1、AMERICAN NATIONAL STANDARDDESIGN RESPONSE OF WEIGHTINGNETWORKSFOR ACOUSTICAL MEASUREMENTSAccredited Standards Committee S1, AcousticsStandards SecretariatAcoustical Society of America35 Pinelawn Road, Suite 114EMelville, New York 11747-3177ANSI S1.42-2001ANSIS1.42-2001The American National Standards
2、 Institute, Inc. (ANSI) is the na-tional coordinator of voluntary standards development and the clear-inghouse in the U.S. for information on national and internationalstandards.The Acoustical Society of America (ASA) is an organization of sci-entists and engineers formed in 1929 to increase and dif
3、fuse theknowledge of acoustics and to promote its practical applications.American National StandardDesign Response of Weighting Networksfor Acoustical MeasurementsSecretariatAcoustical Society of AmericaApproved 22 October 2001American National Standards Institute, Inc.AbstractThis Standard provides
4、 the design criteria for both the frequency-domain response (amplitude and phase)and time-domain of the A- and C-weighting networks used in acoustically related measurements. The polesand zeros for each weighting network are given, along with equations for computing the amplitude andphase responses
5、as functions of frequency and impulse and step responses as functions of time. Otherknown weighting networks that had been standardized, such as the B-, D- and E-weightings, or weightingsthat were published in the past, are listed in the Annexes for reference.ANSI S1.42-2001AMERICAN NATIONAL STANDAR
6、DS IN ACOUSTICSThe Acoustical Society of America (ASA) provides the Secretariat for AccreditedStandards Committees S1 on Acoustics, S2 on Mechanical Vibration and Shock,S3 on Bioacoustics, and S12 on Noise. These committees have wide represen-tation from the technical community (manufacturers, consu
7、mers, and general-interest representatives). The standards are published by the Acoustical Society ofAmerica through the American Institute of Physics as American National Stan-dards after approval by their respective standards committees and the AmericanNational Standards Institute.These standards
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9、), is responsiblefor developing, voting upon, and maintaining or revising its own standards. TheASA Standards Secretariat administers committee organization and activity, andprovides liaison between the Accredited Standards Committees and ANSI. Afterthe standards have been produced and adopted by th
10、e Accredited StandardsCommittees, and approved as American National Standards by ANSI, the ASAStandards Secretariat arranges for their publication and distribution.An American National Standard implies a consensus of those substantially con-cerned with its scope and provisions. Consensus is establis
11、hed when, in thejudgment of the ANSI Board of Standards Review, substantial agreement hasbeen reached by directly and materially affected interests. Substantial agreementmeans much more than a simple majority, but not necessarily unanimity. Consen-sus requires that all views and objections be consid
12、ered, and that a concertedeffort be made toward their resolution.The use of American National Standards is completely voluntary. Their existencedoes not in any respect preclude anyone, whether he has approved the standardsor not, from manufacturing, marketing, purchasing, or using products, processe
13、s,or procedures not conforming to the standards.CAUTION NOTICE: This American National Standard may be revised or with-drawn at any time. The procedures of the American National Standards Instituterequire that action be taken periodically to reaffirm, revise, or withdraw a standard.Standards Secreta
14、riatAcoustical Society of America35 Pinelawn Rd. Suite 114EMelville, New York 11747USATelephone: 11 631 390-0215Telefax: 11 631 390-0217E-mail: asastdsaip.orgInternet: http:/asa.aip.org 2001 by the Acoustical Society of America. This standard may not be reproduced in wholeor in part in any form for
15、sale, promotion, or any commercial purpose, or any purpose notfalling within the provisions of the Copyright Act of 1976, without prior written permission ofthe publisher. For permission, address a request to the Standards Secretariat of the Acous-tical Society of America. ContentsPageForeword . iii
16、1 Scope . 12 Normative references . 12.1 American National Standards 12.2 International Standards . 13 Frequency-weighting characteristics 13.1 Frequency domain 14 Time-domain characteristics . 44.1 Time domain . 4AnnexesA Other weighting networks . 6B G-weighting network for infrasound measurements
17、 . 11B.1 G-weighting network 11C U-weighting network for measurement of audiblesound in the presence of ultrasound 13C.1 U-weighting network 13D Bibliography . 14Figures1 Relative amplitude response level of the A- and C-weightingnetworks to a steady-state sinusoid. 32 Phase response of the A- and C
18、-weighting network to asteady-state sinusoid. . 43 Time-domain responses of the A- and C-weighting networksto an impulse (delta function). 5A1 Relative amplitude response level of the B-, D- and E-weightingnetworks to a steady-state sinusoid. 6A2 Phase response of the B-, D- and E-weighting networks
19、 toa steady-state sinusoid. . 8B1 Relative amplitude response level of the G-weighting network toa steady-state sinusoid. . 12C1 Relative amplitude response level of the U-weighting networksto a steady-state sinusoid . 14Tables1 Poles, zeros, and normalization constants of the transferfunctions for
20、the A-, and C-weighting networks . 12 Relative amplitude response level (re: response at 1000 Hz)and phase response of the A-, and C-weighting networks toa steady-state sinusoid. Band numbers and nominal (orpreferred) frequencies are as specified in ANSI S1.6-1984.Exact frequencies, shown to four si
21、gnificant figures, aregiven by 100.1N, where N is the integer band number 23 Coefficients for the impulse responses of the A-, andC-weighting networks . 4iA1 Relative amplitude response level (re: response at 1000 Hz)and phase response of the B-weighting networks to asteady-state sinusoid. Band Numb
22、ers and nominal(or preferred) frequencies are as specified in ANSIS1.6-1984. Exact frequencies, shown to four significantfigures, are given by 100.1N, where N is the integer bandnumber. . 7A2 Poles, zeros, and normalization constants of the transferfunctions for the B-, D- and E-weighting networks.
23、. 8A3 Relative amplitude response level (re: response at 1000 Hz)and phase response of the D- and E-weighting networks toa steady-state sinusoid. Band numbers and nominal(or preferred) frequencies are as specified in ANSI S1.6-1984.Exact frequencies, shown to four significant figures, are givenby 10
24、0.1N, where N is the integerband number. 9A4 Coefficients for the impulse responses of the D- and E-weighting networks. . 10B1 Nominal coordinates of the poles and zeros of the transferfunction, in the complex frequency plane 11B2 Poles, zeros, and normalization constants of the transferfunctions fo
25、r the G-weighting. 11C1 Pole locations for U-weighting. . 13C2 U-weighting network relative frequency response level. . 13PageiiForewordThis foreword is for information only and is not an integral part of ANSI S1.42-2001 Ameri-can National Standard Design Response of Weighting Networks for Acoustica
26、l Measure-ments.Weighting networks have been widely used for many years to provide standard-ized means to select preferred information from acoustical signals. For example,the A- weighting has the property to enhance information over the human hearingrange. Where as, the C-weighting is designed to e
27、ncompass information from awider spectrum. There is no concrete data to prove that the weighting networksare perfectly in agreement with the intent, such as the human hearing range.However, over the years, the design goals of the previously standardized weight-ing networks have proven to be acceptab
28、le to a majority of users, and the designgoals have not been changed. Therefore it is possible to compare measured datafrom a vast data pool that has been accumulated over a period of more than 40years.For acoustical measurements, the weighting networks and the measuring instru-ments play important
29、roles in arriving at correct answers. In this standard, ANSIS1.42-2001, only the design goals of the weighting networks are given. The tol-erances in implementation of the weighting networks are subjected to specifica-tions given in instrument standards. It must be pointed out that in view of thespe
30、cification tolerances of weighting networks in acoustical instruments, it is pos-sible to have instruments of the same class specification to give different mea-sured readings for the same acoustical signal input. This is particularly true insound level meters with relatively wide weighting network
31、tolerances at the highand the low frequency range.For the sake of completeness, information on other weighting less popular seldomused networks such as B-, D- and E-weightings are listed in the Annexes.This standard was developed under the jurisdiction of Accredited Standards Com-mittee S1, Acoustic
32、s, which has the following scope:Standards, specifications, methods of measurement and test, and terminology,in the fields of physical acoustics, including architectural acoustics, electroa-coustics, sonics and ultrasonics, and underwater sound, but excluding thoseaspects which pertain to safety, hu
33、man tolerance and comfort.At the time this standard was submitted to Accredited Standards Committee S1,Acoustics, for final approval, the membership was as follows:G. S. K. Wong, ChairT. J. Kuemmel, Vice ChairS. B. Blaeser, SecretaryAcoustical Society of America G.S.K.WongT. J. Kuemmel (Alt.)Air Con
34、ditioning and Refrigeration Institute R.ComparinM. Darbeau (Alt.)iiiAmerican Industrial Hygiene Association D.DriscollL.H. Royster (Alt.)Audio Engineering Society D.QueenM.R. Chial (Alt.)Bruel there are N complex poles pnof order rn; H0is the gain constant; and j2521.NOTE: The poles and zeros of a n
35、etwork are usu-ally given as radian frequency values in the complexplane. In this standard, those values have been di-vided by 2p in order to facilitate relating the poles andzeros to actual frequencies, in hertz.3.1.2 The amplitude level of the network responseis given by,Wf !510 logK H *jf !Hjf !#
36、, (2)where K is a normalization constant chosen so thatthe weighted level is zero decibels at 1000 Hz.3.1.3 Writing the poles in the form pn5an1jbnand the zeros as zm5gm1jdm, the amplitude levelof the network response can be written in terms ofreal quantities as,Wf !510 logUKS)m51Mgm21f2dm!2#qmD3S)n
37、51Nan21f2bn!2#rnD21U. (3)The phase response isu f !5arctan$ImHif !# /ReHif !#%, (4)which can be written in terms of real quantities asuf !5(n51NrnarctanSf2bnanD2(m51MqmarctanSf2dmgmD. (5)3.1.4 The poles and zeros of the A-, and C-weight-ing networks are listed in Table 1. Note that forthese networks
38、 all of the poles are on the real axis.The poles for the A-weighting network include thesame poles as for the C-weighting network.3.1.5 The relative amplitude response levels andthe phase responses of the A-, and C-weightingnetworks, computed from the equations givenabove and from the zeros and pole
39、s listed in Table1, are tabulated in Table 2.3.1.6 The amplitude response and the phase re-sponse are plotted in Figs. 1 and 2 for the fre-quency range from 1 Hz to 100 kHz.Figure 1 Relative amplitude response level of the A- and C-weighting networks to a steady-state sinusoid.ANSI S1.42-20013 2001
40、Acoustical Society of America4 Time-domain characteristics4.1 Time domainIn the time domain, a linear time-invariant filter willtransform an input signal, si(t), into an output sig-nal, s0(t), according tos0t!5E0sit2t!ht!dt, (6)where h(t), the impulse response of the filter, isthe inverse transform
41、of the (frequency-domain)transfer function of the filter.4.1.1 For a filter with N poles, the impulse re-sponse can be expressed asht!5(n51N(l 51rnCn ltl 21e2pant3cos 2pbnt1lnsin 2pbnt!, (7)where anand bnare, as defined in Sec. 3, the realand imaginary parts for the nth pole. The constantcoefficient
42、s, Cnland ln, are complicated func-tions of the poles and zeros. Since all of the polesfor the A-, and C-weighting networks are on thereal axis, bn50, and the impulse response forthese three networks is given simply byht!5(n51N(l 51rnCn ltl 21e2pant. (8)The values for Cnlare listed in Table 3.Figure
43、 2 Phase response of the A- and C-weighting network to a steady-state sinusoid.Table 3 Coefficients for the impulse responses of the A-, and C-weighting networks.n A weighting C weighting1 C1120.47424440310120.262031673103C120.1437903531030.1692838331052 C210.2264147131030.262031673103C220 0.5932410
44、3310103 C3120.819287933104flC320 fl4 C410.797120703104flC420.7963012131010flANSI S1.42-20014 2001 Acoustical Society of America4.1.2 The impulse responses for the A-, and C-weighting networks, as computed from Eq. (8), areplotted in Figure 3.Sometimes it is desired to know the response of afilter to
45、 a step function rather than to an impulse.The unit step-function response is given bygt!5E0tht!dt. (9)4.1.3 For the networks of interest in the presentstandard, the step function response is given by:gt!5(n51N(l 51rnDnl12122pant!l 21e2pant3cos 2pbnt1mnsin 2pbnt!#, (10)whereDn152Cn12pan2lnbnan21bn2,
46、 (11a)Dn25Cn2/4p2an2, (11b)andmn5lnan1bnan2lnbn. (11c)4.1.4 For the A-, and C-weighting networks, whichhave all of the poles on the real axis,gt!5(n51N(l 51rnDn l12122pant!l 21e2pant#.(12)Figure 3 Time-domain responses of the A- and C-weighting networks to an impulse deltafunction .ANSI S1.42-20015
47、2001 Acoustical Society of AmericaAnnex A(Informative)Other weighting networksA.1.1 The B-, D-, and E-weighting networks aresome of the previously standardised weightingnetworks that have not been in common use inacoustical measurements. However, informationon these networks is listed here for refer
48、ence.Over the past thirty years, there were other net-works proposed in various publications and a list ofthese proposals can be found in ref 1 in Annex D.Table A1 lists the amplitude and phase responsesof the B-weighting network.A.1.2 International Standard IEC 537 (1976), Fre-quency Weighting for
49、the Measurement of AircraftNoise (D Weighting), provides the pole-zero speci-fications for a network, known as the D-weightingnetwork, that is included in some sound levelmeters. Stevens ref 2 in Annex D, proposed anE-weighting network to provide a weighted soundlevel that is related to the loudness level computedaccording to his Mark VII procedure. Arnold P. G.Peterson1provided pole-zero specifications for theE-weighting network.A.1.3 The poles and zeros of the B-,
