Implementation of Vector Directional Distance Rational Hybrid Filter Using TMS320C6416

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1 06 The Internatonal Arab Journal of Informaton Technology, Vol. 7, No., Aprl 00 Implementaton of Vector Drectonal Dstance Ratonal Hybrd Flter Usng TMS0C646 Ans Boudabous, Lazhar khrj, and Nour Masmoud Laboratory of Electroncs and Informaton Technology, Tunsa Department of Electrcal and Computer Engneerng, Sultan Qaboos Unversty, Oman Abstract: Ths paper proposes a novel dgtal sgnal processng mplementaton of vector drectonal dstance ratonal hybrd flter for mpulsve, Gaussan and mxed nose suppresson and fne-detals preservaton n color mages. The Implementaton was done, ntally, based on dgtal sgnal processng, whch proves the need to a large executon tme for flterng based on vector approach. Then, we propose effcent optmzatons and approxmatons of the man functons whch have no nfluence on the fltered mage qualty. Indeed, we could ncrease the flterng speed compared to the ntal vector drectonal dstance ratonal hybrd flter mplementaton. Comparatve studes of mplemented vector drectonal dstance ratonal hybrd flter wth other nonlnear flters are reported. It demonstrates a good color mage qualty for dfferent nose ntenstes. Ths effcent system mplementaton can perform well n several mage processng applcatons. Keywords: Color mage, DSP, optmzaton, nonlnear flter. Receved July, 008; accepted November 5, 008. Introducton Nose removal s an mportant task n mage processng. Many flters are often appled to gray value mages. The extenson of the concept of scalar flterng to color mage processng s not smple and straght forward task. Wth the extensve use of color n modern applcatons, the demand for hgh qualty mages s also ncreasng. Consequently, the nterest n color percepton and processng has been rsng rapdly and the area of color mage processng has been the subject of extensve research recently [9, 0,, ]. Flterng s one of the most mportant elements of color mage processng systems. Its most mportant applcatons are nose removal, mage enhancement, and mage restoraton. Nose may be ntroduced to an mage due to mperfect formaton or storage systems, nosy communcaton channels, and other varous factors, such as atmospherc turbulence [8]. However, color mage flterng dd not have the same development n the past that other areas of dgtal sgnal processng have enjoyed. Another mportant factor s the dffculty n understandng and modelng the human percepton of color [8] due to the complexty of the Human Vsual System (HVS). Therefore, lnear flters used n mage flterng applcatons, cannot cope wth the nonlnearty of the mage formaton model and transmsson channels and cannot take nto account the nonlnearty of human vson [8]. Flters havng good edge and mage detal preservaton propertes are hghly sutable for dgtal mage flterng. Most of the classcal lnear dgtal mage flters have low pass characterstcs. They tend to blur edges and to destroy lnes, edges, and other fne mage detals []. These reasons have led researchers to use nonlnear flterng technques. These technques were consdered n many applcatons n dgtal mage processng. Many classes of nonlnear dgtal mage flterng technques have appeared n the lterature such as order statstcs flters, polynomal flters, morphologcal flters, and neural networks [, 9]. Indeed, nonlnear vector flterng technques have generated much research nterest due to ther mportance n color mage restoraton [8, 0, 7, 0]. A varety of flterng technques proposed to date are based on multvarate order statstcs [], whch take the advantage of color nter-channel dependence and avod unpleasant drawbacks (pxel value rearrangng and chromatc shft) of component-wse flterng technques. The well known vector flters nclude the Vector Medan Flter (VMF) [, ], the Vector Drectonal Flter (VDF) [4], and the Drectonal Dstance Flter (DDF) [9]. Detecton based flterng technques were desgned to remove mpulsve nose [4, 0]. Such a structure, whle effcent for mpulsve nose removal, s napproprate n dealng wth Gaussan nose or mxed nose contamnaton. In comparson, a class of flters based on ratonal functons was desgned to cope wth dfferent types of nose. Among these flters we menton the Vector Medan Ratonal Hybrd Flter (VMRHF) and the Vector Drectonal Dstance Ratonal Hybrd Flter (VDDRHF) [7, 9]. They consttute very accurate estmators n long and short taled nose dstrbutons and, at the same tme, preserve the chromatcty of the color mage. Moreover, they act n small wndow and requre lttle

2 Implementaton of Vector Drectonal Dstance Ratonal Hybrd Flter Usng TMS0C number of operatons, resultng n smple and fast flter structures. The man goal of ths paper s to fnd a way on mplementng the VDDRHF for real tme applcaton purposes. To do so, we propose effcent optmzatons and approxmatons of the man functons whch have no nfluence on the fltered mage qualty yeldng to a much better and reduced consumng tme (up to 95% of the flterng speed) compared to the ntal VDDRHF s mplementaton. The paper s structured as follows. Secton presents an overvew of the nonlnear flter VDDRHF. A computer smulaton of ths flter s the object of secton. In secton 4, we provde the mplementaton by means of use of Dgtal Sgnal Processng (DSP) technology. Secton 5 descrbes the effcent optmzaton and approxmaton technques of the man functons of VDDRHF for mplementaton. Fnally, conclusons are drawn n secton 6. Image Lena Mandrll Butterfly Flower Table. Flterng results usng mpulsve nose %. Metrc Nosed VDF VMF VMRHF VDDRHF Bref Overvew of the Vector Nonlnear Flters.. Color Image Flterng There are two approaches to flter colour mages [4]. The frst approach breaks up the mage nto three components R, G and B and ensures the treatment ndependently. It s called margnal approach. The second s called vector approach as shown n Fgure, where colour mage pxels are consdered as - component vectors n the colour space that s more approprate for the human vsual system. Therefore, the nherent correlaton that exsts between the dfferent colour components s not gnored. decade n whch a lot of related work has been done. Ths secton descrbes the desgn of VDDRHF flter. The DSP mplementaton of some nonlnear flters lke VMF and VDF s publshed [6], where a floatng pont DSP technque (DSP C67) has been used. Table. Flterng results usng Gaussan nose ( σ =00). Image Lena Mandrll Butterfly Flower Metrc Nosed VDF VMF VMRHF VDDRHF In addton to ts detal preservng capablty, the VRF removes Gaussan nose and small magntude mpulsve nose [8]. The specfc of VDDRHF [9] s the combnaton between the drecton and the magntude process whch s sutable for human vsual system and can gve better balanced result between nose reducton and chromatcty retenton. The VDDRHF structure s made of two flterng stages as shown n Fgure. x (n) and Φ (n) are respectvely the nput (nosy pxel) and the output (fltered pxel) of the VDDF. y (n) s the fnal output (fltered pxel) of the VDDRHF gven by equaton. y ( n ) = Φ ( n ) + = h + k. D [ Φ β Φ ( n ) () ( n ), Φ ( n )] The term D[.] s an edge sensng term, expressed as, p p ( n), Φ( n)] = Φ Φ. θ( Φ, Φ) D[ Φ ().. VDDRHF Desgn Fgure. Vector approach. Nonlnear flterng technques were consdered as premature n dgtal mage processng. Research n ths area has been a dynamc development n the past Fgure. Block dagram of VDDRHF flter. To fnd Φ ( n), Φ ( n) and Φ ( n) we use the VDDF. They combne n the frst stage the L -norm crtera and angular dstance crtera to produce three output vectors n whch three vector drectonal dstance flter

3 08 The Internatonal Arab Journal of Informaton Technology, Vol. 7, No., Aprl 00 outputs to elmnate mpulsve nose, preserve edges and color chromatcty. In the second stage a vector ratonal operaton acts on the above three output vectors to produce the fnal output vector. Furthermore, as ponted out n [7, 9], a vector ratonal flter performs well for relatvely hgh SNR Gaussan contamnated envronments. When both mpulsve and Gaussan noses are present, nether the vector ratonal flter nor VDDF performs well. For ths reason, t was necessary to use a hybrd structure flter. The most popular nonlnear multchannel flters are based on the orderng of vectors n a predefned flter wndow. The output of these flters s defned as the lowest ranked vector accordng to a specfc orderng technque [4]. Let y (X ) represent a multchannel mage and let W (n) be a wndow of fnte sze N, where the nosy mage vectors nsde the wndow are denoted as X j (n), j=,,,n and the central sample n) = X ( ( n) determnes the poston of the flter wndow. X ( N+) / If the Eucldan dstance (L -norm) between two vectors X, X s denoted as, ( X X ) / m, j = X X j = X X j l= N M = j = dx X j j d, then the scalar quantty ( ), s the dstance assocated wth the nosy vector X n W. An orderng of the M s ( M ( ) M ( )... M ) mples the same orderng scheme to the nput set W (n) resultng n the ordered sequence X ( ) X ( )... X. If the angle between two vectors as X, X s denoted j T X X j θ( X, X ) = cos, then the scalar j X. X j N A X, X s the angular dstance quantty = = θ( ) j assocated wth the nosy vector X n W. An orderng of the A s ( A( ) A( )... A( N ) ) mples the same orderng scheme to the nput set W (n) resultng n the ordered sequence X ( ) X ( )... X. Combned magntude and drectonal dstances: the scalar quantty, p p γ M A =. () s the dstance assocated wth the nosy vector X n W. The power parameter p s a desgn parameter ranged from 0 to. It controls the mportance of the angle crteron versus the dstance crteron n the overall flter process. In the two extremes, p=0 or p=, the operator behaves as ether magntude processng or drectonal processng, respectvely. The case of p=0.5 s gvng equal mportance to both j crtera. For an ntermedate value of p (0<p<) both, magntude dstance (to process nose attenuaton) and angular dstance (to process chromatcty retenton) are consdered, whch ft better the concept of human vsual system [9]. An orderng of the γ s ( γ( ) γ( )... γ ) mples the same orderng scheme to the nput set W (n) resultng n the ordered sequence X ( ) X ( )... X. Nonlnear ranked type multchannel estmators defne the vector X ( ) W( n) assocated wth the mnmum aggregated dstance γ ( ) { γ, γ,..., γ N } as the flter output, whch s called a Vector Drectonal Dstance Flter (VDDF). Therefore, the VDDF conssts of computng and comparng the values of γ nsde the sldng flterng wndow W (n) and the output s the vector X k for whch γ k reaches t s mnmum.. Computer Smulatons In ths secton we compare the subjectve qualty, the objectve qualty of VDDRHF wth other well known algorthms. For ths purpose two metrcs, gvng a dstncton between two dgtal mages, have been used: the Peak Sgnal to Nose Rato () and the Structural SIMlarty Metrc () [0]. The s defned as: = 0 log 0 M max N = j = o, j M f N, j (4) where max s the range of allowable gray scale (55 for 8 bts). MxN s the number of vector samples, and f, j o, j are the ampltudes of the orgnal and fltered vectors. Some tradtonal metrcs lke Mean Absolute Error (MAE) and Mean Square Error (MSE) are proved to be nconsstent wth human eye percepton. Therefore, the use of metrc as a method for measurng the smlarty between two mages wll go perfectly wth the human vsual system. It s an mproved verson of the unversal mage qualty ndex []. The s defned as follow: µµ + + I J+ C σσ I J C σ IJ C = (5) µ + C + + C I µ J σi σj C σσ I J µ Iµ J s the weghted local lumnance, σ Iσ s the J weghted local contrast, σ s the weghted local correlaton (structure) between orgnal mage fltered mage j IJ o, and j f and C s a stablzng constant., The proposed algorthms were tested usng mages

4 Implementaton of Vector Drectonal Dstance Ratonal Hybrd Flter Usng TMS0C wth artfcally njected mpulse nose, Gaussan nose or mxed nose. The mplementaton of nose and dfferent flters s developed usng ANSI C Language. All of the orgnal mages were 4 bt, RGB color mages. A fxed probablty of an mpulse has been assumed for every byte n the mage. If a byte was replaced by an mpulse, the mpulse could take any value n the range [0, 55] wth unform probablty [4]. Tables, and show the comparatve results between the VDDRHF flter and others common flters lke VMF, VDF and VMRHF usng varous types of addtve nose. Table. Flterng results usng mxed nose (%, σ = 00 ). of on board devces that sut a wde varety of applcaton envronments. The code composer studo development tools are bundled wth the 646 DSK, ntegrated development envronment for C/C++ and assembly programmng [5]. In addton to a hgh clock rate, C64x DSPs can do more work each cycle wth bult n extensons. These extensons nclude new nstructons to accelerate performance n key applcaton areas such as dgtal communcatons nfrastructure, vdeo and mage processng. The DSP kernel s composed of two data paths: A and B, each, contanng four functonal unts (S, D, M, L, S, D, M and L) whch allow a maxmum of eght nstructons n one cycle. Fgure shows dfferent blocks of DSP archtecture: Image Metrc Nosed Vdf Vmf Vmrhf Vddrhf Lena Mandrll Butterfly Flower Theoretcally, VDDRHF flter seems more complcated than other flters. But we wll notce that t s more powerful n mage qualty. Ths smulatons show that the VDDRHF flter has better and than other algorthms. We noted that the mage qualty dffers accordng to the parameter p. we can test ths for varous mages. In order to fnd the best value of parameter p, we used an teratve optmzaton algorthm. The MSE s consdered as a cost functon. The parameter p changes slghtly by usng dfferent mages as shown by Table 4. Table 4. Optmum value of parameter p usng dfferent color mage. Image Lena Peppers Mandrll Flower Butterfly p Values 0,5 0,4 0,06 0,5 0, To smplfy the mplementaton, we choose an approprate value of p (p=0.5) that seems sutable for all tested mages. The choce s based on the desgn aspect of the power p that needs a smple shftng operaton, whch can be executed very fast by DSP. 4. DSP Board and Archtecture DSP offers technologes for nnovatve system development and applcaton desgn. The DSP s able to provde a hgh number of MIPS. The prmary features of the DSK are: 70 MHz, AIC stereo codec, four poston users DIP swtch and four user LEDs, flash and SDRAM. The DSK comes wth a full complment Fgure. Internal DSP archtecture The code development was done through seres of steps as follows: Step : we comple and profle natve C/C++ code (It valdates orgnal C/C++ code and determnes whch loops are the most mportant n terms of MIPS requrements). Step : we add const declaratons, loop, memory bank, and data algnment nformaton (It reduces potental ponter alasng problems, allows loops wth ndefnte teraton counts to execute eplogs, uses pragmas to pass count nformaton to the compler, uses memory bank pragmas and asserts ntrnsc to pass memory bank and algnment nformaton to the compler). Step : we optmze C code usng other C6000 ntrnsc and other methods (It facltates the use of some C6000-nstructons that are not easly represented n C, optmzes data flow bandwdth, uses word access for short data and double word access for word). Step 4: lnear assembly can be wrtten and parttonng nformaton can be added [5]. One Tmer has been used to measure the number of cycles. In fact, the most delcate parts are the SDRAM well managng, the cache memory and the fle manpulatons. In our present work, we are nterested by the valdaton of steps and and.

5 0 The Internatonal Arab Journal of Informaton Technology, Vol. 7, No., Aprl Implementaton of VDDRHF Flter The frst mplementaton of VDDRHF flter requres a y large number of cycles (due to the use of x functons and Arc cosne operatons). Therefore, our goal s to reduce CPU tme as much as possble usng dfferent approxmatons and optmzaton technques. One way s to use Taylor seres expanson of sn to substtute cos functon as follow: π π cos ( x) = sn ( x) x (6) Va smulaton, we can vary the order of the expanson of sn. Indeed, the calculated values are very close to zero, then, they have angles that are close toπ. We can clearly notce that when x s close to 0, the dfference between the theoretcal functon and ts approxmaton s neglgble (error s about.8x0-4 ). In addton, we can use the expanson of the power functon usng the followng equaton: x wth; a = e alogx ( alogx) + alogx+ ( alogx) +! + (7) x x ln( + x ) x + + (8)! By changng the varable to X = +x then x = X- and equaton 7 becomes: X a = e a log X ( X ) ( a. ( X ) ( X ) + a. ( X ) ( X ) + ) ( X ) (9) Ths approxmaton s used to calculate the VDDF dstances, but not to calculate the edge sensng term D[.] as n () snce t has nfluence on the and values, thus, the mage qualty. Moreover, the optmzaton s obtaned by usng technques gven by TI wth ts software CCS II, whch are ntrnsc and standard assembly nstructons [5, 5]. On one hand the ntrnsc technque of C646 has many advantages such as: the reducton of compled code and executon tme, more comprehensble code, varous nstructons, easy to ntegrate n the C code, syntax very close to the standard assembler and good documentaton on the Code composer level. On the other hand, the dsadvantage of the «ntrnsc» technque resdes n the fact that t does not replace all the assembly nstructons. The C64x provdes a number of nstructons whch combne common operatons together. These nstructons reduce the overall nstructon count n the code. Thereby, reducng code sze and ncreasng code densty. Also, they tend to smplfy programmng. Some used macro operatons are lsted n Table 5. Table 5. Descrpton of some ntrnsc nstructons. Intrnsc Instructons _MPY and _MPYU _DOTP _DOTPU4 Descrpton Multples the 6 LSBs of data by the 6 LSBs of data and returns the result. Values can be sgned or unsgned. Performs two 6x6 multples and adds the products together. Performs four 8x8 multples and adds products together. We can also explan the operatons as shown n Fgure 4: 6 a_h a_l 0 DOTP b_h b_l 0 = 0 5 a_h * b_h + a_l 0 * b_l 0 Fgure 4. DOTP Descrpton. Another ntrnsc nstructon _DOTPU4 as shown n Fgure 5 s used n our work when the nteger values are between 0 and 55. Usng _DOTPU4 nstructon, we can load, smultaneously, 4 pxels and calculate ther product and summaton n one cycle. Ths nstructon was used for dstance/norm calculatons. To extract the pxel values after flterng, we use the functon named _ROUNDF whch returns value rounded to the nearest nteger. 4 6 a a a a4 4 DOTPU4 6 b b b b4 a * b + a * b + a * b + a4 * b4 = Fgure 5. DOTPU4 Descrpton All these deas have no nfluence on the mage qualty, yeldng to a faster executon tme. Usng the kt C646 DSK, Table 6 shows the average CPU tme for each approxmaton usng Lena mage corrupted by % of mpulsve nose (sze: 76x44x). In addton, Table 6 shows the and values of the mplementaton results usng TMS0C646 DSK board wth a C646 DSP clocked at 70 MHz. We can conclude that the and of the mplemented flter are clearly dentcal for the three stages of optmzaton. 0

6 Implementaton of Vector Drectonal Dstance Ratonal Hybrd Flter Usng TMS0C646 Table 6. Average CPU tme for dfferent optmzaton steps of VDDRHF. VDDRHF Executon Tme (ms) Usng Orgnal Source Fle Usng cos Developmen t Usng y x Development Usng Intrnsc Instructons (a) (b) (c) (d) (e) (f) (g) (h) () (j) (k) (l) (m) (n) (p) Fgure 6. Orgnal (a, d, g, j, m), nosy (b, e, h, k, n) (mpulsve nose %) and fltered mages (c, f,, l, p) by optmzed VDDRHF flter usng C646 DSP. Therefore, wth these optmzatons, we ganed n the tme crteron whle keepng the same mage qualty. Dfferent test mages are dsplayed n Fgure 6. The orgnal color mages were 4-bt n RGB color space. These mages are contamnated by an mpulsve nose (mages (b), (e), (h), (k), (n)). The fltered mages by the mplemented flter are dsplayed also n Fgure 6 (mages (c), (f), (), (l), (p)). 6. Conclusons In ths paper, a novel DSP mplementaton of VDDRHF flter for mpulsve, Gaussan and mxed nose suppresson and fne-detal preservaton n color mage s presented. The desgned VDDRHF demonstrates a good color mage qualty for dfferent ntensty and varous noses compared to other well known nonlnear flters. Implemented n DSP (TMS0C646 70Mhz), the VDDRHF gves large executon tme. Therefore, the challengng task was n desgnng and developng approxmaton technques whch answer hgher processng speed and have no nfluence on the mage qualty. Subsequently, our approxmatons mprove the flterng speed compared to the ntal algorthm (0 tmes faster) and would be useful n some colour mage applcatons that do not need fast dsplay, lke medcal magng, tomography, etc., Future work wll be focused and challenged on reducng further the processng tme to deal more wth real tme applcatons usng combned HardWare/SoftWare (HW/SW) mplementaton n codesgn context. References [] Astola J. and Kuosmanen P., Fundamentals of Nonlnear Dgtal Flterng, CRC Press, 997. [] Astola J., Haavsto P., and Neuvo Y., Vector Medan Flter, n Proceedngs of IEEE, USA, pp , 990. [] Caselles V., Sapro G., and Chung D., Vector Medan Flters Inf Sup Operatons, and Coupled PDE s: Theoretcal Connectons, Computer Journal of Mathematcal Imagng and Vson, vol., no., pp. 09-9, 000. [4] Chekh F., Hamla R., Gabbouj M., and Astola J., Impulsve Nose Removal n Hghly Corrupted Color Images, n Proceedngs of Internatonal Conference on Image Processng, Swtzerland, pp , 996. [5] Chen J., Code Composer Studo Tutoral, Techncal Reference TMS0C646 DSK, 00. [6] Domínguez L. and Ponomaryov V., Non Lnear Flters for Colour Imagng Implemented by DSP, n Proceedngs of XI Conference on Electrcal Engneerng, Mexco, pp. 7-9, 005. [7] Khrj L. and Gabbouj M., Generalzed Class of Nonlnear Type Hybrd Flters, Computer Journal of IEE Electroncs Letters, vol. 8, no. 5, pp , 00. [8] Khrj L. and Gabbouj M., Vector Medan Ratonal Hybrd Flters for Multchannel Image Processng, n Proceedngs of ISCAS, New York, pp. 90-9, 999. [9] Khrj L., Vector Drectonal Dstance Ratonal Hybrd Flters for Color Image Restoraton,

7 The Internatonal Arab Journal of Informaton Technology, Vol. 7, No., Aprl 00 Computer Journal of Engneerng Research, vol., no., pp. -, 005. [0] Km J. and Wlls S., Fast Vector Medan Flter Implementaton Usng the Color Pack Instructon Set, n Proceedngs of Dgtal Sgnal Processng Workshop of IEEE, Germany, pp. 9-4, 00. [] Koschan A. and Abd M., A Comparson of Medan Flter Technques for Nose Removal n Color Images, n Proceedngs of 7 th Workshop on Color Image Processng, Germany, pp , 00. [] Lukac B., Applcaton of the Adaptve Center Weghted Vector Medan Framework for the Enhancement of Cdna Mcroarray Images, Internatonal Computer Journal of Applcaton Mathematc Computng Scence, vol., no., pp. 69-8, 00. [] Lukac R., Platanots N., Smolka B., and Venetsanopoulos A., Weghted Vector Medan Optmzaton, n Proceedngs of 4 th EURASIP Conference Vdeo-Image and Multmeda Communcatons, USA, pp. 7-, 00. [4] Lukac R., Smolka B., Martn K., Platanots N., and Venetsanopoulos N., Vector Flterng for Color Imagng, Computer Journal of IEEE Sgnal Processng Magazne, vol. 5, no., pp , 005. [5] Pedra M. and Frtsh A., Texas Instrument Code Composer Studo Tutoral Spru89f, Techncal Reference TMS0C6000, 000. [6] Ptas I. and Venetsanopoulos A., Order Statstcs n Dgtal Image Processng n Proceedngs of the IEEE, Canada, pp. 89-9, 99. [7] Ptas I. and Venetsanopoulos A., Nonlnear Dgtal Flters: Prncples and Applcatons, Klumer Academc, New York, 990. [8] Trahanas P., Ptas I., and Venetsanopoulos N., Color Image Processng, Academc Press, 994. [9] Vnayagarnoorthy S., Order Statstcs Flterng of Colour Images: A Perceptual Approach, Master Thess, Unversty of Toronto, 997. [0] Wang S., L Y., Chung F., and Xu M., An Iteratve Self Adaptve Algorthm to Impulse Nose Flterng for Color Images, Internatonal Computer Journal of Informaton Technology, vol., no. 0, pp. 5-59, 005. [] Wang Z., Bovk A., Shekh H., and Smoncell P., Image Qualty Assessment: From Error Vsblty to Structural Smlarty, Computer Journal of IEEE Transactons on Image Processng, vol., no. 4, pp , 004. Ans Boudabous receved BEng degree n electrcal engneerng from the Natonal Engneerng School of Sfax n 00, and hs MS degree n electroncs from Unversty of Sfax n 004, Actually, he s lecturer at the Unversty of Sfax, Tunsa and he s persuadng hs PhD studes wth the Laboratory of Electroncs and Informaton Technology. Lazhar khrj receved hs BS degree n electroncs, and hs MS and PhD degrees n electrcal engneerng from Unversty of Tuns II, Tunsa, n 990, 99 and 999, respectvely. In 00, he receved the Doctor of technology degree n nformaton technology from Sgnal Processng Insttute, Tampere Unversty of Technology, Fnland. Nour Masmoud receved electrcal engneerng degree from the Faculty of Scences and Technques- Sfax, Tunsa, n 98, the DEA degree from the Natonal Insttute of Appled Scences-Lyon and Unversty Claude Bernard- Lyon, France n 984. From 986 to 990, he prepared hs thess at the Laboratory of Power Electroncs at the Natonal School Engneerng of Sfax. He receved hs PhD degree from the Natonal School Engneerng of Tuns, Tunsa n 990.

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9 06 The Internatonal Arab Journal of Informaton Technology, Vol. 7, No., Aprl 00