Here's some notes from Jeffrey Lim on how Impulse Tracker processes resonant filters.

Gosh it has been *SOO* long since I looked at any of this.

Digging up tables/code:

                FILD    [CS:FilterFreqValue]         ; 0->127*256 ; I believe this is the cutoff frequency specified in IT, pre-multiplied by 256
                FMul    [CS:FreqParameterMultiplier] ; -i/(24*256)
                FLd     ST
                FRndInt
                FSub    ST(1), ST
                FXCh
                F2XM1
                FLd1
                FAdd
                FScale                              ; = 2^(i/24*256)
                FMul    [CS:FreqMultiplier]         ; = r
                FLd     ST                              ; r, r
                FMul    ST(1), ST                       ; r, r^2

                FLd     [CS:QualityFactorTable+BX]      ; 2d, r, r^2 ; BX is an index into the table dependent on the Quality factor
                FMul    ST(1), ST                       ; 2d, 2dr, r^2
                FLd1                                    ; 1, 2d, 2dr, r^2
                FSubP   ST(1), ST                       ; 2d-1, 2dr, r^2
                FAdd

                FLd1                                    ; 1, d, e ; This looks like just a variable rename for my sanity of the above.
                FAdd    ST, ST(1)
                FAdd    ST, ST(2)                       ; 1+d+e, d, e
                FLd1                                    ; 1, 1+d+e, d, e
                FDivRP  ST(1), ST                       ; 1/(1+d+e), d, e
                FSt     DWord Ptr [CS:BP+8]
                FXCh                                    ; d, 1/(1+d+e), e
                FAdd    ST, ST(2)
                FAddP   ST(2), ST                       ; 1/(1+d+e), d+2e
                FMul
                FStP    DWord Ptr [CS:BP+0Ch]
                FStP    ST

So the final coefficients here are:

a = 1/(1+d+e)
b = (d+2e) / (1+d+e)
c = -e / (1+d+e)

where d,e here are the 2dr+2d-1, r^2 defined previously

Where:

FreqMultiplier          DD      3A9F7867h   ; = 1/(2*PI*110.0*2^0.25)
FreqParameterMultiplier DD      0B92AAAAAh  ; = -1/(24*256)

QualityFactorTable Label DWord
  DD  3F800000h, 3F7A8874h, 3F752ECBh, 3F6FF262h
  DD  3F6AD298h, 3F65CED3h, 3F60E678h, 3F5C18F1h
  DD  3F5765ACh, 3F52CC19h, 3F4E4BACh, 3F49E3DCh
  DD  3F459421h, 3F415BF8h, 3F3D3AE1h, 3F39305Ch
  DD  3F353BEFh, 3F315D21h, 3F2D937Ch, 3F29DE8Ch
  DD  3F263DE0h, 3F22B109h, 3F1F379Ah, 3F1BD12Ah
  DD  3F187D50h, 3F153BA8h, 3F120BCDh, 3F0EED5Fh
  DD  3F0BDFFDh, 3F08E34Bh, 3F05F6EEh, 3F031A8Ch
  DD  3F004DCEh, 3EFB20BEh, 3EF5C3D4h, 3EF0843Ch
  DD  3EEB6156h, 3EE65A84h, 3EE16F2Dh, 3EDC9EBBh
  DD  3ED7E89Bh, 3ED34C3Ch, 3ECEC913h, 3ECA5E95h
  DD  3EC60C3Bh, 3EC1D181h, 3EBDADE7h, 3EB9A0EEh
  DD  3EB5AA1Ah, 3EB1C8F2h, 3EADFCFFh, 3EAA45CEh
  DD  3EA6A2EDh, 3EA313EEh, 3E9F9862h, 3E9C2FE1h
  DD  3E98DA02h, 3E95965Fh, 3E926494h, 3E8F4440h
  DD  3E8C3504h, 3E893681h, 3E86485Dh, 3E836A3Eh
  DD  3E809BCCh, 3E7BB965h, 3E765939h, 3E711670h
    DD  3E6BF06Ah, 3E66E68Ah, 3E61F836h, 3E5D24D6h
    DD  3E586BD9h, 3E53CCADh, 3E4F46C5h, 3E4AD998h
    DD  3E46849Eh, 3E424752h, 3E3E2134h, 3E3A11C4h
    DD  3E361887h, 3E323503h, 3E2E66C2h, 3E2AAD4Fh
    DD  3E270838h, 3E23770Fh, 3E1FF965h, 3E1C8ED2h
    DD  3E1936ECh, 3E15F14Ch, 3E12BD91h, 3E0F9B56h
    DD  3E0C8A3Eh, 3E0989E9h, 3E0699FDh, 3E03BA20h
    DD  3E00E9F9h, 3DFC5268h, 3DF6EEF8h, 3DF1A8FCh
    DD  3DEC7FD5h, 3DE772E5h, 3DE28191h, 3DDDAB43h
    DD  3DD8EF67h, 3DD44D6Ch, 3DCFC4C4h, 3DCB54E6h
    DD  3DC6FD4Ah, 3DC2BD6Ah, 3DBE94C7h, 3DBA82DFh
    DD  3DB68738h, 3DB2A157h, 3DAED0C5h, 3DAB150Eh
    DD  3DA76DC0h, 3DA3DA6Ch, 3DA05AA3h, 3D9CEDFCh
    DD  3D99940Eh, 3D964C71h, 3D9316C3h, 3D8FF2A1h
  DD  3D8CDFABh, 3D89DD84h, 3D86EBCFh, 3D840A32h

All of these are floating point coefficients written in integer form for the assembler to work...

Not sure if that helps, or makes you more confused! :)

Floating-point conversion of the above table:

1.000000000000000000000000000, 0.978644609451293945312500000, 0.957745254039764404296875000, 0.937292218208312988281250000,
0.917275905609130859375000000, 0.897687137126922607421875000, 0.878516674041748046875000000, 0.859755575656890869140625000,
0.841395139694213867187500000, 0.823426783084869384765625000, 0.805842161178588867187500000, 0.788633108139038085937500000,
0.771791517734527587890625000, 0.755309581756591796875000000, 0.739179670810699462890625000, 0.723394155502319335937500000,
0.707945764064788818359375000, 0.692827284336090087890625000, 0.678031682968139648437500000, 0.663552045822143554687500000,
0.649381637573242187500000000, 0.635513842105865478515625000, 0.621942162513732910156250000, 0.608660340309143066406250000,
0.595662117004394531250000000, 0.582941532135009765625000000, 0.570492565631866455078125000, 0.558309495449066162109375000,
0.546386539936065673828125000, 0.534718215465545654296875000, 0.523299098014831542968750000, 0.512123823165893554687500000,
0.501187205314636230468750000, 0.490484178066253662109375000, 0.480009675025939941406250000, 0.469758868217468261718750000,
0.459726989269256591796875000, 0.449909329414367675781250000, 0.440301328897476196289062500, 0.430898517370223999023437500,
0.421696513891220092773437500, 0.412690997123718261718750000, 0.403877824544906616210937500, 0.395252853631973266601562500,
0.386812061071395874023437500, 0.378551512956619262695312500, 0.370467394590377807617187500, 0.362555921077728271484375000,
0.354813396930694580078125000, 0.347236216068267822265625000, 0.339820832014083862304687500, 0.332563817501068115234375000,
0.325461775064468383789062500, 0.318511426448822021484375000, 0.311709463596343994140625000, 0.305052787065505981445312500,
0.298538267612457275390625000, 0.292162865400314331054687500, 0.285923600196838378906250000, 0.279817581176757812500000000,
0.273841977119445800781250000, 0.267993956804275512695312500, 0.262270838022232055664062500, 0.256669938564300537109375000,
0.251188635826110839843750000, 0.245824411511421203613281250, 0.240574732422828674316406250, 0.235437154769897460937500000,
0.230409294366836547851562500, 0.225488811731338500976562500, 0.220673412084579467773437500, 0.215960830450057983398437500,
0.211348906159400939941406250, 0.206835463643074035644531250, 0.202418401837348937988281250, 0.198095679283142089843750000,
0.193865269422531127929687500, 0.189725190401077270507812500, 0.185673534870147705078125000, 0.181708395481109619140625000,
0.177827939391136169433593750, 0.174030348658561706542968750, 0.170313864946365356445312500, 0.166676744818687438964843750,
0.163117289543151855468750000, 0.159633859992027282714843750, 0.156224802136421203613281250, 0.152888566255569458007812500,
0.149623572826385498046875000, 0.146428287029266357421875000, 0.143301263451576232910156250, 0.140240997076034545898437500,
0.137246102094650268554687500, 0.134315147995948791503906250, 0.131446793675422668457031250, 0.128639698028564453125000000,
0.125892534852027893066406250, 0.123204052448272705078125000, 0.120572984218597412109375000, 0.117998093366622924804687500,
0.115478195250034332275390625, 0.113012112677097320556640625, 0.110598690807819366455078125, 0.108236812055110931396484375,
0.105925373733043670654296875, 0.103663295507431030273437500, 0.101449519395828247070312500, 0.099283024668693542480468750,
0.097162798047065734863281250, 0.095087841153144836425781250, 0.093057207763195037841796875, 0.091069929301738739013671875,
0.089125096797943115234375000, 0.087221793830394744873046875, 0.085359133780002593994140625, 0.083536252379417419433593750,
0.081752300262451171875000000, 0.080006450414657592773437500, 0.078297875821590423583984375, 0.076625794172286987304687500,
0.074989423155784606933593750, 0.073387987911701202392578125, 0.071820758283138275146484375, 0.070286996662616729736328125,
0.068785987794399261474609375, 0.067317038774490356445312500, 0.065879456698894500732421875, 0.064472571015357971191406250,