Advanced Signal Processing Techniques for Feature Extraction in Data Mining

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1 Volume 9 o.9, April 0 Advanced Signal Processing Techniques or Feature Extraction in Data Mining Maya ayak Proessor Orissa Engineering College BPUT, Bhubaneswar Bhawani Sankar Panigrahi Asst. Proessor Orissa Engineering College BPUT, Bhubaneswar ABSTRACT This paper gives a description o various signal processing techniques that are in use or processing time series databases or extracting relevant eatures or pattern recognition. In addition to describe the normally used signal processing methods, we also present a novel signal processing technique, which is a modiication o the well-known Short-Time Fourier Transorm (STFT) and Wavelet Transorm or extracting suitable eatures or both visual and automatic classiication o non-stationary time-series databases [3][5]. Although the new signal processing technique is useul or speech, medical, inancial, and other types o time varying databases, only the power network disturbance time series is used or computing eatures or visual and automatic recognition. General Terms Signal processing, Time series database, pattern recognition, data mining. Keywords Feature extraction, Short Time Fourier Transorm (STFT), Wavelet Transorm, S-transorm, Transient, Swell, and Sag.. ITRODUCTIO Spectral analysis using the Fourier Transorm is a powerul technique or stationary time series where the characteristics o the signal do not change with time. For non-stationary time series, the spectral content changes with time and hence timeaveraged amplitude spectrum ound by using Fourier Transorm is inadequate to track the changes in the signal magnitude, requency or phase. The signals with time varying characteristics that occur in electrical networks with power electronically controlled static devices, geophysical systems such as earth tremors, speech and acoustic systems, cardio vascular systems, inancial and currency markets are typical cases or consideration o the advanced signal processing techniques, such as Short Time Fourier Transorm and more recently Wavelet Transorms or mining time-series databases.advanced signal processing techniques such as Wavelet transorm and interesting modiication o wavelet transorm approach known as S-Transorm are used or extracting pertinent eature vectors rom sampled time series data either obtained by simulation o ield test. The S- Transorm on the other hand produces a time-requency representation o a time series. It uniquely combines a requency dependent resolution that simultaneously localizes the real and imaginary spectra. The basic unctions or the S-Transorm are Gaussian modulated cosinusoids, so that it is possible to use intuitive notions o cosinusoidal requencies in interpreting and exploiting the resulting time-requency spectrum. With the advantage o ast loss-less invertibility rom time to timerequency; and back to the time domain, the usage o the S- transorm is very analogous to the Fourier Transorm. In the case o non-stationary disturbances with noisy data, the S- Transorm provides patterns that closely resemble the disturbance type and thus requires simple classiication procedure. Further, the S-transorm can be derived rom the continuous wavelet transorm (CWT) choosing a speciic mother wavelet and multiplying a phase correction actor. Thus the S-Transorm can be interpreted as a phase corrected continuous wavelet transorm. The S-Transorm approach provides a variable window, inversely proportional to requency, thus acilitating the capture o both low and high requency transient s signals o the electricity supply network subected to disturbances.. PHASE CORRECTED WAVELET: S- TRASFORM The S-Transorm o a time series y( t ) is deined as: i ( τ ) S( τ, ) y( t) g t, e π t (.) where the Gaussian modulation unction g(τ, ) is given by g( τ, ) e σ π t (.) with the spread parameter inversely proportional to the requency σ the inal expression becomes ( τt ) iπ t S( τ, ) y( t) e e dt π where is the requency, t and τ, are both time. (.3) (.4) The S-Transorm o the continuous time unction y( t ) can also be deined as a CWT with a speciic mother wavelet W( τ, d) multiplied by a phase actor. 30

2 Volume 9 o.9, April 0 iπ τ S( τ, ) e W ( τ, d) (.5) where the mother wavelet is deined as and ψ ( t, ) e π ( τ ) (.6) W, d y( t) w( tτ, d) dt t e iπt (.7) where the dilation actor is the inverse o the requency.the phase actor in equation (.9) is in act a phase correction o the deinition o the Wavelet Transorm [9][0]. It eliminates the concept o wavelet analysis by separating the mother wavelet into two parts, the slowly varying envelope (the Gaussian unction) that localizes in time, and the oscillatory exponential kernel that selects the requency being localized. It is the time localizing Gaussian that is translated while the oscillatory exponential kernel remains stationary. By not translating the oscillatory exponential kernel, The S-Transorm localizes the real and imaginary components o the spectrum[] independently, localizing the phase spectrum as well as the amplitude spectrum. This is reerred to as absolutely reerenced phase inormation.the choice o windowing unction is not limited to the Gaussian unction. Other windowing unction was tried with success. The inverse S-Transorm is given by τ τ iπ t y( t) S(, ) d e d and since S( τ, ) is complex, it can be written as where A(, ) S( τ, ) A(, ) e iθ τ (.8) (, ) τ (.9) τ is the amplitude o the S-spectrum and (, ) θ τ is the phase o the S-spectrum. The phase spectrum is an improvement on the wavelet transorm in that the average o all the local spectra does indeed give the same result as the Fourier Transorm.Equation (.4) is derived on the assumption that the spread o the Gaussian modulation unction is proportional to the inverse o requency. To increase the requency resolution, the spread o the Gaussian window σis written as α σ and the generalized S-Transorm is obtained as ( τt ) α iπ t S( τ, ) y( t) e e dt α π (.) (.0) In equation (.0) α controls the requency resolution. I α is above, the requency resolution would increase. Likewise i α is below, the time resolution improves. The S-Transorm is a linear operation on the signal y( t ). I additive noise is added to the signal y( t ),it can be modeled as y noisy (t) y( t ) +η(t). The operation o the S-Transorm leads to { noisy ( )} { ( )} { η( )} S y t S y t + S t (.) The amplitude and phase spectrum o S-transorm are given by A abs( S( n, )) φ( n, ) ang (Im( S( n, ) ) / Re( (.3) S( n, ) )) The discrete version S-Transorm o a signal is obtained as S[, n] Y m 0 πm i [ m+ nw ] [ m, n] e (.4) where Y[m + n] is obtained by shiting the discrete Fourier Transorm (DFT) o y(k) by n, Y[m] being given and k 0 πmk Y[ m] y[ k] e (.5) -πm β W[m+n] e n (.6), m and n 0,,.., -. Another version o the discrete S- Transorm used or computation S[m,n] e πnm - πnk - i * k- [ ] x m+k w (k,n)e (.7) or m,,, M and n 0,,, / (.8) where M is the number o data points o the signal y[m], is the width o the window, the signal vector y[m] is padded at the beginning or at the end with FOURIER TRASFORM The Fourier Transorm is one o the oldest and most powerul tools in signal processing. This transorm maps the signal in time domain to a requency domain where certain useul eatures about the signal can be seen. The Fourier Transorm o a signal y( t) is given as: iπ t Y( ) y( t) e dt and its inverse relationship is: (3.) y( t) Y( ) e i π t d (3.)A discrete version o the Fourier Transorm called the Discrete Fourier Transorm (DFT) o a time series o length is deined as: iπ nkt T n Y y[ kt ] e (3.3) T k 0 where T is the sampling interval. The inverse relationship is: n y[ kt] Y e n 0 T iπ nkt T (3.4) 3

3 Volume 9 o.9, April 0 The time inormation is obscured in the phase inormation o the Fourier Transorm. The Fourier Transorm correctly detects the two requency components. The Fourier Transorm is thus not suitable or analyzing non-stationary signals. 4. SHORT TIME FOURIER TRASFORM The Short Time Fourier Transorm (STFT) is an attempt to improve on the traditional Fourier Transorm. The STFT is the result o repeatedly multiplying the signal with shited short time windows and perorming a Fourier Transorm on it. The STFT or a signal y( t) is deined as: π t STFT y t w t e dt i ( τ, ) ( ) ( τ ) (4.) where w(t) is the windowing unction. The purpose o the windowing unction is to dissect the signal to smaller segments where the segments o the signal are assumed to be stationary. The resulting spectrum o this window and the signal is the local spectrum. This localizing window is then translated along the time axis to produce local spectra or the entire range o time.due to the constant window used in the STFT, all parts o the signal are analyzed with the same resolution. This constant windowing is a drawback o the STFT because at high requency, good time resolution is needed while good requency resolution is needed at low requency. The requency resolution is proportional to the bandwidth o the windowing unction while time resolution is proportional to the length o the windowing unction. Consequently a short window is needed or good time resolution while a long window is needed or good requency resolution. This limitation is due to the Heisenberg- Gabor inequality that states that t * (4.) where t is the time resolution, is c w the requency resolution and Cw is a constant that is dependent on the type o windowing unction used.consequently in most applications, STFT must be used. 5. WAVELET TRASFORM AD MULTI-RESOLUTIO AALYSIS The Continuous Wavelet Transorm (CWT) associated with the mother wavelet ψ ( t) is deined as: W ( a, b) y( t) ψ ( t) dt * a, b (5.)where y( t ) is any square integrable unction, a is the scaling parameter, b is the translation parameter and ψ a, b ( t ) is the dilation and translation o the mother wavelet deined as: ψ ( ) a, b t t b ψ a a (5.) This CWT [9][0] provides a redundant representation o the signal in the sense that the entire support o W ( a, b) need not be used to recover y( t ). By only evaluating the CWT at dyadic intervals, the signal can be represented compactly as: ( ) ( ) ψ k ( ) y t d k t k (5.3) where d ( k) is called the discrete wavelet transorm (DWT) o y( t ) associated with the wavelet is a scaling unction ϕ ( t). The scaling unction along with the wavelet creates a multiresolution analysis (MRA) o the signal. The scaling unction o one level can be represented as a sum o a scaling unction o the next iner level. ϕ ( t) h( n) ϕ( t n) (5.4) n The wavelet is also related to the scaling unction by ϕ (5.5) n ψ ( t) h ( n) ( t n) scaling unction used to represent the signal as (5.6) y t c k t k d k t k o o ( ) o( ) ϕ( ) + ( ) ψ( ) k k o where o represents the coarsest scale spanned by the scaling unction.the scaling and wavelet coeicients o the signal y( t) can be evaluated by using a ilter bank o quadrature mirror ilters (QMF). c ( k) c ( m) h( m k) (5.7) m + (5.8) + m d ( k) c ( m) h ( m k) Equations (5.7) and (5.8) show that the coeicients at a coarser level can be attained by passing the coeicients at the iner level to their respective ilters ollowed by a decimation o two. The decomposition process is shown in Fig.5.. For a signal that is sampled at a requency higher than the yquist requency, the samples are used as c ( ) + m. A three level decomposition o time series data obtained rom power signal disturbances, sampled at.8 khz is shown below. The approximation coeicients contain the low requency inormation while the detail coeicients contain the high requency inormation o the oscillatory transient. d - detail level coeicientc - approximate level coeicient Fig. 5.. Three level wavelet decomposition 3

4 Volume 9 o.9, April 0 6. A QUALITATIVE COMPARISO BETWEE DWT AD S-TRASFORM FOR AALYSIS OF TIME SERIES EVETS The discrete wavelet transorm is one o the most popular tools used or power signal time series disturbance classiication today due to its multi-resolution capabilities and ast calculation o its coeicients. The eature vectors used or classiying the power signal time series events usually involve perorming some kind o transormation on the DWT coeicients, comparing between the DWT coeicients o the disturbance signal with the DWT coeicients o a pure signal, compressed DWT coeicients,and the direct use o the DWT coeicients.the ollowing igures show the -D plot o the S-Transorm with α0., and the 4-level decomposition o the DWT with db4 wavelet or some o the time series databases like the oscillatory transient, notch, swell, sag, interruption, harmonics, swell with harmonics and sag with harmonics, etc. 6. Oscillatory transient In Fig.6.. an oscillatory transient is clearly detected and localized by the S-Transorm. This localization ability o the S-Transorm could be used to quantiy the duration o the disturbance. By observing the concentric contours, we see that the transient is undergoing damping. While the transient event is detected or all requency values, it is possible to determine its requency by noting the location in requency o the highest contour. Fig. 6.. shows the 4 level decomposition o the same transient with the db4 wavelet. The transient is detected and localized very well by coeicients at all levels. This can determine the duration o the transient disturbances. Unlike the S-Transorm, we are not able to pin point the requency o the transient by looking at the DWT coeicients. This is because each level o the decomposition corresponds to a range o requencies. For example, in this case with the sampling requency set at.8 khz, the irst level coeicients are obtained by passing the samples to a band pass ilter whose requency band is between 6.4 khz-.8 khz. Level coeicients contain inormation o requency band 3. khz-6.4 khz, level 3 or.6 khz-3. khz and level 4 or 800Hz-.6 khz. Observing Fig.6.. we can guess that the transient requency is in level 3 or level 4 by looking at the magnitude o the detail coeicients at this level. The transient requency is actually 900Hz. 6. Impulsive Transient The S-Transorm correctly detects and localized the impulsive transient as shown in Fig. 6.. The impulsive transient is represented as a long line in the time-requency plane that last or a wide range o requencies. This is because a very short impulse in the time domain would result in a Fourier Transorm that spreads out or a wide range o requencies. In Fig.6.3., the DWT coeicients at all levels detect and localizes the impulsive transient disturbance. Fig.6.. Oscillatory transient S-Transorm output o oscillatory transient Fig.6.. Oscillatory transient Level 4 detail coeicients Level 3 detail coeicients Level detail coeicients Level detail coeicients Fig. 6.. Impulsive transient S-Transorm output o impulsive transient 6.3 Multiple notches The S-Transorm produces a unique representation o multiple notches. In Fig.6.3. the notches are represented as short lines in the time-requency plane. The length o the lines is much shorter than that or the impulsive transient. Only the deeper notches are detected. This law may be remedied by using a smaller value o the actor. Fig shows that the notches are accurately detected by DWT coeicients at level and. 33

5 Volume 9 o.9, April 0 The DWT coeicients look like random noise at higher levels Fig.6.3. Impulsive transient Level 4 detail coeicients Level 3 detail coeicients Level detail coeicients Level detail coeicients Fig Swell S-Transorm output o voltage Fig.6.3. Multiple notches S-Transorm output o multiple notches. Fig Multiple notches Level 4 detail coeicients Level 3 detail coeicients Level detail coeicients Level detail coeicients 6.4 Swell Swell is uniquely identiied by the S-Transorm in three distinct ways. Looking at the concentric contours in Fig.6.4., we see that the highest valued contour is located at the region o the swell. Furthermore i we look at the shape o the lowest valued contour, we see that its requency values increases at the time o the swell and decreases when the signal is back to its normal amplitude again.. Another easy way to see is to note that the number o contours in the swell region is larger than in the normal region. The DWT coeicients (Fig.6.4.) detect the time o the rise and all o the swell disturbance. Fig.6.4. Swell Level 4 detail coeicients Level 3 detail coeicients Level detail coeicients Level detail coeicients 6.5 Sag Fig.6.5. shows the S-Transorm output o sag. The highest contours are located at the beginning and end o the timerequency plane. The density o the contour decreases in the middle. This shows that there is a decrease in magnitude in the middle o the time axis. The lowest contour maintains a requency value at roughly 0.07 until the occurrence o the sag in which it rises in requency or a short time then decreases and settles at0.0 until the end o the sag. At the end o the sag its requency values rises to a peak and then settles down to its original value o The two peaks can be used to quantiy the length o the sag. The DWT in Fig.6.5. on the other hand does not produce a pattern that can be used to classiy the disturbance as sag. Looking at Fig.6.4. and Fig.6.5., we see that the DWT is unable to distinguish between swell and sag. Fig Voltage sag S-transorm output o voltage sag 34

6 Volume 9 o.9, April 0 Fig.6.5. Voltage sag Level 4 detail coeicients Level 3 detail coeicients Level detail coeicients Level detail coeicients 7. FEATURE SELECTIO 7. Based on Wavelet Transorm Our approach to time series data mining is to irst extract a set o eatures rom each time series and then base urther analysis on the eature vectors. There are many dierent wavelet based methods reported in the literature or eature extraction. They involve perorming some kind o transormation on the DWT coeicients, comparing between the DWT coeicients o the disturbance signal with the DWT coeicients o a pure signal, compressed DWT coeicients, direct use o the DWT. In this chapter we will be comparing the perormance o and the hybrid FFT-DWT methods or pattern classiication o electrical network disturbances along with the new approach based on statistical eature selection by S-transorm. These three methods were chosen on the basis that the eature vectors were o low dimensionality and were translation invariant. Each disturbance will give a dierent signature that can be used or classiication purposes. 7. Based on S-Transorm The output rom the S-Transorm is an by M matrix called the S-matrix whose rows pertain to requency and whose columns pertain to time. Each element o the S-matrix is complex valued. The S-matrix can be represented in a time-requency plane similar to that o the wavelet transorm. Here α is normally set to 0.4 or best overall perormance o the S- Transorm, where the contours exhibit the least edge eects and or computing the highest requency component o an oscillatory transient waveorm α is set equal to or 3 as required. The S- Transorm perorms multi-resolution on a time varying power network signal, because its window width varies inversely with requency. This gives high time resolution at high requency and high requency resolution at low requency. The detailed computational steps have been outlined in sotware originally developed by Stockwell [] and modiied by the author. Feature extraction is done by applying standard statistical techniques to the contours o the S-matrix as well as directly on the S-matrix. These eatures have been ound to be useul or detection, classiication or quantiication o relevant parameters o the signals. The power network signal is normalized with respect to a base value, which is the normal value without any disturbance.the resolution actor α was set to 0.4 or better time resolution. Ten eatures were extracted rom the S-transorm output. They are.f max (A)+min (A)-max (B). where A is the amplitude versus time graph rom the S-matrix under disturbance and B is the amplitude versus time graph o the S-matrix without disturbance.. F Standard deviation (σ ) o contour o. having the largest requency 3. F Energy 3 4. F4 Magnitude i ( y y) Total harmonic distortion o the signal where is the number o points in the FFT, nth harmonic component o the FFT. 5. F 5 Maximum Frequency o the signal i n V V n Vn the value o the 6. F 6 Mean o the lowest contour above twice the normalized undamental requency. 7. F7 3 Skewness o Cr. ( yi y) i 3 ( ) σ 8. F8 max( Cr) min( Cr) 9. F 9 Standard deviation o Cr. wherecr is the amplitude versus time graph o the S-matrix or requencies above twice the normalized undamental requency magnitude versus time. 0. F Average power or requencies above.5 times the 0 undamental requency. These eatures are ound to be well suited to distinguish the twelve () classes o power quality events studied here. 8. FEATUREEXTRACTIO USIG SIMULATED AD RECORDED DATA The proposed approach is applied to detect, localize and classiy signal patterns in electrical power networks. The power network disturbances that produce time varying databases are broadly due to the ollowing events: (i ) Sag (ii) Swell (iii) Interruption (iv) Oscillatory transients. (v) Spikes (vi) otches 35

7 Volume 9 o.9, April 0 To illustrate the relative values o these eatures, several typical power network time series data rom various disturbance events like voltage sag, swell, interruption, harmonics, transients, spikes, and notches, etc. are simulated using the MATLAB code. A random white noise o zero mean and signal to noise ratio (SR) varying rom 50dB to 0dB is added to the signals. A typical SR value o 30dB is equivalent to a peak noise magnitude o nearly 3.5% o the voltage signal. A sampling requency o.6 khz is chosen or computation o S-Transorms or the simulated waveorms. As the S-Transorm sotware uses analytic signals, only positive requency spectrum is evaluated and FFT o the signal samples is automatically computed as a part o the sotware. The sotware developed by author was an extension to the original version o the S-transorm by Stockwell.Laboratory recorded data is also used or eature extraction and time series classiication. The various time series disturbance signals belonging to the described classes namely voltage swell, sag, interruption, transient, spike, and notch, sag with harmonics, swell with harmonics etc. are shown in Figs.6.. to 6.5. In these igures also the multi-resolution S- transorm output contours along with the instantaneous amplitude o signal versus time graphs are shown. The S- transorm contours clearly present the distinguishing characteristics o the non-stationary signal patterns in the data samples that are pertinent eatures o each individual disturbance class. Table shows the eatures o voltage sag, swell and interruption with both simulated and recorded data. The voltage sag and swell magnitude and duration are varied to show the change in eature magnitudes. These disturbances belong to steady state undamental requency category and the class C 0 to C 7. Table-II shows the eatures o the disturbances that include very ast changing signals such as oscillatory and impulsive transients, notches, etc. These disturbances are categorized into classes C 8 to C. From Tables- and dierent classes o power network disturbance signals exhibit dierent eature magnitudes, which can be used or an automatic recognition o their class. It is quite evident that the standard deviation F is generally small and 0.05 or power requency disturbances like voltage sag, swell, interruption, etc. (F 0. or 0% sag, F.6 or 60% swell etc). The eature F is not very much inluenced by the noise level up to 0dB (which is quite high). However, when the harmonic content in the signal is within 5%, the exact magnitudes o sag, swell, interruption, etc. are minimally inluenced. With more than 0% harmonic content in the signal, an interruption may be misclassiied as sag. From Table-, it is ound that the transient disturbances have a higher value o the eature F (F > 0.) and the eature F lies in the range o The eature F is, however, an important one or distinguishing between oscillatory and impulsive transients and notches since F is less than 0.9 or notches, however when notch is mixed with harmonics the eature value might higher than 0.9. Further the eature F 3 distinguishes between oscillatory transients and impulsive transients as F 3 <.05 or oscillatory transients and >0.05 or spikes or impulsive transients. The actor α inluences the size o the window and eects the variation o eatures F and F during steady and transient disturbances as shown in Table-3. It is also ound rom the table that as α increase rom 0.4 to., the peak amplitude o the signal (which is 0.6 in this case) becomes inaccurate. The standard deviation also decreases considerably with increasing values o α. Table. Features extracted rom S-transorm Disturbances F F F 3 F 4 F 5 ormal.00 Sag (60%) Swell (50%) Momentary Interruption (MI) (5%) Flicker (5 Hz, %) otch harmonics Spike harmonics Transient (low requency) Transient (high requency) Table. Features extracted S-transorm with SR 0 db Disturbances F F F 3 F 4 F 5 ormal Sag (60%) Swell (50%) Momentary Interruption (MI) Harmonics Sag with Harmonic (60%) Swell with Harmonic (50%) Flicker (4%, Hz) otch harmonics Spike harmonics Transient (low requency) Transient (high requency)

8 Volume 9 o.9, April 0 Table 3. Eects o Window parameter α Steady state variations Transient variations Factor α F F F F The tables presented above provide a relative comparison o the relevant eatures or pattern recognition and classiication o the time series events. 9. COCLUSIO The paper presents several signal processing techniques along with some advanced ones like Wavelet and S-transorms or extracting the relevant eatures rom time series databases that could provide visual and automatic classiication o these time series databases. Time series databases occurring in power networks [3] are processed through these time-requency transorms to provide valuable inormation o their class and other characteristics or data mining o these events and subsequent knowledge discovery.overall, wavelet and S- transorm based methods are showing promising results in the area o multiple pattern recognition and data mining o time series data rom an electricity supply network. Further the approach o utilizing wavelets and sot computing methods [4] or pattern recognition o non-stationary time series data is a general one and can be applied to medical, inancial, and other types o temporal data. In a large data set partitioning the data into several sections and applying the above approach the similarity o patterns present in the data set can be determined. The new approach presented in this paper outperorms the other existing techniques as ar as accuracy, sensitivity to noise are concerned. 0. REFERECES [] S. Santoso, E.J. Powers, W.M. Grady and A.C. Parsons, Power quality disturbance waveorm recognition using wavelet-based neural classiier. I. Theoretical oundation, IEEE Trans. on Power Delivery, vol.5, pp.-8, 000. [] D. Borras et al, Wavelet and neural structure: A new tool or diagnostic o power system disturbances, IEEE Trans. on Industry Applications, vol.37, no., pp.84-90, 00. [3] C.H. Lee, J.S. Lee, J.O. Kim, and S.W. am, Feature Vector Extraction or the Automatic Classiication o Power Quality Disturbances, 997 IEEE International Symposium on Circuits and Systems, pp , 997. [4] B. Perunicic, M. Malini, Z. Wang, Y. Liu, Power Quality Disturbance Detection and Classiication Using Wavelets and Artiicial eural etworks, Proc. International Conerence on Harmonics and Quality o Power, pp.77-8, 998. [5] A.M. Gaouda, M.M.A. Salama, S.H. Kanoun, and A.Y. Chikhani, Wavelet-Based Intelligent System or Monitoring on-stationary Disturbances, International Conerence on Electric Utility Deregulation and Restructuring and Power Technologies, pp.84-89, 000. [6] A.M. Gaouda, M.M.A. Salama, M.R. Sultan, and A.Y. Chikhani, Power quality detection and classiication using wavelet multiresolution signal decomposition, IEEE Trans. on Power Delivery, vol., no.4, pp , 996. [7] A.M. Gaouda, S.H. Kanoun, M.M.A. Salama and A.Y. Chikhani, Wavelet-based signal processing or disturbance classiication and measurement, IEE Proc- Gener. Transm. Distrib, vol.49, no.3, May 00. [8] A.M. Gaouda, M.M.A. Salama, S.H. Kanoun, and A.Y. Chikhani, Pattern Recognition Applications or Power System Disturbance Classiication, IEEE Trans. on Power Delivery, vol.7, no.3, pp , 00. [9] S.C. Burrus, R.A. Gopinath, and H.Guo, Introduction to wavelets and wavelet transorm, Prentice Hall, ew Jersey, 997. (Book) [0] M.Rao. Raghuveer and A.S. Bopardikar, Wavelet Transorms Introduction to Theory and Applications, Addison-Wesley, Massachusetts, 998. (Book) [] R.G. Stockwell, L. Mansinha, and R.P Lowe, Localization o the Complex Spectrum: The S- Transorm, IEEE Trans. Sig. Proc., vol.44, no.4, pp , 996. [] R.G. Stockwell, S-Transorm Analysis o Gravity Wave Activity rom a Small Scale etwork o Airglow Imagers, Ph.D. Thesis, University o Western Ontario, 999. [3] S. Santoso, E.J. Powers, W.M. Grady, and A.C. Parsons, Power quality disturbance waveorm recognition using wavelet-based neural classiier. II.Application, IEEE Trans. Power Delivery, vol.5, pp.9-35, Jan.000. [4] Yean Yin, Liang Zhang, Miao Jin and SunyiXie Wavelet Packet and Generalized Gaussian Density Based Textile Pattern Classiication Using BP eural etwork, Lecture otes in Computer Science, Volume 646/00, , DOI: 0.007/ _70, 00. [5] Michael Häner, Roland Kwitt,Andreas Uhl,Friedrich Wrba, Alred Gangl,Andreas Vécsei, Computer-assisted pit-pattern classiication in dierent wavelet domains or supporting dignity assessment o colonic polyps, Journal Pattern Recognition archive Volume 4 Issue 6, Elsevier Science Inc. ew York, Y, USA doi0.06/.patcog , June