Cours Fourier Nn

lectronique analogique*lectronique analogiquetransformation de Fourier signal priodiquesignal non priodique

systmes linaires

amplificationamplificateuramplificateur oprationnel

filtrage

oscillateurs

lectronique analogique

lectronique analogique*transformation de Fourier :

x(t) somme de signaux sinusodaux si x(t) est priodique, sa TF est discrte :

si x(t) est non priodique, sa TF est continue :


lectronique analogique*transformation de Fourier d'un signal priodique :namplitude


lectronique analogique*transformation de Fourier d'un signal priodique :tTT/2reconstruction de x(t) : la courbe rougeest la somme des 4 premires harmoniques


lectronique analogique*transformation de Fourier d'un signal non priodique :trac de X(f) pour M=1 etT=1, T=4 et T=0,4


lectronique analogique*transformation de Fourier la TF est linaire

dualit temps/frquence

temps "brefs" frquences levestemps "longs" frquences faibles

enjeu : augmentation des dbits de traitementde l'information frquences leves



systmes linaires


filtrage

oscillateurs


lectronique analogique*systmes linairesS.L.x(t)y(t)la relation reliant y(t) x(t) estune quation diffrentiellelinaire coefficients constants : exemple : RCx(t)y(t)i(t)


lectronique analogique*systmes linairesexemple : RCx(t)y(t)i(t)si x(t) est sinusodal : x(t)=Xsin(wt),alors y(t) est aussi sinusodal : y(t)=AXsin(wt+j)


lectronique analogique*systmes linairesexemple : RCx(t)y(t)i(t)Xwt2px(t)y(t) pour RCw=0,1y(t) pour RCw=1y(t) pour RCw=10


lectronique analogique*systmes linairesS.L.Aejwtexemple : R1/jCwX(w)IdoncA G(w) ejwtY(w)G(w) =


lectronique analogique*systmes linaires lien avec la transformation de FourierX(w)X(f)x(t)y(t)TF-1Y(w) = G(w) X(w)Y(f) = G(f) Y(f)G(w)les signaux harmoniques sont les fonctions propresdes systmes linaires


lectronique analogique*systmes linairesexemple : RCx(t)y(t) ?101001031041w(rd/s)|G(w)|dB


lectronique analogique*systmes linairesexemple : 101001031041w(rd/s)ttt



systmes linaires


filtrage

oscillateurs


lectronique analogique*amplificationsystme linaire caractris par G(f)>1 apport d'nergie amplificateur idal:Ve(w)Vs(w)A(w)i=0le courant d'entre est nulla sortie est une source de tension parfaite


lectronique analogique*amplification amplificateur non idal (modle linaire):Ve(w)Vs(w)A(w).Ve(w)ieisReRsVsA.VeieisReRsVeRgEgRc


lectronique analogique*amplification cascade d'amplificateurs:VeA.VeieReRsV'eVsA'.V'eR'eR'samplificateur d'entre : Re leveamplificateur de sortie : Rs faible


lectronique analogique*amplificateur oprationnel amplificateur oprationnel idal:A.(v+-v-)ieReRs+-v+v-vsv+-v-A Re Rs 0v+-v- 0is 0


lectronique analogique*amplificateur oprationnel exemples de montages linaires :vsveR1R2ve0vsveR1R200


lectronique analogique*amplificateur oprationnel exemples de montages linaires :vsveR'R00vsieR00C



systmes linaires


filtrage

oscillateurs


lectronique analogique*filtrage rduction du bruit:

V(f)sf antirepliement:

V(f)ffe2fe


lectronique analogique*filtrage slection (ou limination) d'une bande frquentielledans le spectre d'un signal :fV(f)fp1fp2fp3s1s2s3slection d'un signal modul en amplitude


lectronique analogique*filtrage slection (ou limination) d'une bande frquentielledans le spectre d'un signal :tfV(f)rjection de parasitesv(t)fV(f)


lectronique analogique*filtrageSystme linaire: Les signaux harmoniques sont fonctions propres de loprateurlinaires.Fonction de transfert:Stabilit:p k et ples parties relles ngatives


lectronique analogique*filtrageLes ples sont rels ou complexes conjugus est dcomposable en 2me ordre1er ordreUn filtre dordre quelconque peut tre raliser par la cascade de filtres du premier et du deuxime ordre.


lectronique analogique*filtrageFiltre du 2me ordre normalis:Q=0,707 ButterworthQ=0,577 BesselQ=1,128 Chebyshev


Graph3

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-0.0069431587-0.17761731830.2089021532

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-3.9165832872-5.65671768350.0214602821

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-30.8376630558-30.9610075167-30.6836184273

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-36.340409529-36.4063258338-36.2593121119

-36.5535145589-36.6178454381-36.4744001954

Butterworth

Bessel

Chebychev

Feuil1

ButterworthBesselChebychevButterworthBesselChebychev

0111ButterworthBesselChebychev

0.10.99995000370.99496999051.00607528730.1-0.0004342728-0.04380035780.0526096269

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0.60.94088741190.81898141891.20165451120.6-0.5292468371-1.73451902811.5955924239

0.70.89799030160.7598719971.244948880.7-0.934567075-2.38519119871.9030303767

0.80.84227140070.69810145021.25729698820.8-1.4909589107-3.1216291961.9887575047

0.90.77706387850.636407011.21923998940.9-2.1908655717-3.92530090551.7217839696

10.70710678120.5771.1281-3.0102999566-4.77648373691.0461819929

1.10.63704606240.52139170291.0024737611.1-3.9165832872-5.65671768350.0214602821

1.20.57039580950.47042046220.86863507191.2-4.8764734752-6.5502759141-1.2232527924

1.30.50924392410.42439006160.74446412491.3-5.8614828791-7.4446958995-2.5631245143

1.40.45447034170.38323625680.63731569091.4-6.8498890634-8.3306682073-3.9129077784

1.50.40613846610.34667308740.5479280071.5-7.8265175161-9.2015974358-5.2255300059

1.60.36385052710.3143018550.47428153141.6-8.7815398309-10.0530611161-6.4792757309

1.70.32699825040.28568362610.41368158851.7-9.70909142-10.8822930071-7.6666761511

1.80.29491468760.26038307660.36360027981.8-10.6060719552-11.6877449151-8.7875158255

1.90.26695537190.23799236810.32192316951.9-11.4712267104-12.468739391-9.8449553007

20.2425356250.21814220970.28696200292-12.3044892138-13.2252058391-10.8435121022

2.10.22114316440.20050523810.25739335242.1-13.1065296037-13.9574855414-11.7880534729

2.20.20233796590.18479511220.2321849652.2-13.878452407-14.6661904015-12.6833181217

2.30.18574626530.17076343960.21053028192.3-14.6215981942-15.3521021193-13.5337085621

2.40.17105241840.1581957980.19179577832.4-15.3374156268-16.0161011265-14.3432191289

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2.70.13590155640.12755614580.14858742192.7-17.3355113913-17.8859722338-16.56035905

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2.90.11807428830.11168567360.12749695552.9-18.55689327-19.0400506418-17.8900037124

30.11043152610.10480960190.11861692153-19.1381385238-19.5919785702-18.5170670274

3.10.1034994290.09853430860.11064434913.1-19.7012409206-20.1282505274-19.1214152316

3.20.09719389310.0927937250.10345877213.2-20.2472204346-20.6496278253-19.7046536069

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3.50.08136200950.07824037980.08568942643.5-21.7915666775-22.1313809977-21.3414552825

3.60.07693181760.07413128220.08078524773.6-22.2778801347-22.5999697579-21.8533587788

3.70.07285191880.07033260530.07629466953.7-22.7511801015-23.0568658937-22.3501160811

3.80.06908661120.06681438420.07217209633.8-23.2121221925-23.502600601-22.8326136048

3.90.06560458240.0635501140.06837808033.9-23.6613164875-23.9376733197-23.3016619235

40.06237828620.06051629250.06487834994-24.0993312333-24.3625537367-23.7580040922

4.10.05938341750.05769202910.06164301274.1-24.526696254-24.7776837186-24.2023228859

4.20.05659847060.05505871130.05864589854.2-24.943906079-25.1834791543-24.6352471122

4.30.05400436450.05259971790.05586401474.3-25.3514228036-25.5803316979-25.0573571319

4.40.05158412460.05030017310.05327709244.4-25.7496786989-25.9686104072-25.4691897007

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6.90.02099935920.02078155420.02127221446.9-33.5558791736-33.6464395316-33.4437459681

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7.10.01983343180.01963896940.02007657097.1-34.0520426474-34.1376261357-33.9462092512

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7.60.01731042530.01716200730.01749521457.6-35.2338452532-35.3086383286-35.1416145737

7.70.01686385220.01672294550.01703915877.7-35.4608642705-35.5337444895-35.3710370379

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7.90.01602101670.01589376160.01617911667.9-35.9061985113-35.975466105-35.8209039269

80.0156230930.01550204430.01577338228-36.1246596395-36.192220526-36.0415034536

8.10.0152398090.01512459340.01538276468.1-36.340409529-36.4063258338-36.2593121119

8.20.01487045550.01476072630.015006528.2-36.5535145589-36.6178454381-36.4744001954

Feuil1

Butterworth

Bessel

Chebychev

Feuil2

Feuil3

Graph4

111

0.99995000370.99496999051.0060752873

0.99920095870.97975871241.0243423011

0.99597443880.95414465281.0547764088

0.98744063190.91817224791.0967522123

0.97014250010.87256883881.1478480115

0.94088741190.81898141891.2016545112

0.89799030160.7598719971.24494888

0.84227140070.69810145021.2572969882

0.77706387850.636407011.2192399894

0.70710678120.5771.128

0.63704606240.52139170291.002473761

0.57039580950.47042046220.8686350719

0.50924392410.42439006160.7444641249

0.45447034170.38323625680.6373156909

0.40613846610.34667308740.547928007

0.36385052710.3143018550.4742815314

0.32699825040.28568362610.4136815885

0.29491468760.26038307660.3636002798

0.26695537190.23799236810.3219231695

0.2425356250.21814220970.2869620029

0.22114316440.20050523810.2573933524

0.20233796590.18479511220.232184965

0.18574626530.17076343960.2105302819

0.17105241840.1581957980.1917957783

0.15799050110.14690755970.175480354

0.14633651890.1367398970.161184561

0.13590155640.12755614580.1485874219

0.12652593110.11923859060.1374289559

0.11807428830.11168567360.1274969555

0.11043152610.10480960190.1186169215

0.1034994290.09853430860.1106443491

0.09719389310.0927937250.1034587721

0.09144263960.0875303190.0969591304

0.086183330.08269386090.0910601399

0.08136200950.07824037980.0856894264

0.07693181760.07413128220.0807852477

0.07285191880.07033260530.0762946695

0.06908661120.06681438420.0721720963

0.06560458240.0635501140.0683780803

0.06237828620.06051629250.0648783499

0.05938341750.05769202910.0616430127

0.05659847060.05505871130.0586458985

0.05400436450.05259971790.0558640147

0.05158412460.05030017310.0532770924

0.04932261230.04814673440.0508672066

0.04720629310.04612740960.0486184572

0.04522303830.04423139820.0465166994

0.04336195430.04244895370.0445493153

0.04161323590.04077126430.0427050192

0.03996803830.03919034850.040973692

0.03841836760.03769896360.0393462388

0.03695698440.03629052630.0378144662

0.03557732030.03495904250.036370977

0.03427340520.03369904570.0350090785

0.03303980290.03250554280.0337227034

0.03187155530.03137396590.0325063408

0.03076413270.03030013020.0313549754

0.02971339060.0292801960.0302640351

0.02871553070.02831063590.0292293447

0.02776706720.02738820440.0282470848

0.02686479650.02650991180.0273137561

0.02600576980.02567300050.0264261477

0.02518727010.02487492380.0255813088

0.02440678980.02411332690.0247765237

0.02366201220.02338603010.0240092898

0.02295079420.0226910130.0232772975

0.0222711510.02202640150.0225784128

0.02162124210.02139045470.0219106614

0.02099935920.02078155420.0212722144

0.02040391470.02019819350.0206613758

0.01983343180.01963896940.0200765709

0.01928653540.01910257320.0195163361

0.01876194370.01858778360.0189793094

0.01825846060.01809345940.0184642222

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0.01731042530.01716200730.0174952145

0.01686385220.01672294550.0170391587

0.01643433510.01630047120.0166007602

0.01602101670.01589376160.0161791166

0.0156230930.01550204430.0157733822

0.0152398090.01512459340.0153827646

0.01487045550.01476072630.01500652

Butterworth

Bessel

Chebychev

Feuil1



0.10.99995000370.99496999051.00607528730.1-0.0004342728-0.04380035780.0526096269

0.20.99920095870.97975871241.02434230110.2-0.0069431587-0.17761731830.2089021532

0.30.99597443880.95414465281.05477640880.3-0.0350361474-0.40771558490.4632081551

0.40.98744063190.91817224791.09675221230.4-0.1097801217-0.74151676210.8021703825

0.50.97014250010.87256883881.14784801150.5-0.2632893872-1.18400601251.1976877243

0.60.94088741190.81898141891.20165451120.6-0.5292468371-1.73451902811.5955924239

0.70.89799030160.7598719971.244948880.7-0.934567075-2.38519119871.9030303767

0.80.84227140070.69810145021.25729698820.8-1.4909589107-3.1216291961.9887575047

0.90.77706387850.636407011.21923998940.9-2.1908655717-3.92530090551.7217839696

10.70710678120.5771.1281-3.0102999566-4.77648373691.0461819929

1.10.63704606240.52139170291.0024737611.1-3.9165832872-5.65671768350.0214602821

1.20.57039580950.47042046220.86863507191.2-4.8764734752-6.5502759141-1.2232527924

1.30.50924392410.42439006160.74446412491.3-5.8614828791-7.4446958995-2.5631245143

1.40.45447034170.38323625680.63731569091.4-6.8498890634-8.3306682073-3.9129077784

1.50.40613846610.34667308740.5479280071.5-7.8265175161-9.2015974358-5.2255300059

1.60.36385052710.3143018550.47428153141.6-8.7815398309-10.0530611161-6.4792757309

1.70.32699825040.28568362610.41368158851.7-9.70909142-10.8822930071-7.6666761511

1.80.29491468760.26038307660.36360027981.8-10.6060719552-11.6877449151-8.7875158255

1.90.26695537190.23799236810.32192316951.9-11.4712267104-12.468739391-9.8449553007

20.2425356250.21814220970.28696200292-12.3044892138-13.2252058391-10.8435121022

2.10.22114316440.20050523810.25739335242.1-13.1065296037-13.9574855414-11.7880534729

2.20.20233796590.18479511220.2321849652.2-13.878452407-14.6661904015-12.6833181217

2.30.18574626530.17076343960.21053028192.3-14.6215981942-15.3521021193-13.5337085621

2.40.17105241840.1581957980.19179577832.4-15.3374156268-16.0161011265-14.3432191289

2.50.15799050110.14690755970.1754803542.5-16.0273804686-16.659117109-15.1154299644

2.60.14633651890.1367398970.1611845612.6-16.6929456079-17.2820950342-15.853531186

2.70.13590155640.12755614580.14858742192.7-17.3355113913-17.8859722338-16.56035905

2.80.12652593110.11923859060.13742895592.8-17.9564091585-18.4716633227-17.2384350594

2.90.11807428830.11168567360.12749695552.9-18.55689327-19.0400506418-17.8900037124

30.11043152610.10480960190.11861692153-19.1381385238-19.5919785702-18.5170670274

3.10.1034994290.09853430860.11064434913.1-19.7012409206-20.1282505274-19.1214152316

3.20.09719389310.0927937250.10345877213.2-20.2472204346-20.6496278253-19.7046536069

3.30.09144263960.0875303190.09695913043.3-20.7770249203-21.1568297736-20.2682257653

3.40.086183330.08269386090.09106013993.4-21.2915345865-21.6505346157-20.8134337386

3.50.08136200950.07824037980.08568942643.5-21.7915666775-22.1313809977-21.3414552825

3.60.07693181760.07413128220.08078524773.6-22.2778801347-22.5999697579-21.8533587788

3.70.07285191880.07033260530.07629466953.7-22.7511801015-23.0568658937-22.3501160811

3.80.06908661120.06681438420.07217209633.8-23.2121221925-23.502600601-22.8326136048

3.90.06560458240.0635501140.06837808033.9-23.6613164875-23.9376733197-23.3016619235

40.06237828620.06051629250.06487834994-24.0993312333-24.3625537367-23.7580040922

4.10.05938341750.05769202910.06164301274.1-24.526696254-24.7776837186-24.2023228859

4.20.05659847060.05505871130.05864589854.2-24.943906079-25.1834791543-24.6352471122

4.30.05400436450.05259971790.05586401474.3-25.3514228036-25.5803316979-25.0573571319

4.40.05158412460.05030017310.05327709244.4-25.7496786989-25.9686104072-25.4691897007

4.50.04932261230.04814673440.05086720664.5-26.139078592-26.3486632773-25.8712422281

4.60.04720629310.04612740960.04861845724.6-26.520002033-26.7208186706-26.2639765319

4.70.04522303830.04423139820.04651669944.7-26.8928052692-27.0853866478-26.6478221603

4.80.04336195430.04244895370.04454931534.8-27.2578230431-27.4426602033-27.0231793364

4.90.04161323590.04077126430.04270501924.9-27.6153702301-27.7929164122-27.3904215759

50.03996803830.03919034850.0409736925-27.9657433321-28.1364174918-27.7498980203

5.10.03841836760.03769896360.03934623885.1-28.3092218396-28.4734117855-28.1019355214

5.20.03695698440.03629052630.03781446625.2-28.6460694751-28.8041346741-28.4468405077

5.30.03557732030.03495904250.0363709775.3-28.9765353297-29.1288094182-28.7849006596

5.40.03427340520.03369904570.03500907855.4-29.3008549025-29.4476479399-29.1163864166

5.50.03303980290.03250554280.03372270345.5-29.619251052-29.7608515449-29.4415523353

5.60.03187155530.03137396590.03250634085.6-29.9319348685-30.0686115928-29.760638317

5.70.03076413270.03030013020.03135497545.7-30.2391064745-30.3711101175-30.0738707178

5.80.02971339060.0292801960.03026403515.8-30.5409557595-30.668520403-30.381463356

5.90.02871553070.02831063590.02922934475.9-30.8376630558-30.9610075167-30.6836184273

60.02776706720.02738820440.02824708486-31.1293997608-31.2487288055-30.9805273371

6.10.02686479650.02650991180.02731375616.1-31.4163289104-31.5318343559-31.2723714603

6.20.02600576980.02567300050.02642614776.2-31.6986057074-31.8104674216-31.5593228345

6.30.02518727010.02487492380.02558130886.3-31.9763780105-32.0847648216-31.8415447945

6.40.02440678980.02411332690.02477652376.4-32.249786785-32.3548573105-32.1191925533

6.50.02366201220.02338603010.02400928986.5-32.5189665216-32.6208699232-32.3924137353

6.60.02295079420.0226910130.02327729756.6-32.7840456226-32.8829222963-32.6613488668

6.70.0222711510.02202640150.02257841286.7-33.0451467612-33.1411289684-32.9261318264

6.80.02162124210.02139045470.02191066146.8-33.3023872146-33.3955996593-33.1868902608

6.90.02099935920.02078155420.02127221446.9-33.5558791736-33.6464395316-33.4437459681

70.02040391470.02019819350.02066137587-33.8057300307-33.8937494353-33.6968152525

7.10.01983343180.01963896940.02007657097.1-34.0520426474-34.1376261357-33.9462092512

7.20.01928653540.01910257320.01951633617.2-34.2949156049-34.378162528-34.1920342388

7.30.01876194370.01858778360.01897930947.3-34.5344434363-34.6154478371-34.4343919083

7.40.01825846060.01809345940.01846422227.4-34.7707168441-34.8495678059-34.6733796323

7.50.01777496910.01761853350.01796989197.5-35.0038229038-35.080604871-34.9090907061

7.60.01731042530.01716200730.01749521457.6-35.2338452532-35.3086383286-35.1416145737

7.70.01686385220.01672294550.01703915877.7-35.4608642705-35.5337444895-35.3710370379

7.80.01643433510.01630047120.01660076027.8-35.6849572406-35.7559968252-35.5974404569

7.90.01602101670.01589376160.01617911667.9-35.9061985113-35.975466105-35.8209039269

80.0156230930.01550204430.01577338228-36.1246596395-36.192220526-36.0415034536

8.10.0152398090.01512459340.01538276468.1-36.340409529-36.4063258338-36.2593121119

8.20.01487045550.01476072630.015006528.2-36.5535145589-36.6178454381-36.4744001954

Feuil1

Butterworth

Bessel

Chebychev

Feuil2

Butterworth

Bessel

Chebychev

Feuil3

lectronique analogique*filtrageGabarit dun filtre: H(w)critre de " gain plat "dans la bande passanteslectivitphase linaireTransposition de frquence:Exemple: s=w0/sFiltre PB normalis Filtre PHs=w0/sFiltre Passe-BasFiltre Passe-Hauts=s+w02/sFiltre Passe-BasFiltre Passe-Bande


lectronique analogique*filtrageFiltres de Butterworth:Filtre maximally flat:si N est pair, les ples sont les racines de s2N=ejp, donc sk=ekjp/2N.Ex: N=4xxxxsi N est impair, les ples sont les racines de s2N=ej2p, donc sk=ekjp/N.Ex: N=3xxxxxx


lectronique analogique*filtrageFiltres de Chebychev:Plus slectif que B.:Les polynmes de C. sont dfinis par: TN+1(x)=2xTN(x)-TN-1(x) avec, T0(x)=1 et T1(x)=x.


lectronique analogique*filtrageFiltres de Bessel:Pour quun signal ne soit pas dform par un systme linaire,il faut quil subisse un retard pur: s(t)=A.e(t-t).S(f)=A.E(f).exp(-j2pft)Le gain du systme est donc G(f)=A.exp(-j2pft).La phase du filtre varie linairement avec la frquence.Un tel filtre est non causal donc non physique, le filtre de Besselest celui qui approche le mieux un filtre phase linaire.

BN est un polynme de Bessel dfini par:BN(s)=(2N-1)BN-1(s)+s2BN-2(s)avec B0=1 et B1(s)=s+1


lectronique analogique*filtrageComparaison des fonctions de transfert (filtres dordre 3)Phase comparedes filtres de Butterworthet de Bessel


Graph5

10.99955042340.99999

10.99820675460.9999600003

0.99999999960.99598403630.9999100013

0.9999999980.9929068760.9998400043

0.99999999220.9890087780.9997500104

0.99999997670.98433125820.9996400216

0.99999994120.97892278550.9995100399

0.99999986890.97283760380.9993600681

0.99999973430.96613448450.999190109

0.99999950.95887546430.9990001659

0.99999430470.91649356040.9977508356

0.99996800150.86952445430.9960026214

0.9998779520.82404192420.9937563397

0.99963569920.78391864080.9910129975

0.99908213250.75127212970.9877737647

0.99795827010.72717446320.9840399456

0.99587379670.71225175110.9798129512

0.99227787670.70710678120.9750942764

0.98644054010.71260792530.9698854841

0.97745779940.73008339550.9641882

0.96429778580.76137545670.9580041206

0.94590448150.80845631070.9513350367

0.9213641610.87157553710.9441828764

0.89011382510.94326863020.936549767

0.85213705940.99565732790.9284381188

0.80807163990.97745779940.9198507308

0.75916951440.8652188820.9107909168

0.70710678120.70710678120.9012626522

0.65370709140.55972757790.8912707369

0.60067254110.4429561620.8808209729

0.54939575480.35499130520.86992035

0.50087830890.2890445770.8585772359

0.45573827840.23901904710.8468015624

0.41427107260.20043121460.8346050024

0.37652979990.17014906930.8220011292

0.34240279150.1459983520.8090055503

0.31167753830.12645451050.7956360103

0.28408832970.11043152610.7819124532

0.25934910320.09714220990.7678570417

0.23717457190.08600609550.753494127

0.21729281060.07658814870.7388501675

0.19945198470.06855739240.7239535954

0.18342325960.06165852070.7088346333

0.16900134110.05569210120.6935250629

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0.12403473460.03843312210.6310547429

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0.07682648190.02228529260.5222564614

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0.06784221290.019423430.4925151938

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0.05680390050.01599692890.4497591648

0.05365822040.01503849410.4360716295

0.05073982150.014156470.42268867

0.04802865610.01334326570.4096203975

0.04550674340.01259219120.3968748546

0.04315792770.01189733330.3844581294

0.04096766870.01125345140.3723744829

0.03892285850.01065588820.3606264835

0.03701166050.01010049480.3492151479

0.03522336990.00958356610.3381400833

0.03354828970.00910178560.327399629

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0.03050337720.00823207090.3069103945

0.02911828050.00783905360.2971531747

0.02781570720.00747095280.2877139338

0.0265896120.00712580290.2785866355

0.02543447210.00680182340.2697647128

0.02434523520.00649739870.2612411639

0.02331727380.00621106030.2530086395

0.0223463440.00594147160.2450595219

0.0214285490.00568741370.2373859956

0.02056030690.00544777370.229980111

0.01973832110.00522153370.2228338401

0.01895955440.00500776190.2159391256

0.01822120540.00480560370.2092879241

0.01752068750.00461427420.2028722433

0.01685561010.00443305220.196684173

0.01622376140.00426127350.1907159133

0.0156230930.00409832620.1849597962

0.01505170610.00394364570.1794083048

0.01450783880.00379671050.1740540889

0.01398985480.00365703820.1688899764

0.01349623320.00352418230.1639089837

0.01302555880.00339772940.159104322

0.01257651420.00327729550.1544694027

0.01214787130.00316252450.1499978406

0.01173848490.00305308530.1456834552

0.01134728610.00294866980.1415202713

0.01097327620.00284899130.1375025178

0.01061552160.00275378260.133624626

0.0102731490.00266279440.129881227

0.00994534060.00257579410.1262671482

0.00963133040.00249256440.1227774092

0.00933040010.0024129020.1194072181

0.00904187570.00233661690.1161519659

0.00876512470.0022635310.1130072224

0.00849955270.00219347740.1099687305

0.0082446010.00212629980.1070324008

0.0079997440.00206185130.1041943067

0.00776448710.0019999940.1014506787

0.00753836450.00194059840.0987978987

0.00732093710.00188354270.0962324949

0.0071117910.00182871220.0937511366

0.00691053580.0017759990.0913506285

0.00671680270.00172530140.0890279058

0.00653024380.00167652370.086780029

0.00635052990.00162957530.084604179

0.006177350.0015843710.0824976523

0.00601040980.00154083020.0804578564

0.0058494310.00149887680.078482305

0.00569414970.00145843870.0765686139

0.00554431610.0014194480.0747144967

0.00539969340.00138184020.0729177604

0.00526005710.00134555420.0711763019

0.00512519410.00131053240.0694881041

0.00499490210.00127671990.0678512318

0.00486898930.00124406480.0662638289

0.0047472730.00121251790.0647241144

0.004629580.00118203230.0632303797

0.00451574540.00115256360.061780985

0.00440561230.00112406970.0603743568

0.00429903160.00109651040.0590089844

Butterworth-mod

Chebychev-mod

Bessel-mod

Feuil1



0.10.99995000370.99496999051.00607528730.1-0.0004342728-0.04380035780.0526096269

0.20.99920095870.97975871241.02434230110.2-0.0069431587-0.17761731830.2089021532

0.30.99597443880.95414465281.05477640880.3-0.0350361474-0.40771558490.4632081551

0.40.98744063190.91817224791.09675221230.4-0.1097801217-0.74151676210.8021703825

0.50.97014250010.87256883881.14784801150.5-0.2632893872-1.18400601251.1976877243

0.60.94088741190.81898141891.20165451120.6-0.5292468371-1.73451902811.5955924239

0.70.89799030160.7598719971.244948880.7-0.934567075-2.38519119871.9030303767

0.80.84227140070.69810145021.25729698820.8-1.4909589107-3.1216291961.9887575047

0.90.77706387850.636407011.21923998940.9-2.1908655717-3.92530090551.7217839696

10.70710678120.5771.1281-3.0102999566-4.77648373691.0461819929

1.10.63704606240.52139170291.0024737611.1-3.9165832872-5.65671768350.0214602821

1.20.57039580950.47042046220.86863507191.2-4.8764734752-6.5502759141-1.2232527924

1.30.50924392410.42439006160.74446412491.3-5.8614828791-7.4446958995-2.5631245143

1.40.45447034170.38323625680.63731569091.4-6.8498890634-8.3306682073-3.9129077784

1.50.40613846610.34667308740.5479280071.5-7.8265175161-9.2015974358-5.2255300059

1.60.36385052710.3143018550.47428153141.6-8.7815398309-10.0530611161-6.4792757309

1.70.32699825040.28568362610.41368158851.7-9.70909142-10.8822930071-7.6666761511

1.80.29491468760.26038307660.36360027981.8-10.6060719552-11.6877449151-8.7875158255

1.90.26695537190.23799236810.32192316951.9-11.4712267104-12.468739391-9.8449553007

20.2425356250.21814220970.28696200292-12.3044892138-13.2252058391-10.8435121022

2.10.22114316440.20050523810.25739335242.1-13.1065296037-13.9574855414-11.7880534729

2.20.20233796590.18479511220.2321849652.2-13.878452407-14.6661904015-12.6833181217

2.30.18574626530.17076343960.21053028192.3-14.6215981942-15.3521021193-13.5337085621

2.40.17105241840.1581957980.19179577832.4-15.3374156268-16.0161011265-14.3432191289

2.50.15799050110.14690755970.1754803542.5-16.0273804686-16.659117109-15.1154299644

2.60.14633651890.1367398970.1611845612.6-16.6929456079-17.2820950342-15.853531186

2.70.13590155640.12755614580.14858742192.7-17.3355113913-17.8859722338-16.56035905

2.80.12652593110.11923859060.13742895592.8-17.9564091585-18.4716633227-17.2384350594

2.90.11807428830.11168567360.12749695552.9-18.55689327-19.0400506418-17.8900037124

30.11043152610.10480960190.11861692153-19.1381385238-19.5919785702-18.5170670274

3.10.1034994290.09853430860.11064434913.1-19.7012409206-20.1282505274-19.1214152316

3.20.09719389310.0927937250.10345877213.2-20.2472204346-20.6496278253-19.7046536069

3.30.09144263960.0875303190.09695913043.3-20.7770249203-21.1568297736-20.2682257653

3.40.086183330.08269386090.09106013993.4-21.2915345865-21.6505346157-20.8134337386

3.50.08136200950.07824037980.08568942643.5-21.7915666775-22.1313809977-21.3414552825

3.60.07693181760.07413128220.08078524773.6-22.2778801347-22.5999697579-21.8533587788

3.70.07285191880.07033260530.07629466953.7-22.7511801015-23.0568658937-22.3501160811

3.80.06908661120.06681438420.07217209633.8-23.2121221925-23.502600601-22.8326136048

3.90.06560458240.0635501140.06837808033.9-23.6613164875-23.9376733197-23.3016619235

40.06237828620.06051629250.06487834994-24.0993312333-24.3625537367-23.7580040922

4.10.05938341750.05769202910.06164301274.1-24.526696254-24.7776837186-24.2023228859

4.20.05659847060.05505871130.05864589854.2-24.943906079-25.1834791543-24.6352471122

4.30.05400436450.05259971790.05586401474.3-25.3514228036-25.5803316979-25.0573571319

4.40.05158412460.05030017310.05327709244.4-25.7496786989-25.9686104072-25.4691897007

4.50.04932261230.04814673440.05086720664.5-26.139078592-26.3486632773-25.8712422281

4.60.04720629310.04612740960.04861845724.6-26.520002033-26.7208186706-26.2639765319

4.70.04522303830.04423139820.04651669944.7-26.8928052692-27.0853866478-26.6478221603

4.80.04336195430.04244895370.04454931534.8-27.2578230431-27.4426602033-27.0231793364

4.90.04161323590.04077126430.04270501924.9-27.6153702301-27.7929164122-27.3904215759

50.03996803830.03919034850.0409736925-27.9657433321-28.1364174918-27.7498980203

5.10.03841836760.03769896360.03934623885.1-28.3092218396-28.4734117855-28.1019355214

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5.30.03557732030.03495904250.0363709775.3-28.9765353297-29.1288094182-28.7849006596

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60.02776706720.02738820440.02824708486-31.1293997608-31.2487288055-30.9805273371

6.10.02686479650.02650991180.02731375616.1-31.4163289104-31.5318343559-31.2723714603

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6.30.02518727010.02487492380.02558130886.3-31.9763780105-32.0847648216-31.8415447945

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6.80.02162124210.02139045470.02191066146.8-33.3023872146-33.3955996593-33.1868902608

6.90.02099935920.02078155420.02127221446.9-33.5558791736-33.6464395316-33.4437459681

70.02040391470.02019819350.02066137587-33.8057300307-33.8937494353-33.6968152525

7.10.01983343180.01963896940.02007657097.1-34.0520426474-34.1376261357-33.9462092512

7.20.01928653540.01910257320.01951633617.2-34.2949156049-34.378162528-34.1920342388

7.30.01876194370.01858778360.01897930947.3-34.5344434363-34.6154478371-34.4343919083

7.40.01825846060.01809345940.01846422227.4-34.7707168441-34.8495678059-34.6733796323

7.50.01777496910.01761853350.01796989197.5-35.0038229038-35.080604871-34.9090907061

7.60.01731042530.01716200730.01749521457.6-35.2338452532-35.3086383286-35.1416145737

7.70.01686385220.01672294550.01703915877.7-35.4608642705-35.5337444895-35.3710370379

7.80.01643433510.01630047120.01660076027.8-35.6849572406-35.7559968252-35.5974404569

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80.0156230930.01550204430.01577338228-36.1246596395-36.192220526-36.0415034536

8.10.0152398090.01512459340.01538276468.1-36.340409529-36.4063258338-36.2593121119

8.20.01487045550.01476072630.015006528.2-36.5535145589-36.6178454381-36.4744001954

Feuil1

Butterworth

Bessel

Chebychev

Feuil2

Butterworth

Bessel

Chebychev

Feuil3

Butterworth-modButterworthChebychev-modBessel-modBessel

0.011-0.02000033340.99955042340.99999-0.01

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0.080.9999998689-0.16017197140.97283760380.9993600681-0.08

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0.10.9999995-0.20033730460.95887546430.9990001659-0.0999999999

0.150.9999943047-0.30115488240.91649356040.9977508356-0.1499999989

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0.40.9979582701-0.8249255870.72717446320.9840399456-0.3999989854

0.450.9958737967-0.93658187460.71225175110.9798129512-0.4499977014

0.50.9922778767-1.05165021250.70710678120.9750942764-0.49999523

0.550.9864405401-1.17055130210.71260792530.9698854841-0.5499907813

0.60.9774577994-1.29357078120.73008339550.9641882-0.5999832027

0.650.9642977858-1.42076798420.76137545670.9580041206-0.6499708751

0.70.9459044815-1.55187710850.80845631070.9513350367-0.6999515953

0.750.921364161-1.68622298720.87157553710.9441828764-0.7499224478

0.80.8901138251-1.82268334290.94326863020.936549767-0.799879666

0.850.8521370594-1.95972897070.99565732790.9284381188-0.8498184866

0.90.8080716399-2.09555529180.97745779940.9198507308-0.8997330005

0.950.7591695144-2.22828559010.8652188820.9107909168-0.9496160028

10.7071067812-2.35619449020.70710678120.9012626522-0.999458847

1.050.6537070914-2.47789062180.55972757790.8912707369-1.0492513072

1.10.6006725411-2.59241680970.4429561620.8808209729-1.0989814536

1.150.5493957548-2.69926089530.35499130520.86992035-1.1486355458

1.20.5008783089-2.79829917140.2890445770.8585772359-1.1981979481

1.250.4557382784-2.88970563750.23901904710.8468015624-1.2476510732

1.30.4142710726-2.9738559550.20043121460.8346050024-1.2969753563

1.350.3765297999-3.05124383220.17014906930.8220011292-1.3461492652

1.40.3424027915-3.12241692210.1459983520.8090055503-1.3951493474

1.450.3116775383-3.18793231060.12645451050.7956360103-1.4439503179

1.50.2840883297-3.24832832620.11043152610.7819124532-1.4925251863

1.550.2593491032-3.30410850990.09714220990.7678570417-1.5408454244

1.60.2371745719-3.35573394980.08600609550.753494127-1.5888811716

1.650.2172928106-3.40362099630.07658814870.7388501675-1.6366014743

1.70.1994519847-3.4481422090.06855739240.7239535954-1.6839745555

1.750.1834232596-3.48962908340.06165852070.7088346333-1.7309681092

1.80.1690013411-3.52837562410.05569210120.6935250629-1.7775496113

1.850.1560036297-3.56464219140.05050054530.6780579527-1.8236866423

1.90.1442686339-3.59865928790.04595801310.6624673506-1.869347211

1.950.1336540468-3.63063110810.04196304680.6467879506-1.9145000745

20.1240347346-3.66073876780.03843312210.6310547429-1.959115045

2.050.1153007791-3.68914318440.03530056840.6153026562-2.0031632765

2.10.1073556508-3.71598761640.03250947920.5995662048-2.0466175273

2.150.1001145477-3.74139988350.03001334690.5838791467-2.0894523903

2.20.0935029119-3.76549429720.02777323430.5682741637-2.1316444898

2.250.0874551186-3.78837333520.02575634780.5527825697-2.1731726409

2.30.0819133276-3.81012909040.02393491470.5374340538-2.2140179699

2.350.0768264819-3.83084452580.02228529260.5222564614-2.2541639969

2.40.0721494382-3.85059455960.02078725720.5072756179-2.2935966804

2.450.0678422129-3.86944700650.019423430.4925151938-2.3323044268

2.50.0638693293-3.88746339340.01817881370.4779966125-2.370278066

2.550.0601992525-3.90469966870.01704041380.4637389989-2.4075107992

2.60.0568039005-3.92120681980.01599692890.4497591648-2.4439981198

2.650.0536582204-3.93703141170.01503849410.4360716295-2.479737713

2.70.0507398215-3.95221605780.014156470.42268867-2.5147293384

2.750.0480286561-3.96679983290.01334326570.4096203975-2.5489746982

2.80.0455067434-3.98081863510.01259219120.3968748546-2.5824772961

2.850.0431579277-3.99430550530.01189733330.3844581294-2.6152422901

2.90.0409676687-4.00729090820.01125345140.3723744829-2.6472763416

2.950.0389228585-4.01980298140.01065588820.3606264835-2.6785874649

30.0370116605-4.03186775570.01010049480.3492151479-2.709184878

3.050.0352233699-4.04350935120.00958356610.3381400833-2.7390788578

3.10.0335482897-4.05475015140.00910178560.327399629-2.7682806011

3.150.0319776229-4.06561095880.00865217860.3169909947-2.7968020916

3.20.0305033772-4.07611113410.00823207090.3069103945-2.8246559758

3.250.0291182805-4.08626872040.00783905360.2971531747-2.8518554459

3.30.0278157072-4.09610055490.00747095280.2877139338-2.8784141326

3.350.026589612-4.10562236960.00712580290.2785866355-2.9043460056

3.40.0254344721-4.11484888170.00680182340.2697647128-2.9296652838

3.450.0243452352-4.12379387530.00649739870.2612411639-2.9543863537

3.50.0233172738-4.13247027510.00621106030.2530086395-2.9785236959

3.550.022346344-4.14089021330.00594147160.2450595219-3.0020918198

3.60.021428549-4.14906509040.00568741370.2373859956-3.0251052061

3.650.0205603069-4.15700563030.00544777370.229980111-3.0475782557

3.70.0197383211-4.16472193010.00522153370.2228338401-3.0695252454

3.750.0189595544-4.17222350640.00500776190.2159391256-3.09096029

3.80.0182212054-4.17951933670.00480560370.2092879241-3.1118973093

3.850.0175206875-4.18661789730.00461427420.2028722433-3.1323500007

3.90.0168556101-4.19352719880.00443305220.196684173-3.1523318159

3.950.0162237614-4.20025481760.00426127350.1907159133-3.1718559418

40.015623093-4.20680792550.00409832620.1849597962-3.1909352858

4.050.0150517061-4.21319331680.00394364570.1794083048-3.2095824631

4.10.0145078388-4.21941743270.00379671050.1740540889-3.2278097878

4.150.0139898548-4.22548638480.00365703820.1688899764-3.2456292665

4.20.0134962332-4.23140597570.00352418230.1639089837-3.2630525941

4.250.0130255588-4.23718171880.00339772940.159104322-3.280091151

4.30.0125765142-4.24281885610.00327729550.1544694027-3.2967560031

4.350.0121478713-4.24832237490.00316252450.1499978406-3.3130579022

4.40.0117384849-4.25369702360.00305308530.1456834552-3.3290072883

4.450.0113472861-4.25894732540.00294866980.1415202713-3.344614293

4.50.0109732762-4.26407759220.00284899130.1375025178-3.3598887434

4.550.0106155216-4.26909193660.00275378260.133624626-3.3748401669

4.60.010273149-4.27399428360.00266279440.129881227-3.3894777969

4.650.0099453406-4.27878838080.00257579410.1262671482-3.4038105788

4.70.0096313304-4.28347780930.00249256440.1227774092-3.4178471762

4.750.0093304001-4.28806599210.0024129020.1194072181-3.431595978

4.80.0090418757-4.29255620310.00233661690.1161519659-3.445065105

4.850.0087651247-4.29695157540.0022635310.1130072224-3.4582624173

4.90.0084995527-4.30125510860.00219347740.1099687305-3.4711955212

4.950.008244601-4.3054696760.00212629980.1070324008-3.4838717769

50.007999744-4.30959803130.00206185130.1041943067-3.4962983056

5.050.0077644871-4.31364281470.0019999940.1014506787-3.5084819969

5.10.0075383645-4.31760655880.00194059840.0987978987-3.5204295158

5.150.0073209371-4.32149169390.00188354270.0962324949-3.5321473101

5.20.007111791-4.32530055360.00182871220.0937511366-3.5436416173

5.250.0069105358-4.3290353790.0017759990.0913506285-3.5549184716

5.30.0067168027-4.33269832380.00172530140.0890279058-3.5659837107

5.350.0065302438-4.33629145830.00167652370.086780029-3.5768429822

5.40.0063505299-4.33981677330.00162957530.084604179-3.5875017504

5.450.00617735-4.34327618430.0015843710.0824976523-3.5979653024

5.50.0060104098-4.34667153480.00154083020.0804578564-3.6082387544

5.550.005849431-4.35000459950.00149887680.078482305-3.6183270574

5.60.0056941497-4.35327708780.00145843870.0765686139-3.6282350032

5.650.0055443161-4.35649064690.0014194480.0747144967-3.63796723

5.70.0053996934-4.35964686410.00138184020.0729177604-3.6475282278

5.750.0052600571-4.362747270.00134555420.0711763019-3.6569223435

5.80.0051251941-4.36579334090.00131053240.0694881041-3.6661537861

5.850.0049949021-4.36878650120.00127671990.0678512318-3.6752266317

5.90.0048689893-4.37172812540.00124406480.0662638289-3.6841448282

5.950.004747273-4.37461954080.00121251790.0647241144-3.6929121996

60.00462958-4.3774620290.00118203230.0632303797-3.7015324507

6.050.0045157454-4.38025682840.00115256360.061780985-3.7100091714

6.10.0044056123-4.38300513540.00112406970.0603743568-3.7183458405

6.150.0042990316-4.38570810660.00109651040.0590089844-3.72654583

Feuil3

Butterworth-mod

Chebychev-mod

Bessel-mod

Graph6

-0-0.0039058512-0.0000868592

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-39.765928269-51.4932473482-17.729072343

-40.0476067544-51.7817770932-17.9741925662

-40.3262743574-52.0670722693-18.2176307024

-40.6019946749-52.3492061902-18.4593883945

-40.8748293167-52.6282496553-18.6994687043

-41.1448379862-52.904271065-18.9378759869

-41.4120785578-53.1773365304-19.1746157727

-41.676607151-53.4475099757-19.4096946594

-41.9384781997-53.7148532349-19.6431202111

-42.1977445193-53.9794261443-19.8749008656

-42.4544573691-54.2412866281-20.105045848

-42.7086665137-54.5004907809-20.3335650918

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-43.2097656088-55.0111457837-20.7857692036

-43.4567481143-55.2627003507-21.0094768472

-43.7014121261-55.5118061565-21.2316041834

-43.9438007405-55.7585112303-21.452163694

-44.183955865-56.0028621796-21.6711682062

-44.4219182615-56.2449042469-21.888630848

-44.6577275874-56.4846813625-22.1045650068

-44.8914224354-56.7222361963-22.3189842914

-45.1230403709-56.9576102055-22.5319024976

-45.3526179681-57.1908436812-22.7433335757

-45.5801908445-57.4219757921-22.9532916017

-45.8057936941-57.6510446265-23.1617907502

-46.0294603186-57.8780872319-23.3688452701

-46.2512236582-58.1031396535-23.5744694619

-46.47111582-58.32623697-23.7786776572

-46.6891681064-58.5474133287-23.9814842001

-46.9054110412-58.7667019783-24.1829034301

-47.1198743955-58.9841353006-24.3829496665

-47.3325872122-59.1997448408-24.5816371944

Butterworth

Chebychev

Bessel

Feuil1



0.10.99995000370.99496999051.00607528730.1-0.0004342728-0.04380035780.0526096269

0.20.99920095870.97975871241.02434230110.2-0.0069431587-0.17761731830.2089021532

0.30.99597443880.95414465281.05477640880.3-0.0350361474-0.40771558490.4632081551

0.40.98744063190.91817224791.09675221230.4-0.1097801217-0.74151676210.8021703825

0.50.97014250010.87256883881.14784801150.5-0.2632893872-1.18400601251.1976877243

0.60.94088741190.81898141891.20165451120.6-0.5292468371-1.73451902811.5955924239

0.70.89799030160.7598719971.244948880.7-0.934567075-2.38519119871.9030303767

0.80.84227140070.69810145021.25729698820.8-1.4909589107-3.1216291961.9887575047

0.90.77706387850.636407011.21923998940.9-2.1908655717-3.92530090551.7217839696

10.70710678120.5771.1281-3.0102999566-4.77648373691.0461819929

1.10.63704606240.52139170291.0024737611.1-3.9165832872-5.65671768350.0214602821

1.20.57039580950.47042046220.86863507191.2-4.8764734752-6.5502759141-1.2232527924

1.30.50924392410.42439006160.74446412491.3-5.8614828791-7.4446958995-2.5631245143

1.40.45447034170.38323625680.63731569091.4-6.8498890634-8.3306682073-3.9129077784

1.50.40613846610.34667308740.5479280071.5-7.8265175161-9.2015974358-5.2255300059

1.60.36385052710.3143018550.47428153141.6-8.7815398309-10.0530611161-6.4792757309

1.70.32699825040.28568362610.41368158851.7-9.70909142-10.8822930071-7.6666761511

1.80.29491468760.26038307660.36360027981.8-10.6060719552-11.6877449151-8.7875158255

1.90.26695537190.23799236810.32192316951.9-11.4712267104-12.468739391-9.8449553007

20.2425356250.21814220970.28696200292-12.3044892138-13.2252058391-10.8435121022

2.10.22114316440.20050523810.25739335242.1-13.1065296037-13.9574855414-11.7880534729

2.20.20233796590.18479511220.2321849652.2-13.878452407-14.6661904015-12.6833181217

2.30.18574626530.17076343960.21053028192.3-14.6215981942-15.3521021193-13.5337085621

2.40.17105241840.1581957980.19179577832.4-15.3374156268-16.0161011265-14.3432191289

2.50.15799050110.14690755970.1754803542.5-16.0273804686-16.659117109-15.1154299644

2.60.14633651890.1367398970.1611845612.6-16.6929456079-17.2820950342-15.853531186

2.70.13590155640.12755614580.14858742192.7-17.3355113913-17.8859722338-16.56035905

2.80.12652593110.11923859060.13742895592.8-17.9564091585-18.4716633227-17.2384350594

2.90.11807428830.11168567360.12749695552.9-18.55689327-19.0400506418-17.8900037124

30.11043152610.10480960190.11861692153-19.1381385238-19.5919785702-18.5170670274

3.10.1034994290.09853430860.11064434913.1-19.7012409206-20.1282505274-19.1214152316

3.20.09719389310.0927937250.10345877213.2-20.2472204346-20.6496278253-19.7046536069

3.30.09144263960.0875303190.09695913043.3-20.7770249203-21.1568297736-20.2682257653

3.40.086183330.08269386090.09106013993.4-21.2915345865-21.6505346157-20.8134337386

3.50.08136200950.07824037980.08568942643.5-21.7915666775-22.1313809977-21.3414552825

3.60.07693181760.07413128220.08078524773.6-22.2778801347-22.5999697579-21.8533587788

3.70.07285191880.07033260530.07629466953.7-22.7511801015-23.0568658937-22.3501160811

3.80.06908661120.06681438420.07217209633.8-23.2121221925-23.502600601-22.8326136048

3.90.06560458240.0635501140.06837808033.9-23.6613164875-23.9376733197-23.3016619235

40.06237828620.06051629250.06487834994-24.0993312333-24.3625537367-23.7580040922

4.10.05938341750.05769202910.06164301274.1-24.526696254-24.7776837186-24.2023228859

4.20.05659847060.05505871130.05864589854.2-24.943906079-25.1834791543-24.6352471122

4.30.05400436450.05259971790.05586401474.3-25.3514228036-25.5803316979-25.0573571319

4.40.05158412460.05030017310.05327709244.4-25.7496786989-25.9686104072-25.4691897007

4.50.04932261230.04814673440.05086720664.5-26.139078592-26.3486632773-25.8712422281

4.60.04720629310.04612740960.04861845724.6-26.520002033-26.7208186706-26.2639765319

4.70.04522303830.04423139820.04651669944.7-26.8928052692-27.0853866478-26.6478221603

4.80.04336195430.04244895370.04454931534.8-27.2578230431-27.4426602033-27.0231793364

4.90.04161323590.04077126430.04270501924.9-27.6153702301-27.7929164122-27.3904215759

50.03996803830.03919034850.0409736925-27.9657433321-28.1364174918-27.7498980203

5.10.03841836760.03769896360.03934623885.1-28.3092218396-28.4734117855-28.1019355214

5.20.03695698440.03629052630.03781446625.2-28.6460694751-28.8041346741-28.4468405077

5.30.03557732030.03495904250.0363709775.3-28.9765353297-29.1288094182-28.7849006596

5.40.03427340520.03369904570.03500907855.4-29.3008549025-29.4476479399-29.1163864166

5.50.03303980290.03250554280.03372270345.5-29.619251052-29.7608515449-29.4415523353

5.60.03187155530.03137396590.03250634085.6-29.9319348685-30.0686115928-29.760638317

5.70.03076413270.03030013020.03135497545.7-30.2391064745-30.3711101175-30.0738707178

5.80.02971339060.0292801960.03026403515.8-30.5409557595-30.668520403-30.381463356

5.90.02871553070.02831063590.02922934475.9-30.8376630558-30.9610075167-30.6836184273

60.02776706720.02738820440.02824708486-31.1293997608-31.2487288055-30.9805273371

6.10.02686479650.02650991180.02731375616.1-31.4163289104-31.5318343559-31.2723714603

6.20.02600576980.02567300050.02642614776.2-31.6986057074-31.8104674216-31.5593228345

6.30.02518727010.02487492380.02558130886.3-31.9763780105-32.0847648216-31.8415447945

6.40.02440678980.02411332690.02477652376.4-32.249786785-32.3548573105-32.1191925533

6.50.02366201220.02338603010.02400928986.5-32.5189665216-32.6208699232-32.3924137353

6.60.02295079420.0226910130.02327729756.6-32.7840456226-32.8829222963-32.6613488668

6.70.0222711510.02202640150.02257841286.7-33.0451467612-33.1411289684-32.9261318264

6.80.02162124210.02139045470.02191066146.8-33.3023872146-33.3955996593-33.1868902608

6.90.02099935920.02078155420.02127221446.9-33.5558791736-33.6464395316-33.4437459681

70.02040391470.02019819350.02066137587-33.8057300307-33.8937494353-33.6968152525

7.10.01983343180.01963896940.02007657097.1-34.0520426474-34.1376261357-33.9462092512

7.20.01928653540.01910257320.01951633617.2-34.2949156049-34.378162528-34.1920342388

7.30.01876194370.01858778360.01897930947.3-34.5344434363-34.6154478371-34.4343919083

7.40.01825846060.01809345940.01846422227.4-34.7707168441-34.8495678059-34.6733796323

7.50.01777496910.01761853350.01796989197.5-35.0038229038-35.080604871-34.9090907061

7.60.01731042530.01716200730.01749521457.6-35.2338452532-35.3086383286-35.1416145737

7.70.01686385220.01672294550.01703915877.7-35.4608642705-35.5337444895-35.3710370379

7.80.01643433510.01630047120.01660076027.8-35.6849572406-35.7559968252-35.5974404569

7.90.01602101670.01589376160.01617911667.9-35.9061985113-35.975466105-35.8209039269

80.0156230930.01550204430.01577338228-36.1246596395-36.192220526-36.0415034536

8.10.0152398090.01512459340.01538276468.1-36.340409529-36.4063258338-36.2593121119

8.20.01487045550.01476072630.015006528.2-36.5535145589-36.6178454381-36.4744001954

Feuil1

Butterworth

Bessel

Chebychev

Feuil2

Butterworth

Bessel

Chebychev

Feuil3

Butterworth-modButterworthButterworthChebychev-modChebychevBessel-modBesselBessel

0.011-0-0.02000033340.9995504234-0.00390585120.99999-0.0000868592-0.01

0.021-0.0000000003-0.04000266790.9982067546-0.01558991370.9999600003-0.0003474402-0.02

0.030.9999999996-0.0000000032-0.06000900970.9959840363-0.03495244840.9999100013-0.0007817535-0.03

0.040.999999998-0.0000000178-0.08002137420.992906876-0.06182963530.9998400043-0.0013898165-0.04

0.050.9999999922-0.0000000679-0.10004179140.989008778-0.09599707520.9997500104-0.0021716535-0.05

0.060.9999999767-0.0000002026-0.12007231020.9843312582-0.13717446650.9996400216-0.0031272959-0.06

0.070.9999999412-0.0000005109-0.14011500330.9789227855-0.18503125380.9995100399-0.004256782-0.07

0.080.9999998689-0.0000011385-0.16017197140.9728376038-0.23919301320.9993600681-0.0055601573-0.08

0.090.9999997343-0.000002308-0.18024534830.9661344845-0.29924832450.999190109-0.0070374743-0.09

0.10.9999995-0.0000043429-0.20033730460.9588754643-0.3647558790.9990001659-0.0086887926-0.0999999999

0.150.9999943047-0.0000494686-0.30115488240.9164935604-0.75741164380.9977508356-0.0195579964-0.1499999989

0.20.9999680015-0.0002779396-0.4027909490.8695244543-1.21436399040.9960026214-0.034790371-0.1999999919

0.250.999877952-0.0010601599-0.50558105490.8240419242-1.68101384890.9937563397-0.0544017546-0.2499999616

0.30.9996356992-0.0031648533-0.60990703080.7839186408-2.11458016640.9910129975-0.0784129909-0.2999998631

0.350.9990821325-0.0079761573-0.71619839580.7512721297-2.48405444160.9877737647-0.1068502575-0.3499995992

0.40.9979582701-0.0177523699-0.8249255870.7271744632-2.76722762020.9840399456-0.1397454336-0.3999989854

0.450.9958737967-0.0359138911-0.93658187460.7122517511-2.94732948760.9798129512-0.1771364865-0.4499977014

0.50.9922778767-0.0673338266-1.05165021250.7071067812-3.01029995660.9750942764-0.2190678557-0.49999523

0.550.9864405401-0.118581754-1.17055130210.7126079253-2.94298703890.9698854841-0.2655908109-0.5499907813

0.60.9774577994-0.198039674-1.29357078120.7300833955-2.7325505750.9641882-0.3167637563-0.5999832027

0.650.9642977858-0.3157766095-1.42076798420.7613754567-2.36802253930.9580041206-0.3726524584-0.6499708751

0.70.9459044815-0.4830543387-1.55187710850.8084563107-1.84686889150.9513350367-0.4333301664-0.6999515953

0.750.921364161-0.7113736971-1.68622298720.8715755371-1.19389935560.9441828764-0.4988776028-0.7499224478

0.80.8901138251-1.0110890708-1.82268334290.9432686302-0.50729216880.936549767-0.5693827972-0.799879666

0.850.8521370594-1.389810937-1.95972897070.9956573279-0.03780211130.9284381188-0.6449407413-0.8498184866

0.90.8080716399-1.8510026992-2.09555529180.9774577994-0.1980396740.9198507308-0.7256528459-0.8997330005

0.950.7591695144-2.3932248001-2.22828559010.865218882-1.25748022750.9107909168-0.8116261839-0.9496160028

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Feuil3

Butterworth-mod

Chebychev-mod

Bessel-mod

Butterworth

Chebychev

Bessel

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Butterworth

Bessel

Feuil1



0.10.99995000370.99496999051.00607528730.1-0.0004342728-0.04380035780.0526096269

0.20.99920095870.97975871241.02434230110.2-0.0069431587-0.17761731830.2089021532

0.30.99597443880.95414465281.05477640880.3-0.0350361474-0.40771558490.4632081551

0.40.98744063190.91817224791.09675221230.4-0.1097801217-0.74151676210.8021703825

0.50.97014250010.87256883881.14784801150.5-0.2632893872-1.18400601251.1976877243

0.60.94088741190.81898141891.20165451120.6-0.5292468371-1.73451902811.5955924239

0.70.89799030160.7598719971.244948880.7-0.934567075-2.38519119871.9030303767

0.80.84227140070.69810145021.25729698820.8-1.4909589107-3.1216291961.9887575047

0.90.77706387850.636407011.21923998940.9-2.1908655717-3.92530090551.7217839696

10.70710678120.5771.1281-3.0102999566-4.77648373691.0461819929

1.10.63704606240.52139170291.0024737611.1-3.9165832872-5.65671768350.0214602821

1.20.57039580950.47042046220.86863507191.2-4.8764734752-6.5502759141-1.2232527924

1.30.50924392410.42439006160.74446412491.3-5.8614828791-7.4446958995-2.5631245143

1.40.45447034170.38323625680.63731569091.4-6.8498890634-8.3306682073-3.9129077784

1.50.40613846610.34667308740.5479280071.5-7.8265175161-9.2015974358-5.2255300059

1.60.36385052710.3143018550.47428153141.6-8.7815398309-10.0530611161-6.4792757309

1.70.32699825040.28568362610.41368158851.7-9.70909142-10.8822930071-7.6666761511

1.80.29491468760.26038307660.36360027981.8-10.6060719552-11.6877449151-8.7875158255

1.90.26695537190.23799236810.32192316951.9-11.4712267104-12.468739391-9.8449553007

20.2425356250.21814220970.28696200292-12.3044892138-13.2252058391-10.8435121022

2.10.22114316440.20050523810.25739335242.1-13.1065296037-13.9574855414-11.7880534729

2.20.20233796590.18479511220.2321849652.2-13.878452407-14.6661904015-12.6833181217

2.30.18574626530.17076343960.21053028192.3-14.6215981942-15.3521021193-13.5337085621

2.40.17105241840.1581957980.19179577832.4-15.3374156268-16.0161011265-14.3432191289

2.50.15799050110.14690755970.1754803542.5-16.0273804686-16.659117109-15.1154299644

2.60.14633651890.1367398970.1611845612.6-16.6929456079-17.2820950342-15.853531186

2.70.13590155640.12755614580.14858742192.7-17.3355113913-17.8859722338-16.56035905

2.80.12652593110.11923859060.13742895592.8-17.9564091585-18.4716633227-17.2384350594

2.90.11807428830.11168567360.12749695552.9-18.55689327-19.0400506418-17.8900037124

30.11043152610.10480960190.11861692153-19.1381385238-19.5919785702-18.5170670274

3.10.1034994290.09853430860.11064434913.1-19.7012409206-20.1282505274-19.1214152316

3.20.09719389310.0927937250.10345877213.2-20.2472204346-20.6496278253-19.7046536069

3.30.09144263960.0875303190.09695913043.3-20.7770249203-21.1568297736-20.2682257653

3.40.086183330.08269386090.09106013993.4-21.2915345865-21.6505346157-20.8134337386

3.50.08136200950.07824037980.08568942643.5-21.7915666775-22.1313809977-21.3414552825

3.60.07693181760.07413128220.08078524773.6-22.2778801347-22.5999697579-21.8533587788

3.70.07285191880.07033260530.07629466953.7-22.7511801015-23.0568658937-22.3501160811

3.80.06908661120.06681438420.07217209633.8-23.2121221925-23.502600601-22.8326136048

3.90.06560458240.0635501140.06837808033.9-23.6613164875-23.9376733197-23.3016619235

40.06237828620.06051629250.06487834994-24.0993312333-24.3625537367-23.7580040922

4.10.05938341750.05769202910.06164301274.1-24.526696254-24.7776837186-24.2023228859

4.20.05659847060.05505871130.05864589854.2-24.943906079-25.1834791543-24.6352471122

4.30.05400436450.05259971790.05586401474.3-25.3514228036-25.5803316979-25.0573571319

4.40.05158412460.05030017310.05327709244.4-25.7496786989-25.9686104072-25.4691897007

4.50.04932261230.04814673440.05086720664.5-26.139078592-26.3486632773-25.8712422281

4.60.04720629310.04612740960.04861845724.6-26.520002033-26.7208186706-26.2639765319

4.70.04522303830.04423139820.04651669944.7-26.8928052692-27.0853866478-26.6478221603

4.80.04336195430.04244895370.04454931534.8-27.2578230431-27.4426602033-27.0231793364

4.90.04161323590.04077126430.04270501924.9-27.6153702301-27.7929164122-27.3904215759

50.03996803830.03919034850.0409736925-27.9657433321-28.1364174918-27.7498980203

5.10.03841836760.03769896360.03934623885.1-28.3092218396-28.4734117855-28.1019355214

5.20.03695698440.03629052630.03781446625.2-28.6460694751-28.8041346741-28.4468405077

5.30.03557732030.03495904250.0363709775.3-28.

Cours Fourier Nn

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