a personal calculator program for a-weighted soun pressure level and preferres noise criterion

8/12/2019 A Personal Calculator Program for a-Weighted Soun Pressure Level and Preferres Noise Criterion

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PERSONAL CALCULATOR PROGRAMS

Airborne Noise:A Personal Calculator Program for A-WeightedSound-Pressure Level, Noise-RatingEvaluation, and Preferred Noise Criterion

BEN BERNFELDIRCAM, Paris, France '

Guest Editor s Introduction commen_ for eachprogram (with examples), tomakethem accessibleand useful.The publication in the pages of the Journal of a Contributionsbased on any commemially availablesar es of papersdedicated to the useofprogrammable calculators are welcome, although programs writtenpersonal calculators in the fields of audio and acous for Hewlett Packard or Texas Instruments calculatorstics responds to a real need of our readers. In our will find the most users. If alternative programs exist

everyday professional life, we are more and more and not enough space is available for listing them inassisted by this small, clever and reliable instrument, the Journal we expect authors to be willing to sendNevertheless, some users are not aware of the pro such translations to interested readers.gramming potential of their calculators and thus, do Itwill bea pleasure for the guest editor of this sar esnot go further than using simple ad_metic operations, to be at the disposal of potentialcontributors for quedBut the programming pedor_nce of certain per- tions or advice. DOnot hesitate to write even if yousonal calculators approaches that of conventional have in mind a projectnot yet well defined.computers. Even ifa calculator isslower than, and hasa smaller memory capaci_ than an average rom. BenBernfeldputer, because of the prewired functions there are c/e IRCAMactually certain operations that are more easily per- 31RueSt.MerEformed with it: even inpowerful large computers you F 75004Paris,Francecannot (without writing corresponding software) di-rectly convert radians into degrees and rectangularinto polar coordinates, nor directly program commonlogarithms, antilogarithms, factorials, and statistic 0 INTRODUCTIONsummations--operations which are trivial with per Noise specifications for studios, auditoriums, andlivingsonal calculators, environments are usually given, in accordance with interna-

At the present time, apartfrom one ortwo papers on tional standards [1 ], in A-weighted sound-pressure levelspersonal calculator programs from Past convention ofthe Audio Engineering Sec ety, a few invited papers in (SPL). Nevertheless acousticians frequently use the noise-preparation, and some materia[written by this author, rating (NR) index [2] and the preferred noise criterionwe rely mainly on input from Journal readers, we are (PNC) [3]. Unfortunately no fixed relationship exists be-sure that a lot of outstanding programs, created by tween these three evaluations, the results depending on theaudio engineers, are alreadyin existence andcould-- spectrum of the noise.if publ shed--benef t all. lease send them to us. The A-weighting curve is based on the approximation of

The philosophy of this series is not only to report on_ the average spectrum of human hearing sensitivity for thelower range of SPLs; the Iow and high frequencies areattenuated to im itate the effect of hum an hearing.

algorithms are derived and, 0} course, tO provide The measurement of the A-weighted SPL is simple.-. * _ Preceding the measuring instrument ihe signal is routedJOURNAL OF THE AUDIO ENGINEERING SOCIETY, 1979 NOVEMBER,VOLUME 27, NUMBER 11 899


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BERNFELD PERSONALALCULATORROGRAMS

through a network with a frequency response identical to that is, a function of the variable Loct with frequency as thethe weighting curve. If information about the noise spec- parameter. For example, we have to find NR = 50 dB fortrum is required, measurements of the SPL have to be the measuredLoct A = 76 dB at the frequency of 63 Hz. (seecarried for each frequency band (for exam ple, octaves), and Fig. 1). F or better m atching w ith the A - w eighting com puta-the A-weighted SPL is computed by summing the indi- tion, the transformx = logf) was again used.vidualweighted levels [seeEq. 3)]. By computer polynomial curve fitting the following equ-

To obtain the NR index (Fig. 1), the measured SPLs for ation was found:different octaves have to be drawn on the N R graph (pointsA- N in Fig. 1). The highest NR curve on which lies one of NR = 7.8x 3 + (0.098L - 81.8)x 2 - (0.685L - 292.4)xthese p_6ints(in our example point A, NR = 50 dB) repro- + 2.171L - 351.3 (4)sents the N R index. where L is the octave SPL in decibels, x = log f, and fT he PN C value is obtained in a sim ilar way. For point A,PNC=.65dB. theoctavemidfrequencynhertz.The m axim um error in the range of 15 _ NR --_65 is less

than 2 dB .1 ALGORITHM FOR THE AWEIGHTING CURVEA s no analytic expression for the A-weighting curve

seems to be available, a suitable equation has to be obtained 3 ALGORITHM FOR THE PNCby curve fitting. Thus from a recent paper by Bevan etal. By a similar procedure the following equation was found[4, p, 952], the following equation was obtained by com -puter sim ulation of a com plex R C netw ork :W= 2.81 10- (2vrf)4

4[1+(1-_-)2][1+( 31-_)2][1+( f f1)

A lthough the results obtained by the use of this equation areprecise, the com plexity m akes it incom patible with per-sonalcalculatorprograms, forthePNC:A nother approach consists of the use of a logarithm icscale for the frequency and apolynomiai fit. For a polyno- PNC = (0.184L- 14.7)x2- (1.271L- 110.7)xmial of second degree the equation will be + 3.17L - 200. (5)

W = -1 lx 2 + .74.5x - 124.5 (2) For this equation the error is also ess than 2 dB.where x = logf, fbeing in hertz.

In Table 1 the EIC A-weighting figures and the figures 4 DESCRIPTION OF THE PROGRAMobtained by Eqs. (1)_and (2) are listed for octave bands. As The program, given in Tables 2and 3, is suited for HP-29can be seen, the precision of the quite sim ple equation (2) is and HP-67 calculators and can be easily adapted for thenot worse (error --


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PERSONALCALCULATOR PROGRAMS AIRBORNE NOISE

cube, are calculated and stored in registers 02, 03, and 04, Table 2. Program for theHP-29 calculator.respectively.

In subroutine7 steps54-85 Eqs. 3 - 5 are calcu- STEP 0PER. STEP 0PER.lated for the given frequency and octave SPL, the N R andPNC values being stored in registers. 1/C and .2/D, while 131 , LRL 0 51 ST0 9the magnitude of each A-weighted octave sound pressure is 132 RCL. S 52 GSR 7133 STO S 53 RTNsummed in .3/06. 136- 13 54 , LBL 7For programming enthusiasts it is of interest to mention 0S STO. 1 SS [ICL7thatdue to limitedmemorycapacity, the coefficientsof the 06 ST0.2 SG ST0 0equations are stored in pairs. If one coefficient is abc.d 07 ST0.3 57 [ICL iand the second is -e.fgh, they are packed in the form 08 FIX 13 58 INT09 LBL4 59 LSTXabcd.efgh. Steps 57-62 unpack them into their original 113 RCL 5 60 FRCforms. 11 R / S 61 CHS

The four steps 23- 26 are important. A decision has to be 12 ST0 B 62 ENT l'made about the final NR index. Aswe explained in the 13 X


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content of register. 1/C will remain unalte_d; if the new 5 EXAMPLEvalue is larger, it will replace the last value in register. 1/C. To check the program and give you a feeling about how itThe sam e procedure is used for searching the final PNC in works, we took agm n the exam ple of Fig. 1 (levels m arkedsteps 28- 31. by points A- H) and com puted the N R index, the PN C, andIn steps 40-45 the frequency is multiplied by 2, theindex Ar the indirect registers is stored back in 07, the loop the A-weighted SPL. The results are given in Table 5.NOTE: The same keying as Ar the HP-67 is used Ar

. is closed, and the frequency of the next octave is displayed running the TI-59 program . (0 .0000 0000 is displayed when(a ga in ste p 1 1).A fter the introduction of all octave SPLs (display 16 0 00 the com putation is com pleted.)

Hz),HeresultscanbecalledasAllows: Table4.Datastorage.A-weighted SPL by keying GSB 1 /A (steps 86-91)NRindex by keying GSB 2 / B (steps 92-9_ REGISTER DATA STOREDPNC by keying GSB 3 / C (steps 95- 97). HP-19 HP-67 HP-29 HP-G7

Table 3. Program _r the HP-67 calculator. 00 88 used 6.0STEP OPER. STEP OPER. 81 81 1.8 1.882 82 used used81 LBLE S1 STO9 03 83 used used82 RCLA 52 GSB7 84 84 used used83 STOS 53 RTN 85 G5 used used84 8 54 LBL7 8G OG used used85 STO C 55 RCL 7 87 87 25.0 19.886 STOO 56 STOI 88 88 used used87 STO6 57 RCLi 89 09 used used88 DSP8 58 INT .0 10 4.8 - 1245.889 LBL4 59 LSTX .1 11 used 745.818 RCLS 68 FRC .2 12 used - 118.811 R S G1 CHS ,3 13 used - 2_9.3 7012 STO E 62 ENT ? .4 14 18.8 1 07.127113 X+Y 63 RCLB .5 15 62.5 - 147.818414 LOG 64 X 16 16 - 1245.8 - 3513.2 7115 STO2 65 ENT? 17 17 745.8 2924.8G8516 x 2 66 RCL E 18 18 - 118.8 - 818.883817 STO3 67 19 19 - 2888.3178 78.818 LSTX 68 X+_Y 28 A 11871271 62.519 x 69 RCLB 21 B - 1478184 used28 STO4 78 + 22 C - 35132171 used21 4 71 + 23 O 29248685 used22 GSB6 72 STO8 24 E - 8188098 used23 RCLC 73 1 25 I 788 used24 RCL9 74 ST-725 X>Y 75 RCL82G STOC 76 STO I Table5.Computingexample.27 GSB5 77 RCLi28 RCLD 78 RCL8 INSTRUCTIONS DISPLAY29 RCL9 79 38 X > Y 88 ST +9 1. GSB 8 / E 63.31 STO O 81 1 2. input 7G 76.32 GSB S 82 ST -8 3. R/S 125.33 ECL9 83 DSZ 4. input 63 63.34 RCL E 84 OTO 7 5. R/S 258.35 + 85 RTN 6. input 58 58.38 RCL B 86 LBL A 7. RS 588.37 + 87 RCLg 8. input58 58.38 18 x 88 LOG 9. R/S 1888.39 ST +8 89 RCL B 18. input 48 48.48 2 98 11. RS 2888.41 ST S 91 R S 12. input 45 45.42 1 92 . LBL B 13. RS 4888.43 9 93 RCLC 14. input 48 48.44 STO 7 94 R / S 1S. R/S 8888.45 GTO4 95 * LBLC 16. input 32 32.46 LBL 5 9g RCL O 17. RS 16888.47 3 97 R / S48 , LBL 6 18. GSB i / A [ dB(A) = ] 56.49 STO 8 19. GSB 2 / B [ NR = ] 51.58 8 28. GSB 3 C [ PNC = ] 64.

902 JOURNAL OF THE AUDIO ENGINEERINGSOCIETY, 1979 NOVEMBER, VOLUME 27, NUMBER 11


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PERSONALALCULATORROGRAMS AIRBORNEOISE

APPENDIX 6 REFERENCESTable 6 lists the programming steps _r TI-59 cai- [1] IECPubl. 179 1965) and ANSI S1.4-1971.

culators. The symbols _e stand_d. Notice, however, the [2] I S O Recomm endation 1996, Appendix Y._llowingsymbols: [3] L. Beranek,W. E. BlazierandG. Figwer, Re-&_ed Noise Criterion Curves and the Application toRooms, J. Acoust. Soc. Am., vol. 50, p. 1223 (1971).ST*--storeindirect [4] W. R. Bevan,R. B. Schulein,and C. E. Seeler,RC* --recall indirect Design of Studio-Quality Condenser Microphone UsingX--T--change X with T Electmt Technology, J. Audio Eng. Soc., vol. 26, pp.ISBR--invemesubroutine. 947- 951 1978Dec.).

Tab le 6 . P rogram _ r the T I-5 9 calculator.800 LBL 043 S 086 INV 129 X=T 172 )881 E 844 X=T 887 XzT 138 RCL 173 SUM882 0 845 EE 888 0 131 OP 174 14803 STO 046 OP 889 92 132 25 175 DSZ804 11 847 25 090 STO 133 OP 176 88805 STO 848 OP 091 12 134 26 177 B'886 12 849 26 092 3 135 3 178 ISBR807 STO 850 2 093 SBR 136 3 179 LBL808 13 851 PRO 894 CLR 137 STO 188 RCL009 1 852 10 095 RCL 138 87 181 08 0 8 853 GTO 096 13 139 GTO 182 FI)


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THE AUTHOR Benjamin Bernfeld was born in 1928 in Brasov,Rum ania. He graduated wi th a degree in electrical en-gineering from the Leningrad Institute of M otion PictureEngineering in 1954 and in 1975 received the Docteur-Ing6nieur degree from the Louis Pasteur University ofS tra sb ou rg , fo r w hic h h is majo r fie ld w as p sy ch oa co ustic sof sound local izat ion.

Dr. B ernfeld worked in the field of audio engineering as aresearch engineer and was em ployed as a recording en-gineer of classical music from 1957 to 1974 inElectrecordStudios, B ucharest. In 1975, Dr. B em feld joined E. Voel-ker Acoustical Consultants in Frankfurt, Germany, andsince 1977 has been chief sound engineer of the IRC AMRes earc h In stitu te in Pa ris .

== Heis a memberof theAudioEngineeringSocietyandh as p re se nte d sev era l p ap ers at its c on ve ntio ns.

904 JOURNALOFTHEAUDIOENGINEERINGOCIETY,1979NOVEMBER,VOLUME27,NUMBER11

a personal calculator program for a-weighted soun pressure level and preferres noise criterion

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