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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 88 84 00 01 00 00 01 00 | 00 00 00 00 0a 00 00 00 |........|........|
|00000010| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000050| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000060| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000080| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000090| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000100| 00 3b 31 30 21 20 20 20 | 54 68 65 20 66 6f 6c 6c |.;10!   |The foll|
|00000110| 6f 77 69 6e 67 20 69 73 | 20 61 20 74 65 73 74 20 |owing is| a test |
|00000120| 6f 66 20 74 68 65 20 48 | 54 42 61 73 69 63 20 6d |of the H|TBasic m|
|00000130| 61 74 68 20 22 72 75 6e | 74 69 6d 65 22 00 00 3d |ath "run|time"..=|
|00000140| 32 30 21 20 43 6f 6d 6d | 65 6e 74 73 3a 20 20 44 |20! Comm|ents:  D|
|00000150| 69 73 63 72 65 74 65 20 | 46 6f 75 72 69 65 72 20 |iscrete |Fourier |
|00000160| 74 72 61 6e 73 66 6f 72 | 6d 20 6f 66 20 61 20 72 |transfor|m of a r|
|00000170| 65 61 6c 20 73 65 71 75 | 65 6e 63 65 2e 00 00 11 |eal sequ|ence....|
|00000180| 33 30 21 20 46 69 6c 65 | 3a 20 66 66 74 2e 70 72 |30! File|: fft.pr|
|00000190| 67 00 00 2f 36 30 20 20 | 20 20 4c 4f 41 44 53 55 |g../60  |  LOADSU|
|000001a0| 42 20 41 4c 4c 20 46 52 | 4f 4d 20 22 2e 2e 5c 6d |B ALL FR|OM "..\m|
|000001b0| 61 74 68 6c 69 62 5c 4d | 61 74 68 6c 69 62 2e 68 |athlib\M|athlib.h|
|000001c0| 74 73 22 00 00 15 37 30 | 20 20 20 20 46 4f 52 20 |ts"...70|    FOR |
|000001d0| 4c 6f 6f 70 3d 31 20 54 | 4f 20 34 00 00 14 38 30 |Loop=1 T|O 4...80|
|000001e0| 20 20 20 20 20 20 43 4c | 45 41 52 20 53 43 52 45 |      CL|EAR SCRE|
|000001f0| 45 4e 00 15 39 30 20 20 | 20 20 20 20 45 78 61 6d |EN..90  |    Exam|
|00000200| 70 6c 65 28 4c 6f 6f 70 | 29 00 00 20 31 30 30 20 |ple(Loop|).. 100 |
|00000210| 20 20 20 20 50 52 49 4e | 54 20 22 50 6c 65 61 73 |    PRIN|T "Pleas|
|00000220| 65 20 74 79 70 65 20 43 | 4f 4e 54 22 00 0d 31 31 |e type C|ONT"..11|
|00000230| 30 20 20 20 20 20 50 41 | 55 53 45 00 00 0f 31 32 |0     PA|USE...12|
|00000240| 30 20 20 20 4e 45 58 54 | 20 4c 6f 6f 70 00 00 12 |0   NEXT| Loop...|
|00000250| 31 33 30 20 20 20 43 4c | 45 41 52 20 53 43 52 45 |130   CL|EAR SCRE|
|00000260| 45 4e 00 16 31 34 30 20 | 20 20 50 52 49 4e 54 20 |EN..140 |  PRINT |
|00000270| 22 46 69 6e 69 73 68 65 | 64 22 00 18 31 35 30 20 |"Finishe|d"..150 |
|00000280| 20 20 44 45 4c 53 55 42 | 20 46 4e 41 69 20 54 4f |  DELSUB| FNAi TO|
|00000290| 20 45 4e 44 00 09 31 36 | 30 20 20 20 45 4e 44 00 | END..16|0   END.|
|000002a0| 00 17 31 37 30 20 20 20 | 53 55 42 20 45 78 61 6d |..170   |SUB Exam|
|000002b0| 70 6c 65 28 57 68 61 74 | 29 00 00 13 31 38 30 20 |ple(What|)...180 |
|000002c0| 20 20 20 20 49 4e 54 45 | 47 45 52 20 49 2c 4a 00 |    INTE|GER I,J.|
|000002d0| 00 18 31 39 30 20 20 20 | 20 20 52 45 41 4c 20 41 |..190   |  REAL A|
|000002e0| 31 28 31 35 29 2c 41 6e | 65 77 00 2f 32 30 30 20 |1(15),An|ew./200 |
|000002f0| 20 20 20 20 52 45 41 4c | 20 41 6b 28 31 30 32 33 |    REAL| Ak(1023|
|00000300| 29 2c 41 6d 70 28 35 31 | 31 29 2c 50 68 61 73 65 |),Amp(51|1),Phase|
|00000310| 28 35 31 31 29 2c 54 68 | 65 74 61 00 00 1d 32 31 |(511),Th|eta...21|
|00000320| 30 20 20 20 20 20 43 4f | 4d 50 4c 45 58 20 42 31 |0     CO|MPLEX B1|
|00000330| 28 37 29 2c 42 32 28 35 | 31 31 29 00 00 13 32 32 |(7),B2(5|11)...22|
|00000340| 30 20 20 20 20 20 53 45 | 4c 45 43 54 20 57 68 61 |0     SE|LECT Wha|
|00000350| 74 00 00 0e 32 33 30 20 | 20 20 20 20 43 41 53 45 |t...230 |    CASE|
|00000360| 20 31 00 2f 32 34 30 20 | 20 20 20 20 20 20 43 41 | 1./240 |      CA|
|00000370| 4c 4c 20 57 61 76 65 66 | 6f 72 6d 28 31 36 2e 30 |LL Wavef|orm(16.0|
|00000380| 2c 31 2e 30 2c 30 2e 2c | 30 2e 2c 33 2c 41 31 28 |,1.0,0.,|0.,3,A1(|
|00000390| 2a 29 29 00 00 21 32 35 | 30 20 20 20 20 20 20 20 |*))..!25|0       |
|000003a0| 43 41 4c 4c 20 46 66 74 | 28 34 2c 41 31 28 2a 29 |CALL Fft|(4,A1(*)|
|000003b0| 2c 42 31 28 2a 29 29 00 | 00 16 32 36 30 20 20 20 |,B1(*)).|..260   |
|000003c0| 20 20 20 20 46 4f 52 20 | 49 3d 30 20 54 4f 20 37 |    FOR |I=0 TO 7|
|000003d0| 00 19 32 37 30 20 20 20 | 20 20 20 20 20 20 50 52 |..270   |      PR|
|000003e0| 49 4e 54 20 49 2c 42 31 | 28 49 29 00 00 10 32 38 |INT I,B1|(I)...28|
|000003f0| 30 20 20 20 20 20 20 20 | 4e 45 58 54 20 49 00 0e |0       |NEXT I..|
|00000400| 32 39 30 20 20 20 20 20 | 43 41 53 45 20 32 00 2f |290     |CASE 2./|
|00000410| 33 30 30 20 20 20 20 20 | 20 20 52 45 41 4c 20 41 |300     |  REAL A|
|00000420| 32 28 31 35 29 2c 41 6e | 65 77 31 2c 41 6e 65 77 |2(15),An|ew1,Anew|
|00000430| 32 2c 54 68 65 74 61 31 | 2c 54 68 65 74 61 32 00 |2,Theta1|,Theta2.|
|00000440| 00 0d 33 31 30 20 20 20 | 20 20 20 20 52 41 44 00 |..310   |    RAD.|
|00000450| 00 2f 33 32 30 20 20 20 | 20 20 20 20 43 41 4c 4c |./320   |    CALL|
|00000460| 20 57 61 76 65 66 6f 72 | 6d 28 31 36 2e 30 2c 31 | Wavefor|m(16.0,1|
|00000470| 2e 30 2c 30 2e 2c 30 2e | 2c 33 2c 41 32 28 2a 29 |.0,0.,0.|,3,A2(*)|
|00000480| 29 00 00 21 33 33 30 20 | 20 20 20 20 20 20 43 41 |)..!330 |      CA|
|00000490| 4c 4c 20 46 66 74 28 34 | 2c 41 32 28 2a 29 2c 42 |LL Fft(4|,A2(*),B|
|000004a0| 31 28 2a 29 29 00 00 19 | 33 34 30 20 20 20 20 20 |1(*))...|340     |
|000004b0| 20 20 46 4f 52 20 49 3d | 30 20 54 4f 20 31 30 32 |  FOR I=|0 TO 102|
|000004c0| 34 00 00 13 33 35 30 20 | 20 20 20 20 20 20 20 20 |4...350 |        |
|000004d0| 41 6e 65 77 31 3d 30 00 | 00 13 33 36 30 20 20 20 |Anew1=0.|..360   |
|000004e0| 20 20 20 20 20 20 41 6e | 65 77 32 3d 30 00 00 18 |      An|ew2=0...|
|000004f0| 33 37 30 20 20 20 20 20 | 20 20 20 20 46 4f 52 20 |370     |    FOR |
|00000500| 4a 3d 30 20 54 4f 20 37 | 00 26 33 38 30 20 20 20 |J=0 TO 7|.&380   |
|00000510| 20 20 20 20 20 20 20 20 | 54 68 65 74 61 31 3d 32 |        |Theta1=2|
|00000520| 2e 30 2a 50 49 2a 49 2a | 4a 2f 31 30 32 34 2e 30 |.0*PI*I*|J/1024.0|
|00000530| 00 2b 33 39 30 20 20 20 | 20 20 20 20 20 20 20 20 |.+390   |        |
|00000540| 54 68 65 74 61 32 3d 32 | 2e 30 2a 50 49 2a 49 2a |Theta2=2|.0*PI*I*|
|00000550| 28 31 36 2d 4a 29 2f 31 | 30 32 34 2e 30 00 00 49 |(16-J)/1|024.0..I|
|00000560| 34 30 30 20 20 20 20 20 | 20 20 20 20 20 20 41 6e |400     |      An|
|00000570| 65 77 31 3d 41 6e 65 77 | 31 2b 52 45 41 4c 28 42 |ew1=Anew|1+REAL(B|
|00000580| 31 28 4a 29 29 2a 43 4f | 53 28 54 68 65 74 61 31 |1(J))*CO|S(Theta1|
|00000590| 29 2b 49 4d 41 47 28 42 | 31 28 4a 29 29 2a 53 49 |)+IMAG(B|1(J))*SI|
|000005a0| 4e 28 54 68 65 74 61 31 | 29 00 00 49 34 31 30 20 |N(Theta1|)..I410 |
|000005b0| 20 20 20 20 20 20 20 20 | 20 20 41 6e 65 77 32 3d |        |  Anew2=|
|000005c0| 41 6e 65 77 32 2b 52 45 | 41 4c 28 42 31 28 4a 29 |Anew2+RE|AL(B1(J)|
|000005d0| 29 2a 43 4f 53 28 54 68 | 65 74 61 32 29 2d 49 4d |)*COS(Th|eta2)-IM|
|000005e0| 41 47 28 42 31 28 4a 29 | 29 2a 53 49 4e 28 54 68 |AG(B1(J)|)*SIN(Th|
|000005f0| 65 74 61 32 29 00 00 12 | 34 32 30 20 20 20 20 20 |eta2)...|420     |
|00000600| 20 20 20 20 4e 45 58 54 | 20 4a 00 2b 34 33 30 20 |    NEXT| J.+430 |
|00000610| 20 20 20 20 20 20 20 20 | 50 52 49 4e 54 20 49 2f |        |PRINT I/|
|00000620| 31 30 32 34 2e 30 2a 31 | 33 2e 30 2c 41 6e 65 77 |1024.0*1|3.0,Anew|
|00000630| 31 2c 41 6e 65 77 32 00 | 00 10 34 34 30 20 20 20 |1,Anew2.|..440   |
|00000640| 20 20 20 20 4e 45 58 54 | 20 49 00 0e 34 35 30 20 |    NEXT| I..450 |
|00000650| 20 20 20 20 43 41 53 45 | 20 33 00 0d 34 36 30 20 |    CASE| 3..460 |
|00000660| 20 20 20 20 20 20 52 41 | 44 00 00 19 34 37 30 20 |      RA|D...470 |
|00000670| 20 20 20 20 20 20 46 4f | 52 20 49 3d 30 20 54 4f |      FO|R I=0 TO|
|00000680| 20 31 30 32 33 00 00 26 | 34 38 30 20 20 20 20 20 | 1023..&|480     |
|00000690| 20 20 20 20 54 68 65 74 | 61 3d 32 2e 30 2a 50 49 |    Thet|a=2.0*PI|
|000006a0| 2a 49 2a 31 2e 32 35 2f | 31 30 32 34 2e 30 00 5f |*I*1.25/|1024.0._|
|000006b0| 34 39 30 20 20 20 20 20 | 20 20 20 20 41 6b 28 49 |490     |    Ak(I|
|000006c0| 29 3d 28 53 49 4e 28 54 | 68 65 74 61 29 2d 53 49 |)=(SIN(T|heta)-SI|
|000006d0| 4e 28 33 2e 30 2a 54 68 | 65 74 61 29 2f 39 2b 53 |N(3.0*Th|eta)/9+S|
|000006e0| 49 4e 28 35 2e 30 2a 54 | 68 65 74 61 29 2f 32 35 |IN(5.0*T|heta)/25|
|000006f0| 2d 53 49 4e 28 37 2e 30 | 2a 54 68 65 74 61 29 2f |-SIN(7.0|*Theta)/|
|00000700| 34 39 29 2a 38 2e 30 2f | 28 50 49 2a 50 49 29 00 |49)*8.0/|(PI*PI).|
|00000710| 00 10 35 30 30 20 20 20 | 20 20 20 20 4e 45 58 54 |..500   |    NEXT|
|00000720| 20 49 00 22 35 31 30 20 | 20 20 20 20 20 20 43 41 | I."510 |      CA|
|00000730| 4c 4c 20 46 66 74 28 31 | 30 2c 41 6b 28 2a 29 2c |LL Fft(1|0,Ak(*),|
|00000740| 42 32 28 2a 29 29 00 2f | 35 32 30 20 20 20 20 20 |B2(*))./|520     |
|00000750| 20 20 43 41 4c 4c 20 50 | 6f 6c 61 72 28 42 32 28 |  CALL P|olar(B2(|
|00000760| 2a 29 2c 22 44 22 2c 41 | 6d 70 28 2a 29 2c 50 68 |*),"D",A|mp(*),Ph|
|00000770| 61 73 65 28 2a 29 29 00 | 00 18 35 33 30 20 20 20 |ase(*)).|..530   |
|00000780| 20 20 20 20 46 4f 52 20 | 49 3d 30 20 54 4f 20 35 |    FOR |I=0 TO 5|
|00000790| 31 31 00 23 35 34 30 20 | 20 20 20 20 20 20 20 20 |11.#540 |        |
|000007a0| 50 52 49 4e 54 20 49 2c | 41 6d 70 28 49 29 2c 50 |PRINT I,|Amp(I),P|
|000007b0| 68 61 73 65 28 49 29 00 | 00 10 35 35 30 20 20 20 |hase(I).|..550   |
|000007c0| 20 20 20 20 4e 45 58 54 | 20 49 00 0e 35 36 30 20 |    NEXT| I..560 |
|000007d0| 20 20 20 20 43 41 53 45 | 20 34 00 19 35 37 30 20 |    CASE| 4..570 |
|000007e0| 20 20 20 20 20 20 46 4f | 52 20 49 3d 30 20 54 4f |      FO|R I=0 TO|
|000007f0| 20 31 30 32 33 00 00 24 | 35 38 30 20 20 20 20 20 | 1023..$|580     |
|00000800| 20 20 20 20 54 68 65 74 | 61 3d 32 2e 30 2a 50 49 |    Thet|a=2.0*PI|
|00000810| 2a 49 2a 31 2e 32 35 2f | 31 30 32 33 00 5f 35 39 |*I*1.25/|1023._59|
|00000820| 30 20 20 20 20 20 20 20 | 20 20 41 6b 28 49 29 3d |0       |  Ak(I)=|
|00000830| 28 53 49 4e 28 54 68 65 | 74 61 29 2d 53 49 4e 28 |(SIN(The|ta)-SIN(|
|00000840| 33 2e 30 2a 54 68 65 74 | 61 29 2f 39 2b 53 49 4e |3.0*Thet|a)/9+SIN|
|00000850| 28 35 2e 30 2a 54 68 65 | 74 61 29 2f 32 35 2d 53 |(5.0*The|ta)/25-S|
|00000860| 49 4e 28 37 2e 30 2a 54 | 68 65 74 61 29 2f 34 39 |IN(7.0*T|heta)/49|
|00000870| 29 2a 38 2e 30 2f 28 50 | 49 2a 50 49 29 00 00 10 |)*8.0/(P|I*PI)...|
|00000880| 36 30 30 20 20 20 20 20 | 20 20 4e 45 58 54 20 49 |600     |  NEXT I|
|00000890| 00 26 36 31 30 20 20 20 | 20 20 20 20 43 41 4c 4c |.&610   |    CALL|
|000008a0| 20 57 5f 6b 61 69 73 65 | 72 28 41 6b 28 2a 29 2c | W_kaise|r(Ak(*),|
|000008b0| 34 2c 41 6b 28 2a 29 29 | 00 19 36 32 30 20 20 20 |4,Ak(*))|..620   |
|000008c0| 20 20 20 20 46 4f 52 20 | 49 3d 30 20 54 4f 20 31 |    FOR |I=0 TO 1|
|000008d0| 30 32 33 00 00 19 36 33 | 30 20 20 20 20 20 20 20 |023...63|0       |
|000008e0| 20 20 50 52 49 4e 54 20 | 49 2c 41 6b 28 49 29 00 |  PRINT |I,Ak(I).|
|000008f0| 00 10 36 34 30 20 20 20 | 20 20 20 20 4e 45 58 54 |..640   |    NEXT|
|00000900| 20 49 00 22 36 35 30 20 | 20 20 20 20 20 20 43 41 | I."650 |      CA|
|00000910| 4c 4c 20 46 66 74 28 31 | 30 2c 41 6b 28 2a 29 2c |LL Fft(1|0,Ak(*),|
|00000920| 42 32 28 2a 29 29 00 2f | 36 36 30 20 20 20 20 20 |B2(*))./|660     |
|00000930| 20 20 43 41 4c 4c 20 50 | 6f 6c 61 72 28 42 32 28 |  CALL P|olar(B2(|
|00000940| 2a 29 2c 22 44 22 2c 41 | 6d 70 28 2a 29 2c 50 68 |*),"D",A|mp(*),Ph|
|00000950| 61 73 65 28 2a 29 29 00 | 00 18 36 37 30 20 20 20 |ase(*)).|..670   |
|00000960| 20 20 20 20 46 4f 52 20 | 49 3d 30 20 54 4f 20 35 |    FOR |I=0 TO 5|
|00000970| 31 31 00 23 36 38 30 20 | 20 20 20 20 20 20 20 20 |11.#680 |        |
|00000980| 50 52 49 4e 54 20 49 2c | 41 6d 70 28 49 29 2c 50 |PRINT I,|Amp(I),P|
|00000990| 68 61 73 65 28 49 29 00 | 00 10 36 39 30 20 20 20 |hase(I).|..690   |
|000009a0| 20 20 20 20 4e 45 58 54 | 20 49 00 11 37 30 30 20 |    NEXT| I..700 |
|000009b0| 20 20 20 20 43 41 53 45 | 20 45 4c 53 45 00 00 25 |    CASE| ELSE..%|
|000009c0| 37 31 30 20 20 20 20 20 | 20 20 50 52 49 4e 54 20 |710     |  PRINT |
|000009d0| 22 4e 6f 20 65 78 61 6d | 70 6c 65 20 66 6f 72 22 |"No exam|ple for"|
|000009e0| 3b 57 68 61 74 00 00 12 | 37 32 30 20 20 20 20 20 |;What...|720     |
|000009f0| 45 4e 44 20 53 45 4c 45 | 43 54 00 0c 37 33 30 20 |END SELE|CT..730 |
|00000a00| 20 20 53 55 42 45 4e 44 | 00 05 37 34 30 20 21 00 |  SUBEND|..740 !.|
|00000a10| ff ff                   |                         |..      |        |
+--------+-------------------------+-------------------------+--------+--------+