/ The Datafile PD-CD 1 Issue 2 / PDCD-1 - Issue 02.iso / _utilities / utilities / 001 / fft / fft

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|00000000| 0d 00 0a 0a f4 20 3e 46 | 46 54 0d 00 14 34 f4 20 |..... >F|FT...4. |
|00000010| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 46 |        |       F|
|00000020| 61 73 74 20 46 6f 75 72 | 69 65 72 20 54 72 61 6e |ast Four|ier Tran|
|00000030| 73 66 6f 72 6d 20 69 6e | 20 42 41 53 49 43 0d 00 |sform in| BASIC..|
|00000040| 1e 05 f4 0d 00 28 31 f4 | 20 20 20 20 20 20 20 20 |.....(1.|        |
|00000050| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 28 43 |        |      (C|
|00000060| 29 31 39 39 33 20 4a 61 | 6d 65 73 20 52 20 4d 69 |)1993 Ja|mes R Mi|
|00000070| 6c 6c 65 72 0d 00 32 05 | f4 0d 00 3c 32 f4 20 20 |ller..2.|...<2.  |
|00000080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000090| 20 20 4c 61 73 74 20 6d | 6f 64 69 66 69 65 64 20 |  Last m|odified |
|000000a0| 31 39 39 33 20 46 65 62 | 20 30 38 0d 00 46 05 f4 |1993 Feb| 08..F..|
|000000b0| 0d 00 50 3a f4 20 46 72 | 65 65 20 75 73 65 20 65 |..P:. Fr|ee use e|
|000000c0| 6e 63 6f 75 72 61 67 65 | 64 20 70 72 6f 76 69 64 |ncourage|d provid|
|000000d0| 65 64 20 63 72 65 64 69 | 74 20 67 69 76 65 6e 20 |ed credi|t given |
|000000e0| 74 6f 20 61 75 74 68 6f | 72 2e 0d 00 5a 05 f4 0d |to autho|r...Z...|
|000000f0| 00 64 44 f4 20 54 68 69 | 73 20 70 72 6f 67 72 61 |.dD. Thi|s progra|
|00000100| 6d 20 69 6e 63 6c 75 64 | 65 73 20 61 20 46 61 73 |m includ|es a Fas|
|00000110| 74 20 46 6f 75 72 69 65 | 72 20 54 72 61 6e 73 66 |t Fourie|r Transf|
|00000120| 6f 72 6d 20 28 46 46 54 | 29 20 77 68 69 63 68 20 |orm (FFT|) which |
|00000130| 79 6f 75 0d 00 6e 39 f4 | 20 63 61 6e 20 73 70 6c |you..n9.| can spl|
|00000140| 69 63 65 20 69 6e 74 6f | 20 64 61 74 61 20 61 6e |ice into| data an|
|00000150| 61 6c 79 73 69 73 20 70 | 72 6f 67 72 61 6d 73 20 |alysis p|rograms |
|00000160| 6f 66 20 79 6f 75 72 20 | 6f 77 6e 2e 0d 00 78 05 |of your |own...x.|
|00000170| f4 0d 00 82 45 f4 20 59 | 6f 75 20 6d 75 73 74 20 |....E. Y|ou must |
|00000180| 66 69 72 73 74 20 68 61 | 76 65 20 63 61 6c 6c 65 |first ha|ve calle|
|00000190| 64 20 50 52 4f 43 69 6e | 69 74 20 77 68 69 63 68 |d PROCin|it which|
|000001a0| 20 65 73 74 61 62 6c 69 | 73 68 65 73 20 74 68 65 | establi|shes the|
|000001b0| 20 6f 72 64 65 72 0d 00 | 8c 42 f4 20 6f 66 20 74 | order..|.B. of t|
|000001c0| 68 65 20 46 46 54 20 41 | 25 2c 20 74 68 65 20 6e |he FFT A|%, the n|
|000001d0| 75 6d 62 65 72 20 6f 66 | 20 70 6f 69 6e 74 73 20 |umber of| points |
|000001e0| 4e 25 3d 32 5e 41 25 20 | 61 6e 64 20 64 65 63 6c |N%=2^A% |and decl|
|000001f0| 61 72 65 73 20 74 68 65 | 0d 00 96 39 f4 20 52 65 |ares the|...9. Re|
|00000200| 61 6c 20 61 6e 64 20 49 | 6d 61 67 69 6e 61 72 79 |al and I|maginary|
|00000210| 20 69 6e 70 75 74 2f 6f | 75 74 70 75 74 20 61 72 | input/o|utput ar|
|00000220| 72 61 79 73 20 52 28 29 | 20 61 6e 64 20 49 28 29 |rays R()| and I()|
|00000230| 2e 0d 00 a0 05 f4 0d 00 | aa 46 f4 20 54 68 65 6e |........|.F. Then|
|00000240| 20 6c 6f 61 64 20 52 28 | 29 20 61 6e 64 20 49 28 | load R(|) and I(|
|00000250| 29 20 77 69 74 68 20 64 | 61 74 61 2e 20 54 6f 20 |) with d|ata. To |
|00000260| 75 73 65 20 74 68 65 20 | 46 46 54 2c 20 73 65 74 |use the |FFT, set|
|00000270| 20 44 49 52 24 3d 22 54 | 74 6f 46 22 0d 00 b4 45 | DIR$="T|toF"...E|
|00000280| f4 20 6f 72 20 44 49 52 | 24 3d 22 46 74 6f 54 22 |. or DIR|$="FtoT"|
|00000290| 20 64 65 70 65 6e 64 69 | 6e 67 20 6f 6e 20 77 68 | dependi|ng on wh|
|000002a0| 65 74 68 65 72 20 79 6f | 75 20 61 72 65 20 63 6f |ether yo|u are co|
|000002b0| 6e 76 65 72 74 69 6e 67 | 20 66 72 6f 6d 20 74 68 |nverting| from th|
|000002c0| 65 0d 00 be 42 f4 20 54 | 69 6d 65 20 74 6f 20 46 |e...B. T|ime to F|
|000002d0| 72 65 71 75 65 6e 63 79 | 20 64 6f 6d 61 69 6e 73 |requency| domains|
|000002e0| 20 6f 72 20 76 69 63 65 | 20 76 65 72 73 61 2e 20 | or vice| versa. |
|000002f0| 20 54 68 65 6e 20 63 61 | 6c 6c 20 50 52 4f 43 66 | Then ca|ll PROCf|
|00000300| 66 74 2e 0d 00 c8 05 f4 | 0d 00 d2 43 f4 20 54 68 |ft......|...C. Th|
|00000310| 69 73 20 73 61 6d 70 6c | 65 20 70 72 6f 67 72 61 |is sampl|e progra|
|00000320| 6d 20 73 68 6f 77 73 20 | 61 20 33 32 20 70 6f 69 |m shows |a 32 poi|
|00000330| 6e 74 20 74 72 61 6e 73 | 66 6f 72 6d 2e 20 20 49 |nt trans|form.  I|
|00000340| 74 20 6c 6f 61 64 73 20 | 74 68 65 0d 00 dc 45 f4 |t loads |the...E.|
|00000350| 20 52 65 61 6c 20 61 72 | 72 61 79 20 77 69 74 68 | Real ar|ray with|
|00000360| 20 74 77 6f 20 73 69 6e | 65 77 61 76 65 73 2c 20 | two sin|ewaves, |
|00000370| 61 6e 64 20 74 68 65 6e | 20 70 72 69 6e 74 73 20 |and then| prints |
|00000380| 6f 75 74 20 74 68 65 20 | 72 65 61 6c 20 61 6e 64 |out the |real and|
|00000390| 0d 00 e6 2b f4 20 69 6d | 61 67 69 6e 61 72 79 20 |...+. im|aginary |
|000003a0| 63 6f 6d 70 6f 6e 65 6e | 74 73 20 6f 66 20 74 68 |componen|ts of th|
|000003b0| 65 20 73 70 65 63 74 72 | 75 6d 2e 0d 00 f0 05 f4 |e spectr|um......|
|000003c0| 0d 00 fa 43 f4 20 54 68 | 69 73 20 46 46 54 20 69 |...C. Th|is FFT i|
|000003d0| 73 20 63 6f 64 65 64 20 | 66 6f 72 20 63 6c 61 72 |s coded |for clar|
|000003e0| 69 74 79 20 6e 6f 74 20 | 73 70 65 65 64 2e 20 20 |ity not |speed.  |
|000003f0| 49 66 20 79 6f 75 20 70 | 6c 61 6e 20 74 6f 20 63 |If you p|lan to c|
|00000400| 61 6c 6c 0d 01 04 44 f4 | 20 74 68 65 20 46 46 54 |all...D.| the FFT|
|00000410| 20 6d 61 6e 79 20 74 69 | 6d 65 73 2c 20 69 74 20 | many ti|mes, it |
|00000420| 77 6f 75 6c 64 20 6d 61 | 6b 65 20 73 65 6e 73 65 |would ma|ke sense|
|00000430| 20 74 6f 20 73 74 6f 72 | 65 20 74 68 65 20 53 69 | to stor|e the Si|
|00000440| 6e 65 73 20 61 6e 64 0d | 01 0e 46 f4 20 43 6f 73 |nes and.|..F. Cos|
|00000450| 69 6e 65 73 20 28 57 52 | 20 61 6e 64 20 57 49 29 |ines (WR| and WI)|
|00000460| 20 69 6e 20 6c 6f 6f 6b | 2d 75 70 20 74 61 62 6c | in look|-up tabl|
|00000470| 65 73 20 72 61 74 68 65 | 72 20 74 68 61 6e 20 72 |es rathe|r than r|
|00000480| 65 63 6f 6d 70 75 74 65 | 20 74 68 65 6d 0d 01 18 |ecompute| them...|
|00000490| 11 f4 20 65 76 65 72 79 | 20 63 61 6c 6c 2e 0d 01 |.. every| call...|
|000004a0| 22 05 f4 0d 01 2c 21 ef | 32 36 2c 31 32 3a 20 20 |"....,!.|26,12:  |
|000004b0| 20 20 20 20 20 20 f4 20 | 43 6c 65 61 72 20 73 63 |      . |Clear sc|
|000004c0| 72 65 65 6e 0d 01 36 25 | f2 69 6e 69 74 3a 20 20 |reen..6%|.init:  |
|000004d0| 20 20 20 20 20 20 f4 20 | 53 65 74 20 75 70 20 61 |      . |Set up a|
|000004e0| 72 72 61 79 73 20 65 74 | 63 0d 01 40 3f f2 6c 6f |rrays et|c..@?.lo|
|000004f0| 61 64 5f 64 61 74 61 3a | 20 20 20 f4 20 4c 6f 61 |ad_data:|   . Loa|
|00000500| 64 20 52 28 2e 29 20 61 | 6e 64 20 49 28 2e 29 20 |d R(.) a|nd I(.) |
|00000510| 61 72 72 61 79 73 20 77 | 69 74 68 20 65 78 61 6d |arrays w|ith exam|
|00000520| 70 6c 65 20 64 61 74 61 | 0d 01 4a 31 f2 66 66 74 |ple data|..J1.fft|
|00000530| 3a 20 20 20 20 20 20 20 | 20 20 f4 20 44 6f 20 74 |:       |  . Do t|
|00000540| 68 65 20 46 61 73 74 20 | 46 6f 75 72 69 65 72 20 |he Fast |Fourier |
|00000550| 54 72 61 6e 73 66 6f 72 | 6d 0d 01 54 30 f2 72 65 |Transfor|m..T0.re|
|00000560| 73 75 6c 74 73 3a 20 20 | 20 20 20 f4 20 20 2e 2e |sults:  |   .  ..|
|00000570| 20 61 6e 64 20 70 72 69 | 6e 74 6f 75 74 20 74 68 | and pri|ntout th|
|00000580| 65 20 72 65 73 75 6c 74 | 73 0d 01 5e 05 e0 0d 01 |e result|s..^....|
|00000590| 68 49 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |hI::::::|::::::::|
|000005a0| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|000005b0| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
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|000005d0| 3a 3a 3a 3a 3a 3a 3a 0d | 01 72 10 dd 20 f2 6c 6f |:::::::.|.r.. .lo|
|000005e0| 61 64 5f 64 61 74 61 0d | 01 7c 36 f4 20 45 78 61 |ad_data.|.|6. Exa|
|000005f0| 6d 70 6c 65 3a 20 4c 6f | 61 64 20 72 65 61 6c 20 |mple: Lo|ad real |
|00000600| 61 72 72 61 79 20 77 69 | 74 68 20 74 77 6f 20 74 |array wi|th two t|
|00000610| 65 73 74 20 73 69 6e 65 | 77 61 76 65 73 0d 01 86 |est sine|waves...|
|00000620| 1a f1 22 4c 6f 61 64 69 | 6e 67 20 64 61 74 61 20 |.."Loadi|ng data |
|00000630| 61 72 72 61 79 73 22 0d | 01 90 46 44 49 52 24 3d |arrays".|..FDIR$=|
|00000640| 22 54 74 6f 46 22 3a 20 | 20 20 20 20 f4 20 54 69 |"TtoF": |    . Ti|
|00000650| 6d 65 20 74 6f 20 46 72 | 65 71 75 65 6e 63 79 20 |me to Fr|equency |
|00000660| 64 6f 6d 61 69 6e 20 66 | 6c 61 67 20 28 6f 74 68 |domain f|lag (oth|
|00000670| 65 72 20 69 73 20 22 46 | 74 6f 54 22 29 0d 01 9a |er is "F|toT")...|
|00000680| 10 46 31 3d 32 3a 20 20 | 41 31 3d 31 30 0d 01 a4 |.F1=2:  |A1=10...|
|00000690| 10 46 32 3d 38 3a 20 20 | 41 32 3d 32 35 0d 01 ae |.F2=8:  |A2=25...|
|000006a0| 11 e3 20 49 25 3d 30 20 | b8 20 4e 25 2d 31 0d 01 |.. I%=0 |. N%-1..|
|000006b0| b8 3c 52 28 49 25 29 20 | 3d 20 41 31 2a 9b 28 32 |.<R(I%) |= A1*.(2|
|000006c0| 2a af 2a 46 31 2a 49 25 | 2f 4e 25 29 20 2b 20 41 |*.*F1*I%|/N%) + A|
|000006d0| 32 2a b5 28 32 2a af 2a | 46 32 2a 49 25 2f 4e 25 |2*.(2*.*|F2*I%/N%|
|000006e0| 29 3a 20 49 28 49 25 29 | 3d 30 0d 01 c2 05 ed 0d |): I(I%)|=0......|
|000006f0| 01 cc 05 e1 0d 01 d6 49 | 3a 3a 3a 3a 3a 3a 3a 3a |.......I|::::::::|
|00000700| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000710| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000720| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000730| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 0d 01 e0 |::::::::|:::::...|
|00000740| 0e dd 20 f2 72 65 73 75 | 6c 74 73 0d 01 ea 34 40 |.. .resu|lts...4@|
|00000750| 25 3d 26 32 30 32 30 41 | 3a 20 20 20 20 20 20 20 |%=&2020A|:       |
|00000760| 20 f4 20 50 72 69 6e 74 | 6f 75 74 20 74 6f 20 32 | . Print|out to 2|
|00000770| 20 64 65 63 69 6d 61 6c | 20 70 6c 61 63 65 73 0d | decimal| places.|
|00000780| 01 f4 30 f1 22 20 20 20 | 20 20 50 6f 69 6e 74 20 |..0."   |  Point |
|00000790| 20 20 20 20 20 52 65 61 | 6c 20 20 20 20 20 20 49 |     Rea|l      I|
|000007a0| 6d 61 67 20 20 20 20 20 | 20 20 41 6d 70 20 22 0d |mag     |  Amp ".|
|000007b0| 01 fe 30 f1 22 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |..0."---|--------|
|000007c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000007d0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 22 0d |--------|------".|
|000007e0| 02 08 11 e3 20 49 25 3d | 30 20 b8 20 4e 25 2d 31 |.... I%=|0 . N%-1|
|000007f0| 0d 02 12 2a f1 20 49 25 | 2c 20 52 28 49 25 29 2c |...*. I%|, R(I%),|
|00000800| 20 49 28 49 25 29 2c 20 | b6 28 52 28 49 25 29 5e | I(I%), |.(R(I%)^|
|00000810| 32 2b 49 28 49 25 29 5e | 32 29 0d 02 1c 05 ed 0d |2+I(I%)^|2)......|
|00000820| 02 26 30 f1 22 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |.&0."---|--------|
|00000830| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000840| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 22 0d |--------|------".|
|00000850| 02 30 05 e1 0d 02 3a 49 | 3a 3a 3a 3a 3a 3a 3a 3a |.0....:I|::::::::|
|00000860| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000870| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000880| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000890| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 0d 02 44 |::::::::|:::::..D|
|000008a0| 0b dd 20 f2 69 6e 69 74 | 0d 02 4e 24 41 25 3d 35 |.. .init|..N$A%=5|
|000008b0| 3a 20 20 20 20 20 20 20 | 20 20 20 20 20 20 f4 20 |:       |      . |
|000008c0| 4f 72 64 65 72 20 6f 66 | 20 46 46 54 0d 02 58 35 |Order of| FFT..X5|
|000008d0| 4e 25 3d 32 5e 41 25 3a | 20 20 20 20 20 20 20 20 |N%=2^A%:|        |
|000008e0| 20 20 f4 20 4e 75 6d 62 | 65 72 20 6f 66 20 70 6f |  . Numb|er of po|
|000008f0| 69 6e 74 73 20 69 6e 20 | 74 72 61 6e 73 66 6f 72 |ints in |transfor|
|00000900| 6d 0d 02 62 36 de 20 52 | 28 4e 25 29 2c 49 28 4e |m..b6. R|(N%),I(N|
|00000910| 25 29 3a 20 20 f4 20 52 | 65 61 6c 20 61 6e 64 20 |%):  . R|eal and |
|00000920| 49 6d 61 67 69 6e 61 72 | 79 20 70 6f 69 6e 74 73 |Imaginar|y points|
|00000930| 20 61 72 72 61 79 73 0d | 02 6c 05 e1 0d 02 76 49 | arrays.|.l....vI|
|00000940| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000950| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000960| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000970| 3a 3a 3a 3a 3a 3a 3a 3a | 3a 3a 3a 3a 3a 3a 3a 3a |::::::::|::::::::|
|00000980| 3a 3a 3a 3a 3a 0d 02 80 | 0a dd 20 f2 66 66 74 0d |:::::...|.. .fft.|
|00000990| 02 8a 22 f1 22 52 65 2d | 6f 72 64 65 72 69 6e 67 |.."."Re-|ordering|
|000009a0| 20 64 61 74 61 20 70 6f | 69 6e 74 73 20 2e 2e 2e | data po|ints ...|
|000009b0| 22 0d 02 94 08 4a 25 3d | 30 0d 02 9e 11 e3 20 49 |"....J%=|0..... I|
|000009c0| 25 3d 30 20 b8 20 4e 25 | 2d 32 0d 02 a8 50 e7 20 |%=0 . N%|-2...P. |
|000009d0| 49 25 20 3c 20 4a 25 20 | 8c 20 54 31 3d 52 28 4a |I% < J% |. T1=R(J|
|000009e0| 25 29 3a 20 54 32 3d 49 | 28 4a 25 29 3a 20 52 28 |%): T2=I|(J%): R(|
|000009f0| 4a 25 29 3d 52 28 49 25 | 29 3a 20 49 28 4a 25 29 |J%)=R(I%|): I(J%)|
|00000a00| 3d 49 28 49 25 29 3a 20 | 52 28 49 25 29 3d 54 31 |=I(I%): |R(I%)=T1|
|00000a10| 3a 20 49 28 49 25 29 3d | 54 32 0d 02 b2 0b 4b 25 |: I(I%)=|T2....K%|
|00000a20| 3d 4e 25 2f 32 0d 02 bc | 28 c8 95 20 4b 25 20 3c |=N%/2...|(.. K% <|
|00000a30| 3d 20 4a 25 20 20 4a 25 | 3d 4a 25 2d 4b 25 3a 20 |= J%  J%|=J%-K%: |
|00000a40| 4b 25 3d a8 28 4b 25 2f | 32 29 3a 20 ce 0d 02 c6 |K%=.(K%/|2): ....|
|00000a50| 0a 4a 25 2b 3d 4b 25 0d | 02 d0 05 ed 0d 02 da 05 |.J%+=K%.|........|
|00000a60| 3a 0d 02 e4 19 f1 22 50 | 65 72 66 6f 72 6d 69 6e |:....."P|erformin|
|00000a70| 67 20 46 46 54 20 2e 2e | 2e 22 0d 02 ee 08 50 25 |g FFT ..|."....P%|
|00000a80| 3d 31 0d 02 f8 11 e3 20 | 4c 25 3d 30 20 b8 20 41 |=1..... |L%=0 . A|
|00000a90| 25 2d 31 0d 03 02 1e 58 | 25 3d 50 25 3a 20 50 25 |%-1....X|%=P%: P%|
|00000aa0| 3d 50 25 2a 32 3a 20 55 | 52 3d 31 3a 20 55 49 3d |=P%*2: U|R=1: UI=|
|00000ab0| 30 0d 03 0c 1a 57 52 3d | 9b 28 af 2f 58 25 29 3a |0....WR=|.(./X%):|
|00000ac0| 20 57 49 3d b5 28 af 2f | 58 25 29 0d 03 16 1a e7 | WI=.(./|X%).....|
|00000ad0| 20 44 49 52 24 3d 22 54 | 74 6f 46 22 20 8c 20 57 | DIR$="T|toF" . W|
|00000ae0| 49 3d 2d 57 49 0d 03 20 | 11 e3 20 4a 25 3d 30 20 |I=-WI.. |.. J%=0 |
|00000af0| b8 20 58 25 2d 31 0d 03 | 2a 17 e3 20 49 25 3d 4a |. X%-1..|*.. I%=J|
|00000b00| 25 20 b8 20 4e 25 2d 31 | 20 88 20 50 25 0d 03 34 |% . N%-1| . P%..4|
|00000b10| 1c 4b 25 3d 49 25 2b 58 | 25 3a 52 3d 52 28 4b 25 |.K%=I%+X|%:R=R(K%|
|00000b20| 29 3a 49 3d 49 28 4b 25 | 29 0d 03 3e 21 54 3d 52 |):I=I(K%|)..>!T=R|
|00000b30| 2a 55 52 2d 49 2a 55 49 | 3a 20 49 3d 52 2a 55 49 |*UR-I*UI|: I=R*UI|
|00000b40| 2b 49 2a 55 52 3a 20 52 | 3d 54 0d 03 48 16 54 52 |+I*UR: R|=T..H.TR|
|00000b50| 3d 52 28 49 25 29 3a 20 | 54 49 3d 49 28 49 25 29 |=R(I%): |TI=I(I%)|
|00000b60| 0d 03 52 1a 52 28 4b 25 | 29 3d 54 52 2d 52 3a 20 |..R.R(K%|)=TR-R: |
|00000b70| 49 28 4b 25 29 3d 54 49 | 2d 49 0d 03 5c 1a 52 28 |I(K%)=TI|-I..\.R(|
|00000b80| 49 25 29 3d 54 52 2b 52 | 3a 20 49 28 49 25 29 3d |I%)=TR+R|: I(I%)=|
|00000b90| 54 49 2b 49 0d 03 66 05 | ed 0d 03 70 29 54 52 3d |TI+I..f.|...p)TR=|
|00000ba0| 55 52 2a 57 52 2d 55 49 | 2a 57 49 3a 20 55 49 3d |UR*WR-UI|*WI: UI=|
|00000bb0| 55 52 2a 57 49 2b 55 49 | 2a 57 52 3a 20 55 52 3d |UR*WI+UI|*WR: UR=|
|00000bc0| 54 52 0d 03 7a 05 ed 0d | 03 84 05 ed 0d 03 8e 22 |TR..z...|......."|
|00000bd0| e7 20 44 49 52 24 20 3d | 20 22 54 74 6f 46 22 20 |. DIR$ =| "TtoF" |
|00000be0| 54 3d 32 2f 4e 25 20 8b | 20 54 3d 31 2f 32 0d 03 |T=2/N% .| T=1/2..|
|00000bf0| 98 2f e3 20 49 25 3d 30 | 20 b8 20 4e 25 2d 31 3a |./. I%=0| . N%-1:|
|00000c00| 52 28 49 25 29 3d 52 28 | 49 25 29 2a 54 3a 49 28 |R(I%)=R(|I%)*T:I(|
|00000c10| 49 25 29 3d 49 28 49 25 | 29 2a 54 3a ed 0d 03 a2 |I%)=I(I%|)*T:....|
|00000c20| 05 e1 0d ff             |                         |....    |        |
+--------+-------------------------+-------------------------+--------+--------+