tree com- plex wavelets transform （DT-CWT） and the slowness travel time coherence （STC） method. Applications to the 3D finite difference （FD） modeling simulated data and to the field array sonic waveform signals have demonstrated the ability of this method to appropriately extract the reflected waves under severe interference from the guided waves and to suppress noise in the time-frequency domain.
文摘In this paper, a new feature space for PD （partial discharge） signal separation is presented. Three typical PD defects were experimentally reproduced in a laboratory for obtaining independent PD sources. Signals were acquired with a digital storage oscilloscope and then post-processed with DWT （discrete Wavelet transform） for de-noising. The new feature space for PD source separation was constructed with the variance of each Wavelet coefficient vector and was compared with an established feature space for PD source separation; based on the energy of DWT coefficient vectors. After a space reduction by mean of PCA （principal components analysis）, the separation capability among them was measured by comparing the final classification error after training a neural network Results showed that with this new feature space it is possible to separate different sources of PD signals. Later, the feature space proposed was used to separate two PD sources from a real equipment tested. Further analysis on the reduced feature space has shown the band location of PD signals information for separating purpose.
