how much masking is informational masking?

How much masking is informational masking? Robed A. Lutfi

Department of Communicative Disorders and Waisman Center, University of Wisconsin, Madison, Wisconsin 53706

( Received 12 March 1990; accepted for publication 21 August 1990)

It is estimated that 22% of the masking observed in many traditional tone-in-noise detection experiments is due to uncertainty associated with trial-to-trial variation in the noise waveform.

PACS numbers: 43.66.Ba, 43.66.Fe,43.66.Dc [NFV]

INTRODUCTION

Tone-in-noise masking experiments have long served as a useful tool for measuring the limits of auditory frequency selectivity and temporal resolution. The general conclusion to be drawn from these measures is that tone detectability is largely determined by a small portion of noise energy falling within close spectral or temporal proximity to the tone (Fletcher, 1940; Green and Swets, 1966; Penner et al., 1973). The variations in threshold used to gauge selectivity are attributed to differences in the amount of this energetic masking. Another source of masking, not often discussed in these studies, is that resulting from the uncertainty associated with trial-to-trial variation in the noise waveform (cf. Pfafflin and Mathews, 1966). Pollack ( 1975 ) uses the term informational masking to describe this second type of masking. The effects of informational masking are well docu- mented for highly uncertain maskers. Watson et al. (1976) achieve high levels of uncertainty by embedding the signal tone in a sequence of tones with randomly varying frequen- cies. The amount of informational masking may exceed 40 dB in these conditions, even with masker energy far removed from the signal (Leek and Watson, 1984). Given the potential magnitude of these effects, it seems reasonable to ask how much informational masking might exist in more traditional experiments using noise. Ideally, some empirical estimate is sought. This could prove difficult, however, since no single experiment is likely to be representative of all noise- masking experiments. This paper takes an alternative approach in which an estimate is derived based on a theoretical analysis of many of the existing data.

I. THEORETICAL ANALYSIS

Let us begin with some definitions. Quiet threshold (QT in dB) is defined to be the threshold level of the signal in absence of noise. Masked threshold (MT in dB) is the threshold level of the signal in the presence of noise. We identify masked thresholds under two conditions. In the first, the signal and noise waveforms are known exactly, as is the case, for example, when the same signal and noise waveforms are played on all trials. This is often referred to as a minimal-uncertainty condition; however, we prefer to use the term stimulus-known-exactly (SKE). In the second condition, the listener is uncertain regarding the exact waveform played on each trial, but has some information regarding the statistical structure of possible waveforms. In this

case, we say that the stimulus is known statistically (SKS). Clearly, most traditional tone-in-noise masking experiments are SKS experiments. We are now in a position to define precisely what is meant by energetic and informational masking. Masking is presumed to be purely energetic when there is no uncertainty regarding the stimulus waveforms played from trial to trial. In other words, the amount of energetic masking is the threshold elevation caused by the noise in SKE conditions:

E = MTsi• -- QT. ( 1 )

Informational masking is defined to be the additional threshold elevation that results when stimulus uncertainty is introduced. The amount of informational masking is given by

I = MTsi•s -- MTsi•. (2)

These definitions are consistent with common usage in the literature; however, neither describes the amount of masking typically reported in tone-in-noise masking experiments. Most traditional tone-in-noise masking experiments fall in the category of SKS experiments, so the quantity most often reported as the amount of masking is

X = MTsKs -- QT. (3)

Combining Eqs. ( 1 )-(3) yields

X=E+I. (4)

Now, in interpreting the results of traditional tone-in-noise masking experiments, it is frequently assumed that X = E; the effect of waveform uncertainty is often ignored or is con- sidered negligible in these experiments. But, this is the ques- tion we wish to consider. How much of X is I ?

To proceed, we need one further definition. The potential information (uncertainty) in a Gaussian noise is given by Shannon ( 1948):

H= K1 Wlog( 1 + N/Ne ), (5)

where K1 establishes the unit of information, N is average noise power, W is the bandwidth of the noise measurement device, and Ne is normal error introduced by this device. In the present application, the measurement device is the human observer, so Ne may be identified as an average noise variance inherent to the human observer. Also, we are only interested in the bandwidth over which the noise is actually effective in masking the tone. Denoting this value W', the effective masker information is given by

H' = K 1 W' log ( 1 + N/Ne ). (6)

2607 J. Acoust. Soc. Am. 88 (6), December 1990 0001-4966/90/122607-04500.80 @ 1990 Acoustical Society of America 2607

Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 146.189.194.69 On: Sat, 20 Dec 2014 08:42:51

Now, we suspect that informational masking I is related to the effective information in the noise masker H', but how is this relation to be described? An assumption is required relating threshold power for the signal S to noise power N for the special case in which X = I. We assume that S is related to N by a weak version of Weber's law. Specifically,

S= K2 (N + Ne ), (7)

where K 2 is a constant. Combining Eqs. (6) and (7) yields

H' = K• W' log(S/K2N e). (8)

Now note that K2 Ne corresponds to quiet threshold for the signal in power units; that is, $ -- K2 Ne when N = 0 in Eq. (7). By definition, then, 10 log (S/g 2 N e ) is the amount of masking X expressed relative to quiet threshold. It follows, moreover, that, for X = I, H' is just the amount of masking in dB:

H' =X, (9)

with an appropriate selection of unit Kl, K 1 IV': 10. Equation (8) requires one assumption relating thresh-

old to effective noise power, that given by Eq. (7). The assumption merely identifies the observer as an energy detec- tor, as does the more familiar energy detection model of masking ( Green and Swets, 1966). In practice then, it makes little difference whether the amount masking is expressed in units of energy, as in Eq. (3), or units of information, as in Eq. (8). The predictions are the same in both cases. There is, however, one exception to this statement. This is when two or more maskers are combined. Where maskers are com-

bined, we must consider whether the effects of the maskers add as energy or as information. If a and b are energetic maskers (X = E), the individual amounts of masking produced by a and b should add as energy. The combined masking is predicted to be 1

X•o = 10 log( 10 xa/lø -Jr- 10 xø/lø -- 1 ). (10)

If a and b are informational maskers (X = I), X, and Xb should add as information. The combined masking is

X,•,--H; +H•, =X, +Xo. (11)

Figure 1 summarizes the results of a variety of noise masking studies in which two maskers, producing equivalent amounts of masking in isolation, are combined. The figure includes all published studies known to the author in which at least one of the maskers (or the signal) was a noise, and in which the maskers were equated in effectiveness before being combined. The dashed lines represent the predictions of Eqs. (10) and (11). Nearly all of the data fall somewhere in between these two predictions.

The failure of Eqs. (10) and ( 11 ) is anticipated. Realis- tically, any noise masker has the potential simultaneously to produce both informational as well as energetic masking. Assume for the moment that the amount of informational

masking is a constant proportion œ of the total amount of masking, I = pX. Later, we will relax this restriction. The respective amounts of energetic and informational masking are assumed to add as before:

X,o = 10 log(10 e"/•ø + 10 eø/•ø-- 1) + I, + It,, (12)

so that, for X, = Xo,

D o

I

Iniormatxon /

ß

ß / - Green (1967) , . oo o

_ / / - Hanna et al. (1982) _

/ .. = . x - Jesteadt & W•IRe (1982) •' ß ß / - Lutf• (1983,1988)

/l .: o x x - Moore (1985)

- • •'•,,/ - N.'' & Jesteadt (1983) - g'•' - Nelson (1979) ./_• ../ - Patterson &

N•mmo-Sm•th (t98e) - - •. o ./ ß /

ß =•:•/. - Penner (1980)

.• - Penner & Sh•r•n (1980) • - Robinson & Poll•cR (1973) - - W•lson & Carhart (1971)

I I I I I I I I 10 20 30 40 50 60 70 80

Amount Moskxng A, dB

FIG. 1. Summary of the results of experiments in which signal thresholds were obtained in the combined presence of two equally effective maskers, a and b. The simultaneous masker combinations include a broadband noise

and a tone at the same frequency as the signal (Green, !967), a narrow- band noise and a tone at the same frequency as the signal (Neff and Jesteadt, 1983), a tone and a narrow band of noise above and below the signal frequency (Lutfi, 1983 ), two narrow bands of noise on either side of the signal (Lutfi, 1988), two narrow bands of noise both below or both above the signal frequency (Moore, 1985), two tones as maskers and a narrow band of noise as signal (Nelson, 1979), and two wide bands of noise placed asym- metrically around the signal frequency (Patterson and Nimmo-Smith, 1980). The nonsimultaneous combinations include various pairs of forward, and forward and backward noise maskers masking a click (Hanna et al., 1982; Penner, 1980; Penner and Shiffrin, 1980; Robinson and Pollack, 1973). In the study by Jesteadt and Wilke (1973), the two maskers were a simultaneous broadband noise and a forward masking tone of the same frequency as the signal. Where quiet thresholds were not reported in these studies, they were estimated so that the data could be plotted as amounts of masking.

X,o = 10 log(2X 10 (1 --p)Xa/10 __ 1) + 2pX,. (13)

The solid curve drawn through the data of Fig. 2 represents the prediction of Eq. (13), withœ estimated according to the least-squares criterion. The best-fitting value ofp is 0.22. We conclude that roughly 22% of the masking obtained in these studies is due to uncertainty regarding the waveform played on each trial.

II. DISCUSSION

The idea that masking is related to masker information is not new (Pollack, 1975; Spiegel et al., 1981; Watson et al., 1976). As yet, however, no attempt has been made to derive a metric of information that would allow more than ordinal

comparisons between the two. We have shown that the weak version of Weber's law yields a scalar relationship in which the effective masker information is proportional to the amount of masking in dB. A similar informational analysis has been applied to data from tone and noise intensity discrimination experiments (Norwich, 1981; Durlach and Braida, 1969). What evidence is there that informational

2608 J. Acoust. Sac. Am., Vol. 88, No. 6, December 1990 Robert A. Lutfi: Informational masking 2608


- / P•r(•l

ß

10 20 30 40 50 60 70

Amount Nosl,(•ng A, dB

I 8O

FIG. 2. Same as Fig. 1, except the prediction of Eq. (13) is shown. The prediction corresponds to 22% informational masking.

factors actually play a role in noise-masking experiments? Pfafflin (1968) and Pfafflin and Mathews (1966) offer perhaps the most direct evidence. These investigators reduced waveform uncertainty by presenting a single "frozen" noise sample throughout a trial block. In this condition the frozen noise waveform produced significantly less masking than when it was mixed with randomly selected noise samples within a trial block. It has also been shown that a reduction

of masker uncertainty can cause the effects of two maskers to add as energy. Masker uncertainty in this case is reduced by playing the same masker waveform on each trial (Lutfi, 1986; cf. Widin and Viemeister, 1980) by providing a lengthy masker fringe (Lutfi, 1986) or by using maskers with comodulated waveform envelopes (Moore, 1985). These latter studies offer perhaps the strongest evidence to implicate informational masking as a factor underlying the nonadditivity of masking seen in Fig. 1. Previous attempts to account for the data of Fig. 1 have taken a very different approach to that described in this paper (Penner, 1980; Pen- ner and Shiffrin, 1980; Lutfi 1983; Humes and Jesteadt, 1989). The basic assumption of these models is that acoustic inputs separately undergo some compressive nonlinear transform (presumably at some peripheral stage of auditory processing) before they are combined. Because the compression is applied separately to each input, the combined effect of inputs is actually expansive, in particular for two equated maskers XaO = inv F(2 )Xa, where Fis the compression. It is easy to see how such a nonlinear transform might separately apply in the case of sequential maskers, particularly if the nonlinearity is memoryless (Penner, 1980; Penner and Shif- frin, 1980). However, it remains a problem for these models to specify how the nonlinearity might separately apply in the case of simultaneous maskers (Lutfi, 1985; Humes and Jes- teadt, 1989). An advantage of the informational analysis is that it does not require an artificial distinction between simultaneous and nonsimultaneous masking. The fact that

two or more maskers mask a common signal is interpreted to mean that there will always be some effective overlap of maskers. The degree of this effective overlap is taken to re- flect the amount mutual information or perceptual redun- dancy between maskers. 2

The present narrative is intentionally oversimplified. For instance, we have provided a single estimate, but it is almost certain that the relative amount of informational

masking varies from one experiment to the next. The data of Fig. 1 are indicative. Note that, for low levels of masking the prediction of Eq. ( 13 ) tends to underestimate the amount of combined masking; at high levels, it tends to overestimate. Most of the data at low masking levels come from experiments using nonsimultaneous (sequential) maskers, where- as all of the data at high masking levels come from experiments using simultaneous maskers. The fit to the data improves when these two sets of data are analyzed separately. 3 Relaxing the constant p assumption may also be neces- sary when maskers a and b individually produce unequal amounts of masking (Hanna et al., 1982; Jesteadt and Wilke, 1982; Patterson and Nimmo-Smith, 1980; Wilson and Carhart, 1971 ). In these cases the appropriate form of Eq. (13) is

Xab = 10 log( 10 (1 --p)Xa/10 + 10•l--q)Xb/10 __ 1 )

q- pXa q- qXb , (14)

wherep and q are now the respective proportions of informational masking produced by a and b. Though a complete description is beyond the scope of this paper, we have applied Eq. (14) in cases of unequal masking with some suc- cess.

Finally, it should be emphasized that not all combined masking data are, or can be expected to be, consistent with an informational analysis. There are conditions, for instance, in which simple energy summation is achieved for maskers that would be expected to produce partial informational masking (Neff and Jesteadt, 1983 ). There are equally conditions in which combined masking in excess of the energy sum has been obtained for maskers that would not be expected to produce informational masking (Widin and Vie- meister, 1980). Clearly, there are many factors that may determine masked threshold in any given experiment; these are far too complex to be described by any one simple analysis, such as that given here. The present analysis might only serve to suggest that informational masking is an important factor among those that influence noise-masked thresholds.

ACKNOWLEDGMENTS

I would like to thank Dr. Charles S. Watson and Dr.

Donald E. Robinson for useful discussions during the writ- ing phase. Dr. David M. Green and an anonymous reviewer provided helpful comments on an earlier version of this manuscript. The work was supported by grants from the Air Force Office of Scientific Research and the Office of Naval

Research.

Note that, since X, and X0 represent two independently obtained threshold estimates, the amount of masking in quiet must be subtracted once from the sum.

2609 J. Acoust. Soc. Am., Vol. 88, No. 6, December 1990 Robert A. Lutfi: Informational masking 2609


This analysis provides an interpretation of a seemingly paradoxical result regarding the combined effects of maskers. The amount of masking is more than doubled when two equated maskers are combined; however, the doubling of power in any one masker does not produce this effect. In the latter case, the single masker is redundant with itself; the change in effective information is given by doubling N' in Eq. (6). In this case, p = 0 and Eq. (13) reduces to the equation for simple energy summation.

3The resultant estimates of p for simultaneous and nonsimultaneous maskers are 0.35 and 0.18, respectively.

Durlach, N. I., and Braida, L. D. (1969). "Intensity perception. I. Prelimi- nary theory of intensity resolution," J. Acoust. Soc. Am. 46, 372-383.

Fletcher, H. (1940). "Auditory patterns," Rev. Mod. Phys. 12, 47-65. Green, D. M. (1967). "Additivity of masking," J. Acoust. Soc. Am. 41,

1517-1525.

Green, D. M., and Swets, J. A. (1966). SignalDetection Theory and Psycho- physics (Wiley, New York).

Hanna, T. E., Robinson, D. E., Shiffrin, R. M., and Gilkey, R. H. (1982). "Forward masking ofdiotic and dichotic clicks by noise," J. Acoust. Soc. Am. 72, 1171-1177.

Humes, L. E., and Jesteadt, W. (1989). "Models of the additivity of masking," J. Acoust. Soc. Am. 85, 1285-1294.

Jesteadt, W., and Wilke, S. (1982). "Interaction of simultaneous and forward masking," J. Acoust. Soc. Am. Suppl. 1 71, S72.

Leek, M. R., and Watson, C. S. (1984). "Learning to detect auditory pat- tern components," J. Acoust. Soc. Am. 76, 1037-1044.

Lutfi, R. A. (1983). "Additivity of simultaneous masking," J. Acoust. Soc. Am. 73, 262-267.

Lutfi, R. A. ( 1985 ). "A power-law transformation predicting masking by sounds with complex spectra," J. Acoust. Soc. Am. 77, 2128-2135.

Lutfi, R. A. (1986). "Two- versus four-tone masking, revisited," J. Acoust. Soc. Am. 80, 422-428.

Lutfi, R. A. (1988). "Complex interactions between pairs of forward maskers," Hear. Res. 35, 71-78.

Moore, B.C. J. (1985). "Additivity of simultaneous masking, revisited," J. Acoust. Soc. Am. 78, 488-494.

Neff, D. L., and Jesteadt, W. (1983). "Additivity of forward masking," J.

Acoust. Soc. Am. 74, 1695-1701. Nelson, D. A. (1979). "Two-tone masking auditory critical bands," Audio-

logy 18, 279-301. Norwich, K. H. (1981). "The magical number seven: Making a 'bit' of

'sense,' "Percept. Psychophys. 29, 409-422. Patterson, R. D., and Nimmo-Smith, I. (1980). "Off-frequency listening

and auditory filter asymmetry," J. Acoust. Soc. Am. 67, 229-246. Penner, M. J. (1980). "The coding of intensity and the interaction of for-

ward and backward masking," J. Acoust. Soc. Am. 67, 608-616. Penner, M. J., Robinson, C. E., and Green, D. M. (1973). "The critical

masking interval," J. Acoust. Soc. Am. 53, 1661-1668. Penner, M. J., and Shiffrin, R. M. (1980). "Nonlinearities in the coding of

intensity within She context of a temporal summation model," J. Acoust. Soc. Am. 67, 617-627.

Pfafflin, S. M. (1968). "Detection of auditory signal in restricted sets of reproducible noise," J. Acoust. Soc. Am. 43, 487-490.

Pfafflin, S. M., and Mathews, M. V. (1966). "Detection of auditory signals in reproducible noise," J. Acoust. Soc. Am. 39, 340-345.

Pollack, I. (1975). "Auditory informational masking," J. Acoust. Soc. Am. Suppl. 1 $7, S5.

Robinson, C. E., and Pollack, I. (1973). "Interaction between forward and backward masking: A measure of the integration period of the auditory system," J. Acoust. Soc. Am. $3, 13!3-1316.

Shannon, C. E. (1948). "A mathematical theory of communication, Part III: Mathematical preliminaries," Bell System Tech. J. 27, 639.

Spiegel, M. F., Picardi, M. C., and Green, D. M. (1981). "Signal and masker uncertainty in intensity discrimination," J. Acoust. Soc. Am. 70, 1015- 1019.

Watson, C. S., Kelly, W. J., and Wroton, H. W. (1976). "Factors in the discrimination of tonal patterns II: Selective attention and learning under various levels of stimulus uncertainty," J. Acoust. Soc. Am. 60, 1176- 1186.

Widin, G. P., and Viemeister, N. F. (1980). "Masker interaction in pure- tone forward masking," J. Acoust. Soc. Am. 68, 475-477.

Wilson, R. H., and Carhart, R. (1971). "Forward and backward masking: Interactions and additivity," J. Acoust. Soc. Am. 49, 1254-1263.

2610 J. Acoust. Soc. Am., Vol. 88, No. 6, December 1990 Robert A. Lutfi: Informational masking 2610


how much masking is informational masking?

Documents