PAPERS

Audio Engineeringand Psychoacoustics:Matching Signals to the Final Receiver,

the Human Auditory System*

EBERHARD ZWICKER AND U. TILMANN ZWICKER

Institute of Electroacoustics, Technical University Munich, D-8000 Miinchen 2, Germany

The consequences of the fact that the human auditory system is the final receiver inalmost all cases of sound recording, transmission, and reproduction are discussed. Thestrategies of processing and transmitting sound as effectively as possible on one hand,and also as "undistorted" as possible on the other need adaption to the perceptioncharacteristics of the auditory system.' The transformation of frequency to critical-bandrate as well as the transformation of level to specific loudness are the tools used forthis adaption. Examples for practical applications of the basic idea are illustrated.

0 INTRODUCTION digital storage can profit from the possible informationreduction as well.

During the last few years, digital sound processing In fields other than audio, such as the transmission

and storage have been adopted widely in audio, and of electrical power, the adaption to the final receiversare providing excellent sound quality. However, con- is very well established and generally applied forverting an audio stereo signal to a 16-bit digital format transmission from power plant to power plant as wellwith appropriate redundancy for error correction and as from power plant to factories and even to individualwith a minimum sampling rate around 44 kHz requires households. In the field of transmitting information,extremely extended bandwidth for signal transmission the same rule holds as for power transmission. There-and storage, the latter coupled with huge mass-storage fore, all of our efforts in improving electroacousticnecessities. The large bandwidth results in problems information transmission--including recording--havefor radio transmission in particular, so there is consid- to be seen from the perspective of the final receiver,erable interest in avoiding any redundancy in the signal the human auditory system. This perspective has manyother than for error-correction purposes. To achieve more advantages in audio engineering, such as in in-sound transmission or reproduction that is not only strumentation and with public-address applications, asvery good but also efficient, all equipment has to be discussed in this paper.adapted to the characteristics of the final receiver, in

this case the human ear. Any part of the transmitted 1 THE FINAL RECEIVER: THE HUMANsignal that is not recognized by the auditory system AUDITORY SYSTEM AND PERCEPTIONshows bad matching to the receiver and provides un-

necessary redundancy. Considerable progress has been Eventually important is the perception of sound. Wemade to implement methods of reduction of unneces- do not perceive frequency, we rather perceive pitch;sary data derived from findings in the field of psycho- we do not perceive level, but loudness. We do notacoustics. Most of these efforts concern the future digital perceive spectral shape, modulation depth, or frequencyaudio broadcasting (DAB), for example [1]-[3], but of modulation; instead we perceive "sharpness," "fluc-

tuation strength," or "roughness." We also do not per-

* Manuscript received 1990July 18;revised 1990December ceive time directly; our perception is the subjective12. duration,often quite differentfrom the physicaldu-

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ZWICKER AND ZWICKER PAPERS

ration. In all of the hearing sensations mentioned, which equivalent scale, that is, the critical-band-rate scale,are described in detail elsewhere [4]- [6], masking plays is used.an important role in the frequency, as well as in the Masking usually is described as the sound-pressure

time domain. Consequently Sec. 2 deals with masking level of a test sound (a pure tone in most cases) necessaryeffects and the transformation from frequency scale to to be barely audible in. the presence of a masker. Forcritical-band-rate scale and from level scale to specific- narrow-band noises used as maskers and pure tonesloudness scale. The information received by our auditory used as test sounds, masking patterns can be producedsystem can be described most effectively in the three for different center frequencies of the narrow-band noisedimensions of specific loudness, critical-band rate, and maskers, as shown in Fig. 1. The same information istime. The resulting three-dimensional pattern is the given in Fig. l(a) and (b). However, in Fig. l(a) themeasure from which the assessment of sound quality level of the barely audible pure tone is plotted as acan be achieved. Some applications of this pattern, function of frequency on a linear scale, in contrast towhich is reproduced in a modern loudness meter, for the logarithmic scale used in Fig. l(b). In order toexample, are discussed especially in view of modern make the masking patterns directly comparable throughelectroacoustic transmission and reproduction, having the same peak values, the so-called masking

In this paper, the main emphasis is on practical ap- index, a value of 2-6 dB (for details see the literatureplications of psychoacoustics in the field of perception mentioned), is added to the sound-pressure level of theand reproduction of sound, and many scientific details barely audible test tone, and the resulting level, calledare therefore omitted. Rather, the basic, important facts excitation level, is shown as ordinate. The level of theare enhanced. Further information is available from narrow-band maskers is 60 dB for all curves. Comparingbooks on psychoacoustics and electroacoustics [4]-[8]. the results produced from different center frequencies

of the masker, we find the form of the curves to be

2 PSYCHOACOUSTICAL PRINCIPLES rather dissimilar, no matter what frequency scaling weAPPLICABLE IN AUDIO ENGINEERING use. It seems as if the shape of the curves is similarPRACTICE for center frequencies up to about 500 Hz on linear

frequency scale, while for center frequencies above2.1 Transformation from Frequency to Critical- 500 Hz there is a similarity on a logarithmic frequencyBand Rate scale. This intuitive result is quite accurate since the

The effect of masking plays a very important role in hearing-equivalent critical-band-rate scale mentionedhearing, and is differentiated into simultaneous and follows a linear frequency scale up to about 500 Hznonsimultaneous masking. An example for the simul- and then a logarithmic frequency scale above 500 Hz.taneous condition would be the case where we have a This relation is illustrated in Fig. 2 by two differentconversation with our neighbor while a loud truck passes frequency scales, one divided linearly, the other log-by. In this case our conversation is severely disturbed, arithmically. Approximations, which sometimes mayTo continue our conversation successfully we have to be useful within certain frequency ranges, are also in-raise our voice to produce more speech power and dicated. Fig. 2(a) shows the uncoiled inner ear, in-greater loudness. In music, similar effects take place, eluding the basilar membrane. It indicates that the crit-The different instruments can mask each other, and leal-band-rate scale is directly related to the place alongsofter instruments become audible only when the loud the basilar membrane where all the sensory cells areinstrument pauses. Such simultaneous masking is out- located in a very equidistant configuration (one row oflined here for quantitatively easily describable con- inner hair cells and three rows of outer hair cells).ditions, while nonsimultaneous masking is discussed Thus the critical-band-rate scale is closely related toin Sec. 2.3. Simultaneous masking can be understood our physiology, too.more easily if instead of the frequency scale a hearing The critical-band concept is based on the well-proven

801dB ' 0 _ II

3.25 1 4 fc =8kHz IB_ fc = 0.07 0.25 1 4kHz I

°l 5/0 i 2 4 6 8 1'0 12 14kHz16 Q02 0.05 611 012 015 i 2 ' '5kHzl0 20

frequency(a) (b)

Fig. 1. Excitation level (masking level with added masking index) of narrow-band noises of given center frequency as afunction of frequency. Broken lines--threshold in quiet. (a) Linear scale. (b) Logarithmic scale.

116 J. Audio Eng. Soc., Vol. 39, No. 3, 1991 March

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assumption that our auditory system analyzes a broad along the basilar membrane, but also many other effects,spectrum in parts that correspond to critical bands, such as pitch, frequency differences barely noticeable,

Adding one critical band to the next, so that the upper or the growth of loudness as a function of bandwidth.limit of the lower critical band corresponds to the lower Therefore when dealing with hearing sensations, it islimit of the next higher critical band, produces the very effective to transfer first the frequency scale intoscale of the critical-band rate· Since critical bands have the critical-band-rate scale.

a 100-Hz width up to 500 Hz and above 500 Hz take The effect of masking produced by narrow-banda relative width of 20%, it becomes clear why the crit- maskers is level dependent and, therefore, a nonlinearical-band rate is dependent on frequency as illustrated, effect. As shown in Fig. 4(a), all masked thresholdsThis can also be seen in Fig. 2(c), where the critical- show a steep rise from low to higher frequencies up toband rate is plotted as a function of frequency on the the maximum of masking. Beyond this maximum, thelogarithmic scale, a scale more appropriate for ap- masked threshold decreases quite rapidly toward higherproximating the critical-band rate· The latter fact is frequencies for low and medium masker levels. Atespecially advantageous for problems dealing with higher masker levels, however, the slope toward highspeech transmission, where important spectral features frequencies, that is, larger critical-band rate, becomesare located in the spectral region between 300 and 5000 increasingly shallow. This nonlinear rise of the upperHz. However, it is also necessary to realize that the slope of the masked threshold with the masker level islinear relation between frequency and critical-band rate an effect that is assumed to be produced in the innerplays an important role in music based on harmony, ear already. The outer hair cell rows form a feedback

Because the critical-band concept is used in so many system which, through saturation, is effective at lowmodels and hypotheses, a unit for the critical-band rate levels only. At higher levels the feedback automaticallywas defined, which is one critical band wide. It is the disappears. This leads to a shape of the masking curvebark, in memory of Barkhausen, a scientist from Dres- corresponding to the amplitude of the traveling waveden, Germany, who introduced the phon, a unit de- along the basilar membrane, as seen for higher levels.scribing the loudness level for which the critical band Recent data of this traveling wave measured at veryplays an important role· low levels have proven that feedback takes place in

When frequency is transferred into critical-band rate,the masking patterns outlined in Fig. 1 change to thoseseen in Fig. 3. There the level of the barely audible

_7'0.25'0.5' ' fc ': 2k'Hz 4' ' 8'pure tone (again expressed as excitation level, that is, > 60

including the masking index) is plotted as a function c_dB_ _ ._..__

of the critical-band rate for the same narrow-band =o40maskers as shown in Fig. 1 The effectiveness of the '_·natural frequencyscale, that is, the critical-band-rate __2¢ iscale, is obvious. The shapes of the curves for different _=centerfrequenciesareverysimilar.Onlyat very low _r--frequencies, below about 100 Hz, where special masking -

effects (such as the masking-period patterns) lower the critical-bandrateamount of masking, the upper slope is somewhat steeper.

It is not only the masking effect that can be described Fig. 3. Excitation level versus critical-band rate for narrow-band noises of given center frequency and 60-dB sound pres-more simply and become more easily understandable sure level. Broken lines--threshold in quiet. Adopted fromin terms of this natural scale corresponding to location [5].

2_ ,, if, , , i , , , , , , , , , i,

/20 /Az=lBark=lOOme

N 16 _L_I_: Hz- _ f: _r_-I )/_7 f J z :in-2 f /IBQrk-'_ Hz

-_ 12

.121

' 8 {Az =1Bark= 100melh·-_ \ z-Af =0.1kHz /b 4

j [ , i i , ,L 0 2 4 8kHz 16 0.02 0.1 lkHz 10

frequency(a) (b) (c)

Fig. 2. (a) Scale of uncoiled cochlea. (b) (c) Critical-band rate (ordinate, linear scale) as a function of frequency. (b) Linearscale. (c) Logarithmic scale. Useful approximations are indicated by broken lines and related equations. Adopted from [5].

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ZWICKERANDZWICKER PAPERS

the inner ear already, producing a narrower amplitude called spontaneous otoacoustic emissions [9], whichdistribution of the traveling wave and consequently a appear in half of all ears at levels around 0 dB SPL.narrower masking pattern at low masker levels. This These tonal emissions, which are proven to be producedis also seen in data for masking patterns produced by in the inner ear, can be suppressed by adding a sup-a model reproducing peripheral preprocessing in the pressor tone, the level of which is given in the relatedinner ear, including nonlinear feedback with lateral suppression tuning curves as a function of the critical-

coupling. The real masking data [Fig. 4(a)] and the band rate. The curve given belongs to the criterion ofmodel data [Fig. 4(b)] compare very nicely. Therefore, 6-dB amplitude reduction of the spontaneous otoacousticand in accordance with physiological data from animals, emission. These are objective data because they do notitcanbe assumed that simultaneous maskingis already depend on a subject's response at all. By comparing

produced in the peripheral preprocessing of the inner Fig. 4(c) and (d), one can easily see that the psycho-ear, that is, before the information is transferred to the acoustically measured tuning curves, which involveneural level, the highestpossiblesignalprocessinglevel in the brain,

Another possibility to measure masking is psycho- show the same frequency selectivity as the suppressionacoustical tuning curves. In this case the level of the tuning curves resulting from purely peripheral pro-test tone is fixed, while the level of the masker, in most cessing. Therefore the frequency-selective and nonlinearcases also a tone, is increased so that the test tone just effect of simultaneous masking produced in our auditorybecomes inaudible. Plotting this masker level as a system can be assumed as being produced already infunction of critical-band rate results in the so-called the peripheral part of the inner ear and still in the analog

psychoacoustical tuning curves. Such a curve is outlined domain, that is, installed before the signal informationin Fig. 4(c); it has a shape that correlates quite strongly is transferred into neural information using spike rates.with the data seen in Fig. 4(d), as described in the Since the arrangement of the hair cells is equidistantfollowing, and the form of the traveling wave in the inner ear,

The assumption that frequency selectivity takes place besides the shift along the basilar membrane, does notin the peripheral part of the auditory system (the inner change much as a function of frequency, it becomesear) and produces the critical-band-rate scale can also understandable why the natural scale of the critical-be supported by experiments on the suppression of so- band rate, which corresponds to the location along the

100 100.... , ' ' i i , · T ! i

80 [ _psychoocousticol- 80 I _ model

C _ C

o o60 _60

40 _40

20 - 20

o thFe'_s'_d-;'-n_bT_r-"__ _--"' 0i i i i i i i

6 8 10 12 1/, 16Bork 20 6 10 12 1/. 16Bock 20

(a) (b)

100 ..... 100 ......

x _>60_0 60O m

E _ ALsoAE =_L

'_40 o.40fT=2700Hz '_ ¢m

oJ LT=10dB '_ fSOAE=2830Hz- 20 -_ 20

> LSOAE=12dB OO

, , , , , , , o lb ' ' 2o0 6 8 10 12 1/. 16Bork 20 16Borkcriticol-bond rote

(c) (d)

Fig. 4. (a) Level of test tone barely masked by narrow-band noise of given level, (b) Test-tone level needed in model toproduce 1-dB increment anywhere along basilar membrane. (c) Psychoacoustical and (d) suppression tuning curve; each asa function of critical-band rate.

118 J. Audio Eng. Soc., Vol. 39, No. 3, 1991 March

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basilar membrane, is the adequate scale to describe that a 1-kHz tone, although it has an infinitely smallfrequency and frequency-selective effects in hearing, spectral width, does not lead to an infinitesimally nar-

row excitation in our auditory system--the final re-2.2 Transformation from Level to Specific ceiver--and thus on the critical-band-rate scale. In-

Loudness stead, it results in an excitation over a range increasingWhen we talk about loudness in view of quantitative with larger SPL values of the 1-kHz tone. Although

relations, we often think of the loudness function of a easily describable in purely physical terms, the 1-kHz1-kHz tone. This function is established by answering tone produces a complex pattern of excitation, whichthe question of how much louder a sound is heard relative from this point of view does not seem directly usefulto a standard sound. The standard sound in electro- for answering the question we are interested in, namely,acoustics is a 1-kHz tone, and the reference level in transferring the excitation into an equivalent psycho-

this case is 40 dB. Many measurements of different acoustic value.laboratories have produced similar results so that When we talk about loudness, we mean total loudness,eventually the loudness function of a 1-kHz-tone in knowing that this loudness is comprised of very many

the free-field was standardized. It is given in Fig. 5 as partial loudnesses which are located along the critical-a solid curve. With the definition that a l-kHz tone of band-rate scale. The physiological equivalent of this40-dB SPL has the loudness of 1 sone, the curve in- assumption would be that all the neural activity of thedicates that doubling the loudness from 1 to 2 sone is sensory cells along the basilar membrane is summed

equivalent to increasing the sound-pressure level from up into a value that finally leads to the total loudness.40 to 50 dB. The same holds for larger levels: a doubling Many experiments dealing with the loudness of soundsin loudness is achieved with each increment of 10 dB of different spectral widths have shown that the in-of the l-kHz tone. This means that 50 dB corresponds struments our auditory system uses are the critical bandsto 2 sone, while 100 dB corresponds to 64 sone. The that shape and weigh the many partial loudnesses toloudness function of the 1-kHz tone above 40 dB cor- be summed up. If the summation or integral mentionedresponds to a power law if loudness is related to sound leads to the loudness that is given in units of sones,intensity. Its exponent can be extracted easily by the the value we are looking for has to have the dimensionfact that a 10-dB increment produces an increment in of sones per bark. This value is called specific loudnessloudness of a factor of 2, which in logarithmic values and is denoted by N'. The total loudness N is thus theis equivalent to an increment of 3 dB. Therefore the integral of specific loudness over the critical-band rate,exponent of the power law connecting loudness with which can be expressed mathematically as follows [10]:the sound intensity of the 1-kHz tone for sound pressure

f24 barklevels above 40 dB is 0.3. At sound pressure levels N = N'(z) dz . (1)below 40 dB, the loudness function becomes steeper _z=0and steeper toward threshold in quiet, which per def-inition corresponds to a loudness of 0 sone. On the Since the 1-kHz tone produces a complicated excitationlogarithmic loudness scale this zero corresponds to a pattern and therefore also a complicated specific-loud-value of minus infinity, ness pattern, we have to search for a sound that produces

From the masking pattern outlined in Fig. 4(a) and more homogeneous excitation versus the critical-band-the corresponding excitation pattern, we already know rate pattern. This sound is the uniform exciting noise,

which fills up the entire auditory range in such a waythat the same sound intensity falls into each of the 24

100 ........ .:..... abutting critical bands (meaning that all critical bands

sone NUEN _IuEN'_0'23 _f...":_

S0 / .... are positioned adjacent without space between them).

2 ,,,,,.,/' The loudness of such a uniform exciting noise was20 $--b-_=_-T_-0) ..,. " measured. It was found that the loudness of 1 sone is

' 10 ..' _ _..:-'"'_""//_ reached- at a level of about 30 dB for uniform exciting

5 / i. noise. The entire loudness function of uniform excitingnoise is shown by the dotted line in Fig. 5. The curve

7 2 ./' ....-" y rises somewhatmoresteeplywith levelthanthe loudnessit} J' .,'"1 of the 1-kHz tone, at least for levels of uniform excitingt--

-o> 0.5 ....-"/_ noise to about 50 dB. Above 60 dB, the dotted line

o /IlkHz'_ 0'3z2Ltku'-k0dB'i-_-aB can also be approximated by a straight line, which is0.2 shown dotted-dashed in Fig. 5. This straight line again

_i/_. sone 16_I0./ - . . means that a power law holds for the relation between0.1 × , fi' ......... the loudness of uniform exciting noise and the sound0'050 10 20 30 40 50 60 70 80 90dBlO0 110

intensity of that noise. The exponent of this dotted-Fig. 5. Loudness function of 1-kHz tone (solid line) and dashed line is smaller, however, than that for the loud-uniform exciting noise (dotted line). Loudness is given as afunction of sound pressure level. Approximations using power ness function of the 1-kHz tone (dashed straight line).laws are indicated as broken and dashed-dotted lines together It has a value of only 0.23, and thus the two loudnesswith the corresponding equations. Adopted from [5]. functions shown in Fig. 5 come closer together at higher

J. Audio Eng. Soc., Vol. 39, No. 3, 1991 March 119

ZWICKER AND ZWICKER PAPERS

levels. Besides the different exponents of the two loud- Using our assumption that total loudness is the integralness functions at higher levels it is also interesting to over specific loudness along the critical-band-rate scalesee that the loudness of uniform exciting noise is much (as discussed), we can calculate the specific loudnesslarger than the loudness of the 1-kHz tone in almost corresponding to an excitation level of 50 dB from thethe entire level range indicated. For example, the loud- total loudness of uniform exciting noise. According toness of a 60-dB uniform exciting noise is about 3.5 Fig. 5, uniform exciting noise with a level of 64 dBtimes larger than the loudness of the 1-kHz tone with produces a total loudness of 20 sane. Dividing thisthe same level. This difference is a very distinct effect, value by 24 bark, the entire width of the critical-band-which plays an important role in judging and measuring rate scale, leads to the value for the specific loudnessthe loudness of noises. It indicates very clearly that an caused by an excitation level of 50 dB, that is, 20 saneoverall sound-pressure level of broad-band noises is divided by 24 bark leads to about 0.85 sane/bark. Thean extremely inadequate value if loudness is to be ap- same procedure can be used to calculate the relation

proximated. Unfortunately most noises producing an- between specific loudness and the excitation level fornoyance to people are broad-band noises, and the A- different values of the excitation level, that is, differentweighted sound-pressure level is a measure of the total values of the total level and total loudness of uniformlevel, which creates misleading values when used as exciting noise. The results show that specific loudnessan indication for loudness. Almost all sounds occurring is related to the excitation in a similar way as the totalin audio broadcasting and recording not only have a loudness of uniform exciting noise is related to the

large bandwidth but also differ in spectral shape, sound intensity of the noise at high levels, namely,Therefore meters based merely on total level (such as through a power law with an exponent of 0.23. The

VU or peak-level meters) usually give readings quite effect of threshold, which influences the relation be-unrelated to loudness, although these readings should tween specific loudness and excitation level for levels

correspond to loudness sensation as closely as possible ranging between threshold and about 40 dB abovefrom the view of the listener as the final receiver. This threshold, is ignored here for reasons of simplicity andis referred to later, accessibility. For practical applications, the exponent

Because uniform exciting noise produces the same ex- of 0.23 is often approximated with 0.25, as it thencitation along the whole critical-band-rate scale, it can corresponds to the factor 0.5 of the sound pressure,be used very nicely to calculate the value we are searching and this square root is easily available technically.for (the specific loudness) out of its total loudness. Fig. The distribution of specific loudness as a function6 shows the procedure schematically. In Fig. 6(a) the of critical-band rate for the 1-kHz narrow-band noiseexcitation levels of uniform exciting noise (dashed) and with the same level of 64 dB is shown in Fig. 6(b) byof narrow-band noise, one critical band wide and centered a solid line. It is obvious that the loudness of the two

at 1 kHz (solid), are shown. The two distributions are noises, the uniform exciting noise and the narrow-bandgiven for the condition that both the uniform exciting noise, that is, the integral of specific loudness overnoise and the narrow-band noise have the same sound- critical-band rate, is quite different for the two noises.pressure level of 64 dB. This value was chosen because For the narrow-band noise, the area below the curvethe level in each of the 24 abutting critical bands produced corresponding to the integral is only about one quarterby the uniform exciting noise is 50 dB, leading to an of that of the rectangularly shaped area of the uniformoverall sound-pressure level of 50 dB + (10 × log 24) exciting noise. The same relation can be seen in Fig.dB = 64 dB. For the narrow-band noise, the entire 5 for a level of 64 dB, where the two curves indicate

intensity is concentrated around 1 kHz, corresponding a loudness of 20 sane for the uniform exciting noise,to a critical-band rate of 8.5 bark. The distribution of but only 5 sane for the 1-kHz tone, which is as loudthe excitation level as a function of critical-band rate as the narrow-band noise centered at 1 kHz.

reaches a peak value of 64 dB for the narrow-band The distributions of specific loudness as a functionnoise, while it remains constant for the uniform exciting of critical-band rate shown in Fig. 6(b) are the mostnoise at 50 dB. extremecases. Theone produced by uniformexciting

A2 N=24Bark.0.85¢_,n,,60 $sone

'¢-_cdBf40 - _co_B_-=i 5 =20sone'9

, , , _ 0000 /. 8 12 16Bark 24 4 8 12 16Bark 24critical- band rate

(a) (b)

Fig. 6. (a) Excitation level and (b) specific loudness of narrow-band noise (solid lines) and uniform exciting noise (brokenlines) of equal sound-pressure levels (64 dB) as a function of critical-band rate.

120 J. Audio Eng. Soc., Vol. 39, No. 3, 1991 March

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noise is completely flat. However, even this noise pro- It decreases from the value for simultaneous maskingduces a flat shape only if the frequency response between (plotted on the left, outside the logarithmic scale) asthe free-field condition and the sound pressure at the a function of the delay time. However, postmaskingear drum is not accounted for. In our discussion we produced by a very short masker burst (such as 5 ms)

ignore this for didactical reasons, but for precise loud- behaves quite differently. Postmasking in this case (asness measurements all these effects naturally have to indicated by the dotted line in Fig. 7) decays muchbe included [4], [6]. The distribution of specific loudness faster so that already after about a 50-ms threshold inover the critical-band rate is often called the loudness quiet is reached. This implies that postmasking strongly

pattern. This pattern varies for different kinds of noises, depends on the duration of the masker and therefore istones, or complex tones quite drastically. However, another highly nonlinear effect.this loudness pattern is the pattern that is most interesting Specific loudness as calculated from excitation infor the assessment of sound quality in the case of steady- the steady-state condition can also be considered asstate conditions because it shows on both coordinates being a time-dependent value. Simultaneous masking

the adequate hearing values: frequency is expressed and postmasking can be used to approximate the timevia critical-band rate and level is expressed via specific functions of the specific loudness. Using this completeloudness. If temporal effects are taken into account as transformation, the specific loudness for a tone burstwell, then the time-varying specific-loudness versus of 200 ms and that for a tone burst of 5 ms is plottedcritical-band-rate pattern contains all the information over time in Fig. 8. The tone bursts are located on thethat eventually is evaluated by our auditory system, linear time scale in such a way that both bursts end at

the same instant (200 ms). For the 200-ms tone burst,

2.3 Pattern of Specific Loudness versus the specific loudness shows a very steep rise and staysCritical-Band Rate versus Time at the peak value for almost 200 ms. The subsequent

From the many temporal effects included in the decay does not seem to have only one time constant.masking mechanisms only that of postmasking is dis- The specific loudness of the 5~ms tone burst rises justcussed here, because it has the biggest impact on ef- as quickly as for the 200-ms tone burst; the decay,ficient coding for digital audio broadcasting (DAB) [2]. however, is quite different and much faster, as can bePostmasking results from the gradual release of the expected from the postmasking pattern shown in Fig.effect of a masker, that is, masking does not immediately 7. The different behavior of the specific loudness afterstop with switching off the masker but still lasts while the end of the tone bursts is shown by a dotted and athere is actually no masker present. Postmasking de~ solid line. The two different decays can be approximatedpends on the duration of the masker. Fig. 7 shows a very roughly by single time constants of about 30 mstypical result for a 2-kHz test-tone burst of 5-ms du- for a tone-burst duration of 200 ms and about 8 ms forration. The delay time at which the test-tone burst is a duration of 5 ms. Actually, in both cases the slope

presented after the end of the masker is plotted as the is much steeper during the early decay and less steepabscissa. The level of the test-tone burst necessary for during the later decay (compared to the approximationaudibility is the ordinate. For a long masker duration using only one time constant).of at least 200 ms, the solid curve indicates postmasking. These functions of specific loudness versus critical-

band rate versus time illustrate best the information

flow in the human auditory system. As three-dimen-

_-/_ 200mss _ sional patterns, they contain all the information that isDOU'_. ii 5

'B 'a dB[¥ ",2_'""_x- u_i "=t ] subsequently processed and leads to the different hearingI _.I,i _ _ td _ J sensations. An example for such a complete pattern is

*_ 40¢ ,- _="2:>.. _ ft=2kHz] shown in Fig. 9 for the spoken word"electroacoustics"I ..............................] fed into the auditory system. The specific loudness0 5 _0 20ms 50 100 200 500 produced by this sound is plotted for 22 places with a

, detoy time, to l-bark spacing along the critical-band-rate scale. For

Fig. 7. Dependence of postmasking on masker duration: Level speech transmission, the spectral resolution in aboutof barely audible test-tone burst as a function of its delay 20 abutting channels is sufficient; for the transmissiontime (time between end of masker and end of test tone), of music, additional information on pitch is necessary.Duration of maskers 200 and 5 ms; level of masker (uniformmasking noise) 60 dB; duration of 2-kHz test tone 5 ms. However, the most important information, especiallyAdoptedfrom[5]. in music with strong temporal effects, can already be

! -,. 2O0ms:'........[-_\_..o : mmasker= 2 I\ ".,

oi , I',0 100 200 300ms

time

Fig. 8. Specific loudness produced by masker bursts of 200 ms (dotted line) and 5 ms (solid line) as a function of time.

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seen nicely in patterns showing the specific loudness 10(a) shows the loudness versus time function of piecesas a function of critical-band rate and of time. The of broadcast music interrupted by a commercial. In

pattern in Fig. 9 clearly shows the formants of the order to get an estimate of the loudness perceived byvowels and the spectral centers of the consonants, and the listener, the so-called cumulative loudness distri-also indicates the relatively quick rise following the bution is calculated for the different parts of the broad-stimulus, as well as a longer decay corresponding to cast, as indicated by the numbers and the dashed verticalpostmasking, dividing lines. The cumulative loudness distribution

Total loudness can be derived from the 24 specific- supplies information about the probability that a givenloudness channels by summing up all 24 channels and loudness is exceeded. This probability is shown in Fig.feeding this function through a special low pass which 10(b) for the three different temporal parts indicatedin useful approximation reproduces the behavior of our by the numbers in Fig. 10(a). At the start of the specificauditory system in regard to temporal effects in loudness sequence, around (0) a jingle is presented.perception. Through this special low pass, the time Comparisons of the loudnesses perceived by manyfunction of the perceived loudness is strongly smoothed, subjects have indicated that the average loudness cor-but shows single syllables with clear separation. It is responding to Ns0 (the loudness exceeded in 50% ofthen evident that peak loudness, normally assumed to the time) gives an inadequate number, whereas N5 tobe the perceived loudness, is produced by the vowels Nl0 give adequate readings of what the subjects reallyin speech. Consonants and plosives are very important perceive. It becomes very clear from Fig. 10(b) thatfor the understanding of speech and are also very clearly the commercial Q is perceived far louder than the ad-visible in the specific-loudness versus critical-band- jacent pieces of music ®.rate versus time pattern; their contribution to the total Sometimes in broadcasting different voices followloudness, however, is almost negligible, each other in the program, with the level being mon-

itored on a volume meter. Adjustment for equal level

3 APPLICATIONS of the voices often leads to strongly unequal loudnessperceived by the listener (the final receiver), who

3.1 Loudness can be rather annoyed by this. In accordance withLoudness is a sensation of great interest in many the basic idea introduced at the beginning of this

problems related to audio engineering. For example, paper, it would be much better to control the broad-it is of interest how the loudness of a piece of music casting level utilizing a loudness level meter [1 1],is perceived where the level changes drastically as a [12] rather than a volume meter, the reading of whichfunction of time. Often engineers are interested in a is only of importance for preventing equipment over-single number that is comparable with other data. Fig. load but not for the listener.

N

22 - - ' ----- - '21N' _ I --*_lsone/Bork_ , ,. . __ _ _ - ....

o 20 -- - -- " ''L -- --

co18 ..... ' ....... '...., 17 .... i

o° 16 ...... " - -- - "'c 15 ' - "' ' -- -- '--o l_ _ _ A ..... ..,.. __ · , ___ .,

_ 11 ' ' '' ' ' ·_ 10 .... --0 9 ' -- . -- I .... III · ., -- .co

(D

c 7 _ -- _ II II ., , , --

_ ...... _-- ,_ mi

u Z,

1 m m _ -- --

E L E C TR 0 A C 0U S T I C S

200ms ' time

Fig. 9. Specific-loudness versus critical-band-rate versus time pattern of spoken word "electroacoustics." Specific loudnessis plotted for 22 discrete values of critical-band rate. Ordinate scale is marked at panel related to 21 bark. Abscissa--time;200 ms is indicated. Total loudness as a function of time is plotted on top. Adopted from [6].

122 J.AudioEng.Soc.,Vol.39,No.3,1991March

PAPERS AUDIOENGINEERINGANDPSYCHOACOUSTICS

quency shows a maximum near 4 Hz, a value for which3.2 Sharpness the frequency of syllables in running speech has a max-

Sharpness is an important concept correlated with imum as well.the color of sound, and can also be calculated from the Fluctuation strength can also be calculated using thespecific-loudness versus critical-band-rate pattern. It temporal dependence of the specific-loudness versuswas found that the sharpness of narrow-band noises critical-band-rate pattern. The period of the modulationincreases proportionally with the critical-band rate for (or its frequency) as well the ratio between maximumcenter frequencies below about 3 kHz. At higher fro- specific loudness and minimum specific loudness arequencies, however, sharpness increases more strongly, of importance. Without going into detail, the influencean effect that has to be taken into account when the of room acoustics on the fluctuation strength may besharpness S is calculated using a formula that gives illustrated by using a 100% amplitude-modulated 1-the weighted first momentum of the critical-band-rate kHz tone. Such a tone, recorded under free-field con-

distribution of specific loudness, ditions, is played back in a room. The 100% amplitudemodulation is decreased quite strongly to a nonsinu-

!4 barkN' · g(z)z dz soidal amplitude modulation (Fig. 12). The specificS -- 0.11 acum. (2) loudness corresponding to the frequency range around

24barkN' dj 1 kHz is shown as a function of time in Fig. 12(a) forthe recorded sound and in Fig. 12(b) for the soundpicked up by a microphone in the room. The difference

In Eq. (2) the denominator gives the total loudness, between the two time functions is remarkable, indicatingthat room acoustics influence the fluctuation strengthwhile the upper integral is the weighted momentum

mentioned. The weighting factor g(z) takes into account quite strongly and thus the quality of sound reproduc-the fact that spectral components above 3 kHz contribute tion. Actual values in the example illustrated lead tomore to sharpness than components below that fro- a 75% reduction of fluctuation strength.quency. An example of the calculation of sharpness is 3.4 Room Acousticsgiven in Fig. 1 1 for uniform exciting noise and for ahigh-pass noise above 3 kHz. The weighted specific Room acoustics, however, produce positive effects,loudnesses are shown as a function of the critical-band too. For example, reverberation increases the loudness

of a speaker in a room because of the many reflectionsrate together with the location of their first momentum(center of gravity) marked by arrows, When the cutoff

frequency of the high-pass noise is shiftedtoward lower _- c_ [ .... 1values and the noise is finally transformed into a uniform '_ z

Q. _ Bark I xx,e]exciting noise, loudness increases quite strongly; how- _0u_ 2 L . -

ever, sharpness decreases markedly, in agreement with _-,,--, I

psych oacoustical results. ._o '_;7ff,_-ff/ff'_ff,_i_¢- O0 4 8 12 16Bark 243.3 Fluctuation Strength

Fluctuation strength is a sensation correlated to the critical-bond rote

temporal variation of sounds. It was examined quite Fig. 11. Sharpness of uniform exciting noise (broken line,extensively by Fastl [13] during the last decade. It is area hatched lower left to upper right), and high-pass noiseimportant for the transmission of music as well as for (dotted line, hatched upper left to lower right). Weightedspecific loudness is shown as a function of critical-band rate.the transmission of speech. Interestingly, the fluctuation Calculated sharpness is indicated by vertical arrows. Adoptedstrength measured as a function of the modulation fro- from [5].

(0) _---5)-----_i>-d h-........................_ ........................ 100-._-- r , ,20 ' ii I %

i _ 80sane i >, 30s I i ._15 I -o

' _' 60m I _ '-),.n I :..; x

c lO k '_ _ z,O '_1:3

o ax35 Z _ 20 ' x

- _. - ._,, .__..Q) *o _. ,

0 o_ 06 5 10 lSsone20time loudness

(a) (b)

Fig. 10. (a) Loudness--time function of broadcast including a jingle at (0), preparation for a commercial O, commercial(ID,and music ®. (b) Cumulative loudness distributions.

J. Audio Eng. Soc., Vol. 39, No. 3, 1991 March 123

ZWICKERANDZWlCKER PAPERS

that finally lead to a more diffuse field rather than to afree field. As an example, a speaker is approximated 3.5 Digital Transmission and Reproductionas a source of constant volume velocity, and Fig. 13 of Audio Signals at Reduced Bit Rateindicates the effect of increasing reverberation in a Transmission and reproduction at reduced bit rateroom when the same speech source produces loudness (especially in light of the proposed realizations for DAB)versus time functions under three different conditions, as a new and important area in electroacoustics andCurves (a) give the free-field condition, curves (b) the audio engineering were a major motivation for writingcondition for a room with a reverberation time of 0.6 this paper. The pattern of specific loudness versus crit-s, and curves (c) give the same for a room with a re- ical-band rate versus time can be used as a 'yardstick'verberation time of 2.5 s. Short periods from a 10-min that we have to follow in order to reduce informationspeech are shown in the left part of Fig. 13. The right without introducing audible distortion of the sound.part indicates the corresponding cumulative distributions This holds for music as well as for speech. The systemsresulting from the loudness versus time functions for realized in this area are strictly following this basicthe three conditions. Using the loudness exceeded in idea and, so far, mostly masking effects have been10% of the time as an indication of the perceived loud- taken into account. Since this particular area is well

ness, it can be expected that the speech is 1.2 times covered by other publications and this paper deals withlouder in the room with 0.6-s reverberation time and the fundamental ideas behind DAB, there is no need

about two times louder in the room with 2.5-s rever- to go into the technical details here. It should be men-beration compared with the loudness produced in the tioned, though, that in music the physical equivalentfree-field condition. This increment in loudness is often of spectral pitch percepts--which can be extracted byvery helpful for the intelligibility of speech in rooms a hearing-equivalent spectral analysis--can also beas long as the reverberation time does not produce tern- used as a tool to reduce the information flow drasticallyporal masking, which reduces the audibility of faint without making this reduction audible [14].consonants appearing in sequence to loud vowels. The specific-loudness versus critical-band-rate versus

124 I/ ' 8 room

2II held 4/

0_ 0 , J_.-250ms_-q _--250ms

time(a) (b)

Fig. 12. Specific-loudness versus time function of tone with 100% amplitude modulation. (a) in free-field condition. (b)played back in room.

20 -$one(OO) 100b,,e_.,_ , e'-e.,._ , , '

'Bo

g l0 TN=0.6S _ _ s0 ---

o- _§5

5 0 i , ,--0 0.5 1 2 3 5 10sone20I 2s I time totolloudness

Fig. 13. Effect of reverberation time on loudness-time functions (left) and on loudness distributions (right). Data obtained(a) in free-field condition and in rooms with reverberation times of (b) 0.6 s and (c) 2.5 s indicate increase of loudness withincreasing reverberation time. Adopted from [6].

124 J. Audio Eng. Soc., Vol. 39, No. 3, 1991 March

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time pattern produced by music or speech can be seen choakustischer Ph_inomene," Rundfunktech. Mitt., vol.on the screen incorporated in modern loudness meters. 30, no. 3, pp. 117-123 (1986).It is very interesting and impressive to listen to music [2] G. Stoll, M. Link, and G. Theile, Masking-Pat-or speech and at the same time look at this information tern Adapted Subband Coding: Use of the Dynamicflow indicated by the movement of this pattern. It il- Bit-Rate Margin," presented at the 84th Conventionlustrates very strongly what we have tried to convey of the Audio Engineering Society, J. Audio Eng. Soc.to the reader as the basic idea behind the data reduction (Abstracts), vol. 36, p. 382 (1988 May), preprint 2585.necessary for efficient DAB. [3] G. Stoll and Y. Dehery, "High Quality Audio

Bit-Rate Reduction System Family for Different Ap-

4 CONCLUSIONS plications," in Proc. IEEE ITC '90 (1990), pp. 937-941.

The specific-loudness versus critical-band-rate versus [4] E. Zwicker and R. Feldtkeller, Das Ohr als Nach-time pattern contains all the information that is used richtenempfiinger (Hirzel, Stuttgart, 1967).by our auditory system in order to produce the different [5] E. Zwicker, Psychoakustik (Springer, Berlin,hearing sensations. We propose not to transfer less 1982).information than contained in this pattern; however, [6] E. Zwicker and H. Fastl, Psychoacoustics: Factswe also do not need to transfer more than this infor- and Models (Springer, Berlin, 1990).mation. A reproduction accuracy of 1 dB in excitation [7] E. Zwicker and M. Zollner, Elektroakustiklevel, corresponding to a relative value of 7% in specific (Springer, Berlin, 1987).loudness, is sufficient for practical applications. [8] H. Fastl, "Dynamic Hearing Sensations: Facts

and Models," Trans. Comm. on Hearing ResearchA Personal Comment of E.Z. H-84-13, Acoust. Society of Japan, 1984.

In 1950 I had to solve the problem of why tape- [9] E. Zwicker, "The Inner Ear, a Sound Processingrecorded music was accepted differently if recorded and a Sound Emitting System," J. Acoust. Soc. Jpnand played back by different apparatus. The barely (E), vol. 9, pp. 59-74 (1988).noticeable amplitude and frequency modulation as a [10] ISO 532, "Acoustics--Method for Calculatingfunction of modulation frequency and level, as char- Loudness Level," International Organization for Stan-acteristics of the final receiver (our auditory system), dardization, Geneva, Switzerland, 1975.have led to the solution. Today, after having published [11] B. Bauer and E. L. Torick, "Researches inmore than 200 papers related to the field, I am prop- Loudness Measurements," IEEE Trans. Audio Elec-agating the same approach for a solution of the problems troacoust., vol. Au-14, no. 3, 1966.in modern electroacoustics and audio engineering, al- [12] B. L. Jones and E. L, Torick, "A New Loudnessthough at a somewhat higher level. It is obvious that Indicator for Use in Broadcasting," SMPTE (1981we have learned quite a bit during the last 40 years, Sept.).and I would like to thank all those who have contributed [13] H. Fastl, "Fluctuation Strength of Modulated

to that very much. Tones and Broadband Noise," in: R. Klinke and R.Hartmann Eds., Hearing--Physiological Bases and

5 REFERENCES Psychophysics (Springer, Berlin, 1989).[14] W. Heinbach, "Aurally Adequate Signal Rep-

[l] D. Krah6, "Ein Verfahren zur Datenreduktion resentation: The Part-Tone-Time-Pattern," Acustica,bei digitalen Audio-Signalen unter Ausnutzung psy- vol. 67, pp. 113-121 (1988).

THE AUTHORS

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E.Zwicker U.T,Zwicker

Eberhard Zwicker was born in Ohringen, Germany, at the Technical University Stuttgart from 1946 to 1950.in 1924. He studied physics at the University Tiibingen He received a doctor-engineer degree in electroacoustics(1945/46), and electrical engineering (communications) in 1952. That year, as scientific assistant with Professor

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ZWICKERANDZWICKER PAPERS

Dr.R. Feldtkeller at the Technical University Stuttgart awards, Bundesverdienstkreuz am Bande des Ver-(TUS), he began a career of teaching and research. He dienstordens der Bundesrepublik Deutschland, the Karl-spent one year as a researcher at the Harvard University Ktipfmiiller-Ehrenring from the Technical UniversityPsychoacoustics Laboratories, Cambridge, MA (1956/ Darmstadt, and the Preis der H6rger_te-Akustiker.57), as associate professor at the TUS (1957/61), lec- In 1990 October Professor Zwicker retired from histuring with Dr. J. Zwislocki at Syracuse University duties as Director of the Institute of ElectroacousticsBio-Acoustic-Laboratory, Syracuse, NY, with visits at the Technical University Munich. A little more thanto numerous colleges in the USA at the invitation of a month later, on November 22, he died of cancer atthe American Institute of Physics (1961/62); extraor- his home in Icking, Germany. In 1991 February, thedinary professor at TUS (1962/67); research at Bell AES Gold Medal was awarded to him posthumously.Telephone Labs, Murray Hill, NJ (1964); and as Pro- Professor Zwicker's obituary appears in In Memoriamfessor and Director of the Institute of Electroacoustics, in the 1991 March issue of the AES Journal.

Technical University Munich (1967/90). ·During those years, Professor Zwicker was also a

member of the Kuratorium der Technisch-Physikal- Ulrich Tilmann Zwicker was born in Stuttgart, Ger-ischen Bundesanstalt (1970/76), Speaker of the special many, in 1955. He studied physics and electrical en-research group Cybernetics sponsored by the Deutsche gineering at the Technical University Munich (TUM)Forschungsgemeinschaft (1971/77), Dean of the Faculty from which he received a bachelor's degree specializingof Electrical Engineering at the Technical University in communications engineering, electroacoustics, andof Munich (1977/79), Speaker of the special research psychoacoustics in 1978, and a master's degree in 1981,group Hearing sponsored by the Deutsche Forschungs- After graduating, Dr. Zwicker became a researchgemeinschaft (1983/90), and did research and lecturing associate at the Institute of Electroacoustics (TUM) inthroughout the world including the USA, Great Britain, the area of acoustics, electroacoustics, psychoacoustics,Japan, France, Switzerland, The Netherlands, Belgium, acoustical measurements, and audio. In 1983 he becameSpain, Poland, Czechoslovakia, Hungary, Italy, Aus- assistant professor at the Institute of Instrumentationtria, and Argentina. (TUM)where his research moved into the field of high-

Professor Zwicker's committee activity in the field frequency/solid-state acoustics, instrumentation, andof acoustics started in 1955 as a member of the German control. In addition to administrative tasks, his workDIN standardization committees on Acoustic Mea- included teaching instrumentation with associated lab-surements, Loudness and Noise Measurements, and oratory courses, and cooperative projects with SiemensElectronic Filters. In 1958 he became a member of AG, Mercedes-Benz AG, and the 1st Institute of Me-

ISO TC 43/working group Loudness From Objective trology, Beijing, China. In 1988 he received the Dr.-Analysis, and was the German delegate to ISO meetings Ing. degree with a dissertation in instrumentation.in Stockholm (1958), Rapallo (1960), Helsinki (1961), In 1989, Dr. Zwicker continued his research in theand Baden-Baden (1962). In 1959 he was secretary of area of psychoacoustics and acoustics as visiting re-the 3rd Congress of the International Commission on search associate to the Department of Audiology andAcoustics in Stuttgart. He became international cor- Department of Electrical and Computer Engineeringrespondent of the Committee of Hearing and Bio- at Northeastern University, Boston, MA; the Physics/acoustics (CHABA) in 1963, a member of the Inter- Astronomy Department of Michigan State University,national Commission on Acoustics from 1966 to 1972, East Lansing, MI; and the Department of Neurophys_and in 1984 was corresponding member of the Institute iology of the University of Wisconsin Medical School,of Noise Control Engineering. Madison, WI. He became an associate professor at the

In 1956, Professor Zwicker was awarded the venia Institute of Electroacoustics (TUM) in 1990 doing re-legendi in electroacoustics by the Nachrichtentechnische search in binaural hearing. In 1990 September, he joinedGesellschaft. He received a Fellowship from the the European Patent Office, in Munich, as a patentAcoustical Society of America in 1962, and, in 1987, examiner doing substantive examination.he was awarded that society's Silver Medal. In 1982 Dr. Zwicker has published extensively and has givenhe was made an Honorary Member of the Audio En- numerous invited and contributed lectures in his fieldgineering Society, and in 1988 he received the following of interest. He is a member of the AES.

126 J. AudioEng.Soc.,Vol.39, No.3, 1991March