% The multiplicative constants for the 127 point FFT

I = sqrt(-1);
u = [
       -1.007936507936508
        0.089439902139561*I
        0.240262947450275
        0.289544436377018
       -0.176602461275764
       -0.303396707504672*I
       -0.206088548264775*I
        0.169828418589816*I
        0.419828365253973
        0.166933776772187
       -0.146891581602317
       -0.073159677549720
        1.364906672131003
       -0.048711670019834
       -0.024528359070192
        0.293083283220574
        0.051608807892704
       -0.712395820653231
       -0.123705565078046
       -0.047468472567332
       -0.048730567206086
        0.007183623219005
       -0.217503617159257
       -1.014432820029656*I
        0.541261189892349*I
        0.119475655673687*I
       -0.024526708934128*I
       -0.378923179175622*I
       -1.076686633533774*I
        0.546680347973821*I
        0.348311839015605*I
       -0.043877416201291*I
        0.069164912025996*I
        0.697039817854477*I
       -0.362647179288723*I
       -0.155929164896431*I
        0.022801375045140*I
        0.103252755716542*I
       -0.811595453985388
        0.012170584644208
        0.353399799610096
        0.033021041409529
       -0.413032199204283
        0.448097771941436
       -0.603487382792324
        0.114096151297083
        0.118354343243460
       -0.991274232078563
        0.195937486548855
       -0.014842421591366
       -0.131138314214168
        0.001531677401454
       -0.240041702794502
        0.207710703728909*I
       -0.370074409454889*I
       -0.218531298837697*I
        0.042284543560394*I
       -0.019750166656037*I
        0.557933808153235*I
       -0.446888918913408*I
       -0.324749450369100*I
        0.026971323263313*I
        0.678707658072780*I
       -0.284525213187427*I
        0.114690216377197*I
        0.284442792846485*I
        0.013946733519940*I
       -0.832336676989817*I
       -0.463194931034028
       -0.113562769572260
        0.844541385164635
        0.072124078216612
       -1.423802336338749
        1.461662937464599
       -1.132071408560927
       -0.189289959213618
        0.240809959313948
       -2.871505744023579
       -0.555313707954639
        0.323260018941132
       -0.157874273144064
       -0.069992960748395
        0.834488466046246
       -0.283151869861650
        1.242056124036636
       -0.103585638562770
       -0.343632388040693
        3.900714779320568
        1.613516726117825
        0.320613396007012
       -0.399915036215681
       -0.130797744183016
        1.660379319565402
       -0.638290858167974
       -0.716454490833363
        0.405324125394163
        0.225110676335213
       -3.503264775624650
        0.248782266965226
       -0.376164451488125
       -0.246985248867288
        0.090502769941361
       -0.825637480993939
       -1.025059887860808
        0.270486004184638
        0.196401665143100
       -0.036670738376977
        0.403708808152726
        0.397868188707538
        0.131064823964077
       -0.082483284083366
       -0.051705905195606
        0.889592103192801
        1.729392997021672*I
       -1.282382491165031*I
       -0.141582314566792*I
        0.276502701613862*I
       -3.971220866400336*I
       -0.534484067648127*I
        0.326893200054031*I
       -0.790503461231153*I
       -0.073127107487412*I
        1.051713088071996*I
       -0.120117305802610*I
        0.409560731805901*I
        0.197830272695796*I
       -0.113668313817668*I
        2.166838294366128*I
        1.191869046578881*I
        0.238421188799198*I
       -0.088412917598064*I
        0.011347716421399*I
       -2.122736710015956*I
       -1.828227883900301*I
        2.047083919465486*I
       -0.339008267758077*I
       -0.297463605575563*I
        1.698117003300177*I
        0.616793684087407*I
       -0.445504228254208*I
       -0.087733195766311*I
        0.003387350683761*I
        1.919208458032399*I
       -0.973754014533518*I
        0.347987100788611*I
        0.076665077388285*I
       -0.095950139345087*I
        2.031319192138764*I
        0.787570650516143*I
       -0.791325706506505*I
        0.376503909663077*I
        0.123530237687658*I
       -0.916610030457391*I
       -0.165558792761599*I
        0.011981165482769*I
       -0.036699025643162*I
        0.036760321044636*I
       -1.362015584132842*I
        2.061273681640270
       -2.161487846246937
        2.390386992195803
        0.350286409164352
       -5.547652276788590
        0.875424520660010
        0.566311777467386
        0.489278575752784
       -0.181431308752255
       -0.793148649937573
        0.666525942074053
        0.636685355960416
       -1.894466054593347
       -0.196117514569245
        6.248747897366219
       -3.008359182939376
        1.428603206127138
       -1.001320042709276
        0.010390425332731
       -1.238481329485404
       -1.696767665780940
       -0.483711526785026
       -0.597932601797821
        0.265365142865528
       -0.593512563076814
        1.096044450027214
       -0.890780308635418
        1.118345444405576
        0.117098383905729
       -3.231116902747513
        1.228127992950587
       -0.242771916596861
       -0.270095324856058
       -0.107414819659040
        1.302298296521974
        0.311581176971160
        1.346978025644700
       -0.411785380345452
       -0.414778673257286
        5.093420194978701
        0.361621949290974
       -0.643715493697625
        0.075982028893828
        0.192225879441679
       -1.913920310495579
        0.556559679202214
        0.050141533024053
        0.028816887174438
       -0.060527944961346
        0.788304217321961
        0.118640526838238
        0.338958220073144
        0.082791357357200
       -0.077491190427428
        0.243119314969151
       -0.267742992153123
        0.052473159866232
       -0.103940236774001
       -0.001817793122853
        0.334514059129030
       -5.555246116765879
       -2.492069636197837
        1.335631691578320
        0.996769598353361
      -10.797573137867909
        0.279030998697162
       -6.183579600094408
        0.442303058588324
        1.315790083758195
       -9.596450335593000
        1.863736152869308
        1.451348429573516
       -0.273715714433894
       -0.404307247864172
        2.213430407799860
        0.127469083891542
       -3.431732979869170
        3.363322460236219
        0.587904618042327
       -5.794744474753979
        4.856595794811541
       -3.999135017113389
        0.670966437771386
        0.563391280297237
       -6.333055087714708
       -0.694871121135761
        1.956537316753483
       -1.922577442796433
       -0.349743930137407
        5.198251013226268
       -1.612235948315570
        0.770845069382445
       -1.987056031829051
       -0.015795653950222
       -0.162319053681747
       -2.130168770517638
        0.819437413388388
       -1.151144030301486
       -0.169660482178984
        5.890516896489234
        1.660828292321514
       -1.463792073569325
        1.561001307064278
        0.307327862405764
       -5.793332208477348
        0.831598275185916
        0.481210766080112
       -1.070974376307988
       -0.165292956030307
        2.033203694791040
       -1.557493541237954
        1.839966208154369
       -0.128636441963832
       -0.383677719098227
        4.350972030453366
        0.527157166888341
       -0.679433434273860
        0.373346168790201
        0.149144001474728
       -1.633461146304851
        0.437178331510366
        0.107169757490186
        0.195397568358532
       -0.040397693362798
        0.158205721076379
       -0.109708855009755
        0.458755187415202
        0.132630397088700
       -0.070267371723412
       -0.166455600925589
       -0.085592901585350
        0.013967727097641
       -0.222611554377785
       -0.017058093224312
        0.869626460775621
       -7.768105888040981
       -1.699087584816129
       -0.216635110299820
        0.755499143499894
       -3.487236063374790
        4.464029142135246
      -11.049241312533846
       -0.105623593731588
        2.129295090647347
      -13.985527104435086
       -1.582047839676736
        2.534046564175776
        1.719488306635324
       -0.386373128555562
       -4.714780351000349
       -0.729580921843937
        1.864406942038702
       -1.917903150810674
       -0.312730342402226
        3.780798917180855
       -1.910673438490517
        1.144274413215335
       -0.386748337841390
       -0.127319990514994
        2.375401245884094
        0.009448393020570
       -0.864407557571300
        1.272347832463260
        0.181953814902218
       -3.815666303530829
        1.540198377084982
       -0.733149425169861
        0.996125358179442
        0.001801742872497
        0.466933461055717
        1.275645478766193
       -0.111908628867788
        0.583025544033103
       -0.031901553562181
       -1.765668111137474
       -0.918957580782909
        0.784857460734914
       -0.893115583823285
       -0.141475415437165
        3.008149703741620
       -0.686575422712168
       -0.079479616494417
        0.447023233721348
        0.090902591896449
       -1.111833997104338
        0.415304121422265
       -1.062314744599690
        0.180140607436428
        0.266152130785171
       -3.148130741810689
       -0.296259705393105
        0.441049642657162
       -0.149776065894676
       -0.113789960305469
        1.182460485600143
       -0.331246003570860
       -0.052437096838080
       -0.074738151844323
        0.033641879441382
       -0.315503312799447
       -0.002977223942828
       -0.265904469162782
       -0.071807251481967
        0.049252854050280
       -0.025554571347854
        0.117778631246158
       -0.022146962321291
        0.108850597050595
        0.006291962115722
       -0.401380173301550
        4.441117334935619
        1.397052407004655
       -0.372998860426167
       -0.584089580617751
        4.761603067080900
       -1.581020046944135
        5.744273637542752
       -0.112226488285579
       -1.148361724801847
        7.860659146676029
       -0.093896104397524
       -1.328464997916431
       -0.481924197400477
        0.263560125473245
        0.833783314400163
       -3.154272482988389*I
       -0.988711562695005*I
        1.112320482839218*I
        0.673752750287354*I
      -11.020424753012664*I
       -3.837897926488624*I
       -0.036280250048653*I
        0.339108120408630*I
        0.246080099364035*I
       -1.883198647627719*I
        4.106703795634741*I
       -0.578239591839922*I
       -0.884452853731649*I
       -0.135884552656167*I
        3.788061272920423*I
        1.259944738866001*I
       -0.841252807514819*I
       -1.404876165018302*I
        0.282564490100226*I
       -3.661748481120631*I
       -2.424313099069315*I
        0.533587080499447*I
       -0.906695017007178*I
       -0.026718242728243*I
        1.504219563726519*I
        0.114895149148265*I
        0.317777175220746*I
        0.926645609677029*I
       -0.122278987114709*I
        1.245460212302012*I
        1.098847928672731*I
        1.669770016080784*I
       -1.065305953346333*I
       -0.582237090450772*I
        8.161996763232219*I
        0.460099201857030*I
        1.592196279880367*I
        0.261304734506003*I
       -0.390779462064343*I
        3.277895477686711*I
       -1.176421664873148*I
       -0.569033290357782*I
        0.414929565453568*I
        0.225179745744721*I
       -3.433042950087545*I
       -0.071009424571398*I
        0.290146110720480*I
        0.252676596582737*I
       -0.125089936845420*I
        1.824147525357251*I
        0.891451508498131*I
       -0.125614715464666*I
        0.211580967617796*I
       -0.014167780025642*I
       -0.206005117629258*I
       -0.344751401613748*I
       -0.034922038263524*I
       -0.162835311069409*I
        0.041832565267579*I
       -0.625516534741035*I
        0.520247759666454*I
       -5.078719724616722*I
       -1.763540921137831*I
        2.013523416988946*I
      -27.834272413196278*I
      -11.932980305935645*I
       -0.257923514397228*I
       -1.307430441908175*I
        0.705325729808376*I
       -5.411368251529459*I
        4.300548450553039*I
        2.162999192603968*I
        0.732019646486420*I
       -1.004060112700971*I
       15.052960671968448*I
        0.374614893389004*I
       -0.849785134349329*I
       -1.466883662516534*I
        0.379291363273697*I
       -4.774960293508433*I
       -6.290897000063445*I
        2.167976974617545*I
        0.695996959600212*I
       -0.224506368511092*I
        2.290890502162874*I
        2.643147215577871*I
       -0.039232506087439*I
       -0.117517000036318*I
       -0.177616602693078*I
        3.744633715770874*I
       -0.972618422452912*I
        0.240693639792939*I
       -0.108470709114505*I
        0.065736330415819*I
       -2.904841041712187*I
        0.913191303921765*I
        0.079166307387351*I
       -1.792165241359841*I
       -0.075247362183269*I
        3.691615890263455*I
        0.811091090047324*I
       -1.234597779186817*I
        0.977239197304771*I
        0.270073498917553*I
       -4.014670555074631*I
        0.926745147497850*I
        0.743573253348722*I
       -0.170781527336985*I
       -0.280023800475602*I
        4.256075995450018*I
        1.180077698303293*I
       -0.143347337292672*I
        0.261116700258809*I
        0.027988561849681*I
       -1.785099425595017*I
       -1.813665738139245*I
        0.483728312557190*I
        0.102652511979320*I
       -0.040360727294499*I
        0.011258244312228*I
        0.078236967943974*I
        0.055372179039432*I
        0.064293337978096*I
       -0.029085979001550*I
        0.654290381265442*I
       -0.049571769220318*I
       -0.040269021613972*I
        0.310403592071635*I
        0.021046189713715*I
       -0.775690111837059*I
       -0.173878168597379*I
        0.182667813246732*I
       -0.171408264915965*I
       -0.039297958211178*I
        0.584407710530250*I
        0.556049382964769*I
       -3.408817104450304*I
       -0.774555683883214*I
        1.006696668056412*I
      -14.142994972991923*I
       -2.035600045807885*I
       -0.743328856033450*I
       -2.747771990847347*I
        0.107388968804481*I
        4.393504083321446*I
        2.109438865452085*I
       -0.001858691016068*I
        1.316915795962472*I
       -0.096577352358168*I
        0.937472413512261*I
        0.926552529866462*I
        0.612832232348111*I
        0.118187726559105*I
       -0.351014704520350*I
        5.265128348840367*I
        3.376264975517356*I
       -0.710565574856297*I
       -0.345035026669614*I
       -0.007191243617648*I
       -0.135897284845052*I
       -2.249950337070870*I
        0.205824032642454*I
        0.333989951255989*I
        0.104500385116415*I
       -2.510898329563765*I
       -0.095775438804363*I
        0.200186389240627*I
        0.504448958044269*I
       -0.116100273505348*I
        2.188863174277606*I
        0.503707265049183*I
       -0.204251129295599*I
        0.899620086122340*I
        0.033988534970504*I
       -1.731945151329991*I
       -0.308662079731863*I
        0.305606867988690*I
       -0.634628268993933*I
       -0.049264837267615*I
        0.923070114257539*I
       -0.675197692056860*I
       -0.804447756476502*I
        0.412029160227773*I
        0.287420296975458*I
       -4.139357586227412*I
       -0.546725633386774*I
       -0.482949647529232*I
       -0.174140478254937*I
        0.120930300071554*I
       -0.497598684030565*I
        0.996695801004131*I
        0.028434992600197*I
       -0.172527359144296*I
       -0.061606339483407*I
        1.140594901925106*I
       -0.002409181124192*I
       -0.115172763253304*I
       -0.105656644853611*I
        0.051391971948990*I
       -0.826145968874231*I
       -0.280626579759271*I
        0.055294579026213*I
       -0.173994853229810*I
       -0.002292803229358*I
        0.327231743155439*I
        0.172876523403709*I
       -0.049248591661069*I
        0.111414525328458*I
       -0.000844869018800*I
        0.013702941403595*I
       -0.358765714210408*I
        2.829178943022342*I
        0.846032201673681*I
       -1.006740028348452*I
       13.992422462062734*I
        4.656193450581177*I
        0.333750790143560*I
        1.351734144251841*I
       -0.270904899537619*I
        0.339288056069339*I
       -2.136662438668374*I
       -0.720380167195967*I
       -0.682978480816297*I
        0.366879155019713*I
       -5.330144361826904*I
];


% The input permutation for the 127 point FFT

ip = [
   1
   2
   17
   3
   33
   5
   65
   9
   104
   125
   80
   122
   32
   116
   63
   69
   73
   10
   18
   19
   35
   37
   20
   51
   39
   101
   77
   74
   26
   53
   71
   105
   14
   82
   27
   36
   23
   99
   45
   70
   89
   12
   50
   108
   62
   88
   123
   48
   118
   95
   100
   61
   72
   121
   16
   114
   31
   38
   85
   75
   42
   22
   83
   43
   127
   112
   126
   96
   124
   64
   120
   25
   4
   49
   7
   97
   13
   66
   60
   56
   119
   111
   110
   94
   92
   109
   78
   90
   28
   52
   55
   103
   76
   58
   24
   115
   47
   102
   93
   106
   30
   84
   59
   40
   117
   79
   21
   67
   41
   6
   81
   11
   34
   29
   68
   57
   8
   113
   15
   98
   91
   44
   54
   87
   107
   46
   86
];


% The output permutation for the 127 point FFT

op = [
   1
   127
   122
   2
   124
   39
   4
   46
   126
   73
   41
   97
   6
   88
   48
   110
   121
   74
   75
   85
   43
   117
   99
   24
   8
   84
   90
   18
   50
   30
   112
   68
   123
   42
   76
   91
   77
   120
   80
   33
   38
   116
   119
   51
   94
   55
   26
   103
   3
   98
   79
   19
   92
   52
   20
   9
   45
   23
   32
   15
   107
   100
   70
   62
   125
   7
   37
   44
   78
   95
   86
   108
   72
   83
   115
   29
   82
   16
   35
   66
   40
   89
   118
   31
   114
   56
   53
   101
   96
   17
   57
   14
   28
   13
   105
   60
   5
   49
   93
   113
   81
   27
   21
   71
   87
   36
   54
   106
   22
   12
   11
   58
   47
   111
   25
   69
   34
   104
   10
   63
   109
   67
   102
   61
   65
   59
   64
];