Effect of signal phase on the detectability of a tone masked by two tones* AlanR. Phipps t The Physiological Laboratory,CambridgeUniversity,CambridgeCB2 3EG, England
G. Bruce Henning The Departmentof ExperimentalPsychology, Oxford University,Oxford OX13 UD, England (Received24 November 1974; revised2 September1975) The maskingeffectof two pure tonesof equalintensity,startedin phase,on a third pure tone placed midway in frequencybetweenthem was studiedas a functionof the frequencyseparationof the maskers for two differentstartingphasesof the signal.At large separations (50 Hz or more), the signalphasehad no effecton its detectability,but when the separationwas smaller,the maskerswere lesseffectiveat maskinga signalwhich beganin 90* phasewith respectto the maskersthan one which beganin the same phase.These resultsare consideredin terms of the energy-detectormodel frequentlyusedto describe auditory processing;thoseat small separationsare found to be inconsistentwith sucha device.It is suggestedinsteadthat deviationsin the instantaneousfrequencyof the out-of-phasesignalplus maskers complexare responsible for the improvedperformancewith suchsignalswhen the bandwidthis small. SubjectClassification:[43] 65.58, [43] 65.60, [43] 65.75.
INTRODUCTION
The present experiment is an extension of experi-
mentsby Zwieker (1954)andby Green (1965) who related the results of pure-tone masking experiments to the
concept of critical bandwidth (Fletcher, 1940; Zwieker, Flottorp, and Stevens, 1957). In Zwicker's experiment, two continuous pure tones of equal amplitude were
used to mask a narrow
band of noise centered
in
frequency between the two tones. Zwicker found that, as long as the separation of the maskers was small, the detectability of the signal remained constant at different separations. For frequency separations above a certain value, however, the masking effect of the tones fell off rapidly with increasing separation. The critical frequency difference at 1 kHz was about 200 Hz, ap-
proximately the same as Zwicker's "critical bandwidth" at that frequency.
Green's experiment was similar to Zwicker's, except that his signal was a third sinusoid with a frequency halfway between the two maskers. Green determined the detectability of his signal at three center frequencies (250 Hz, 1 kHz, and 4 kHz) for different separations of the masker frequencies.
of the two tones into those arising in each of two spectral regions. He found that for maskers close together in frequency, the degree of masking depended on the
separation of the maskers, but not on the particular frequency region involved. Moreover, in this region, the amount of masking decreased slowly with the increasing masker separation, while above some frequency difference whose value did depend on the signal frequency, the masking effect fell off much more rapidly with. increasing separation of the maskers. Green interpreted his results in terms of an energy detector con-
sistingof a square-lawdevicefollowedby an integraa time
constant
of the order
of 100 msec.
With such a device, maskers close in frequency produce fluctuations in the output of the integrator that oh-
442
The present experiment sought more or less to repeat that of Green, while investigating the effect of signal phase on detectability.
I.
PROCEDURE
Two observers (the authors)were required to detect a 200-msec burst of a sinusoidal tone.
The signal had
a linear
A two-alterna-
J. Acoust.Soc.Am., Vol. 59, No. 2, February1976
rise
and fall
time
of 25 msec.
tive temporal forced-choice technique was used; the signal was presented with equal likelihood in one of two observation intervals in each trial, and the observers were required to indicate in a subsequent 750msec
answer
interval
which
of the two observation
in-
tervals had contained the signal. Each sequence of two obserx•ation intervals
and an answer interval
lasted
3
sec, and the trials were conducted in blocks of 50. The signal was masked by two tones gated in each interval
On the basis of his results, Green divided the effects
tor with
scure the signal. Above some critical value of frequency separation, the fluctuations have fallen below the level of noise inherent in the system so that the two maskers behave independently.
with
the same
25-msec
rise
and fall
time.
The
masking tones were separated in frequency by Af Hz, 1 and were positioned at exactly +•Af and--•Af from the signal. The value of Af varied from 5 to 1500 Hz, but the signal and two maskers were always harmonics of • ,f. Each masker had the same level (73 dB SPL) throughout the experiment; in addition, continuous white noise at a spectrum level of 14 dB, low-pass filtered at 8 or 9 kHz, was present. The maskers were in sine phase at their onset; the signal was either in
sine-phase or advancedby •/2 rad (90 o). For each observer, functions were obtained relating the percentage of correct responses in 200 trials to the level of the signal in each phase condition. In all, three different
signal frequencies were used (250 Hz, 1 kHz, and 4 kHz), but the 1-kHz region was the most thoroughly explored.
Copyright¸ 1976 by the Acoustical Societyof America
442
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
443
A.R. Phippsand G. B. Henning:Signalphasein tonal masking
To achieve precise, reproducible phase relations, the maskers and signal-plus-masker waveforms were generated using the Modular One computer at the M. R. C. 's Applied Psychology Unit in Cambridge. Values of the required waveforms were calculated at discrete intervals and stored in digital form; 4000 samples for each 200-msec observation interval were read out at the appropriate rate through the 10-bit
digital-to-analogue converter (DAC), giving a total dynamic range of approximately 60 dB. The output of the DAC was led through a suitable mixing network to two pairs of TDH-39 headphones driven in phase. II.
443
ß
i
I
/x
x• x
•o
?/
60
?
x
• /
o
x
,, , ,' i i
n- 80 x
•.
x
.a,,M,.,,
oskcrs_+2.5Hz
o
ß ObserverI ß Observer2
'
RESULTS
SignalI½v½1 relativeto maskcrI½v½1
Figures 1 and 2 show the psychometric functions for the detection of a 1-kHz signal centered between maskers 5 Hz apart. Data are shown for each observer for
each phase condition. Along the abscissa of each figure is plotted the level, in decibels, of the signal relative to each masker, while the ordinate shows the percentage of correct responses obtained in 50 trials. The
signal levels for 75%correct detectionover all observations are ip.dicated by arrows on the psychometric func-
FIG. 2. Psychometric function relating performance in a twointerval forced-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
which it lies midway in frequency. Arrows indicate 75% detection levels for each observer. Signal at i kHz; maskers at ñ 2.5 Hz from this. The signal started in 90ø phase relative to the two maskers. 0 riB--73 dB SPL. Observer I is ARP; observer
2 is GBH.
tions for each observer. Results
for
the two observers
are
in reasonable
agreement at this frequency, and it is clear that the signal is more readily detected when advanced by 90 o, i.e., when the maskers and signal together form a highly over-modulated quasi-frequency-modulated waveform, rather than a highly over-modulated amplitude-modulated
one.
in about a 12-dB range of signal level, though there is considerable variability in the slope of the function. No
systematicchangeis apparent,however. Therangeof slopes is similar to that found by Watson in simple detec-
tion experimentswithout external masking (Watson, Franks, and Hood, 1972). The curves for the two obsevers follow agenerally similar path, the notable exception
Results at other frequency separations show a similar form; for both the observers the detectability of
occurring when, with maskers at +/- 750 Hz from a
the signal falls from 100% correct to chance level of performance (50% correct) as the signal level is de-
the 75%levels. These data are shownin Figs. 3 and 4,
creased.
Typically,
this transition is complete
1-kHz signal, there is a discrepancy of some 9 dB in
which also illustrate the changes in slope of the psychometric functions. The discrepancy occurs in both phase conditions, and in Green's terms is perhaps best described in terms of a slightly different "break point" betweentwo sections of the masking function for our observer 2.
IOO
Maskcrs
+ 2.5 Hz IOO
1-KHz signal;0 ø ß Observer ß Observer
I 2
•
90
.,.,
80
-41.4dB
x•
'•'
o
o
75%----->
o
70 o
•
•/xO •-2'5 dB
50 i
-15
-12
-9
-6
i
-3
x
z
•.
i
Psychometric function relating performance in a two-
which it lies midway in frequency. Arrows indicate 75% de-
o x
,
-45
Signal level relative to maskcr I½v½1 FIG. 1.
50 1
0
interval forced-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
70
o
I-KHzsignal•0 ø ß Observer I ß Observer 2
-4:2 -39 -36 -33 -30 -27 SignalI½v½1 relativeto maskcr I½v½1 (dB)
-24 m-
FIG. 3. Psychometric function relating performance in a twointerval forced-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
which it lies midway in frequency. Arrows indicate 75% detection levels for each observer. Signa1 at I kHz; maskers at
tection levels for each observer. Signal at i kHz; maskers at ñ 2.5 Hz from this. The signal and maskers were in phase at onset. 0 dB=73 dB SPL. Observer I is ARP; observer 2 is
ñ 750 Hz from this. The signal and maskers were in phase at onset. 0 dB =73rib SPL. Observer I is ARP; observer 2 is
GBH.
GBH.
.
J. Acoust. Soc. Am., Vol. 59, No. 2, February 1976
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
444
A.R. Phippsand G. B. Henning:Signalphasein tonal masking
444
Figure 5 collects the results for all frequency separations with signal frequency 1 kHz, together with the averaged data from Green's Fig. 3. Along the abscissa
[]
is plotted the frequency separation between the maskers; the ordinate shows the signal level (in decibels relative
to each masker level) correspondingto 75%correct responses.
• • o
obs. 2 - o ø
=•
,, obs.2 - 90ø
•'•-•.
ß obs. • - 90ø
ß
obs. I - o ø
-20
_•
r'- • -30
In Fig. 5, the results for both our observers are included, with the mean of the data at 1 kHz from Green's three observers indicated by the unbroken line. This experiment and Green's were performed at approximately the same SPL (77 dB per masker for Green, 73
dB here); the chief difference between the experiments is that Green's
maskers
were
continuous
while
o • -40
--E
_• •o -so o
U3
1.0
ours
were gated on with the signal, which was 76 msec long-
er than Green's signal, and had a 25-msec rise/fall time, whereas Green's had one of 12 msec. There is quite a close correspondence between our data and those
of Green over much of the range of frequency separations; the results may be profitably compared.
Above a 50-Hz masker separation, both the data for 0 ø-phase and for 90 ø-phase advanced signals coincide with those of Green. At separations below 50 Hz, there
i
i
5'0
IO
._
2.0
i
20
i
i
i
50
IOO
200
i
5OO
i
IOOO 2000
Frequency separation of maskers(Hz) FIG. 5. The data for all values of Af showing theoretical standard errors (based on assumption of a binomial distribution of responses) as vertical lines where these are larger than the physical size of the data points. The ordinate shows the signal level required to achieve 75% detection versus the frequency separations between the maskers plotted along the abscissa. The smooth curve shows the average of Green's results using two sinusoidal maskers with the signal added in random phase.
The dotted line indicates Warren and Egan's prediction of the limit for detecting beats between sinusoidal tones of different intensities.
is a marked divergence between the data from the two
phase conditions: The 0 ø-phase data are approximately coincident with Green's curve, while our observers are more sensitive to the "advanced" signals. Adding the signal leading the maskers by 90 o in phase at time zero produced a more detectable change than adding a signal initially in the same phase as the maskers. The difference increases with decreasing masker separation a•d reaches the order of 12 dB at a separation of 5 Hz.
Similar results obtain with signals at 250 Hz, but not at 4 kHz, as Table I shows. In this table, the signal levels (in decibels relative to the masker levels) for 75% correct detections are shown as a function of the signal frequency for a masker separation of 5 Hz.
IOO
III.
DISCUSSION
The results of our experiment with 1-kHz signals are clearly very similar to the corresponding ones of Green over most of the range of frequency separation of the masking tones; the phase of the signal is irrelevant as long as the separation of the maskers is sufficiently large. There is, however, another important region within.which signal phase crucially affects the detectability of all but the highest frequency signals. The region is relatively small; it is confined to conditions in which the masking tones are less than 50-Hz apart.
Let us consider the model proposed by Green (1965), who hypothesized a detection mechanism capable of accounting for the results of his experiment; the device, a filter followed by a squaring device and a short-term integrator, constitutes the energy detector frequently used to model the behavior of the ear in detecting and
o•
90
n-
80
x
o
• 750lo• •
•
•o
•.
6o
?
50
discriminating signals (Pfaffiin and Mathews, 1962; Green and Swets, 1966). In Green's formulation, the time constant of the integrator (100 msec) allows the
o
o
device to be sensitive to fluctuations in the envelope of Maskcrs + 750 Hz
/ •m / x
c• • •
o
i_KHz signal: +90 o
o
ß Observer I ß Observer 2
o o
1-
-42
-39
-36
-33
-30
-27
-24
TABLE I.
A comparison of the levels of signal relative to the
maskers required for 75% detection where the signal was at different frequencies. case
The masker separation was in every
5 Hz.
Signallevelrelativeto maskcr I½v½1 (dB) Observer
FIG. 4. Psychometric function relating performance in a twointerval force-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
which it lies midway in frequency. Arrows indicate 75% detection levels for each observer. Signal at 1 kHz; maskers at + 750 Hz from this. The signal and maskers were in phase at onset. 0 dB=73 dB SPL. Observer 1 =ARP; observer 2 is
Signal Frequency (Uz) 250
i
Observer
Phase (radians) 0
v/2 - 2.5
-- 13.5
1000
- 2.5
4000
- 16.0
2
Phase (radi•ns) 0
v/2
- 4.0
- 12.0
-- 17.0
- 2.5
-- 13.0
-- 15.0
- 13.0
-- 13.0
GBH.
J. Acoust. Soc. Am., Vol. 59, No. 2, February 1976
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
445
A.R. Phippsand G. B. Henning:Signalphasein tonal masking
the masking waveform, provided that they are sufficiently slow. The rate of change of the masker envelope is proportional to the difference in frequency between the maskers. The fluctuations produced at the output of the integrator, whenever sufficiently large, are assumed to obscure the presence of the signal; the component of this output resulting from the masker interaction decreases with the increasing rate, and thus also with the increasing masker separation. The amplitude of the
masker interaction term (at frequency Af Hz)decreases at a rate which Green used to predict the behavior of his observers. Signal phase, however, does not affect the component of the integrator output crucial to Green's explanation. Our results indicate that signal phase is important and, consequently, that Green's explanation is wrong. Consider the three sinusoidal components of our stimuli, having frequencies of f•, fs and fh, and phases of 0, •, and 0 at onset, corresponding respectively to the frequency and phase of the lower-frequency masker, the signal, and the higher-frequency masker. The amplitude of each masker is nominally unity, while that of
the signal has some value a, less than 1. The waveform of the total stimulus is thus given by the equation,
y( t) = sin27rf , t + a sin(27rfst+ oh)+ sin27rf ht .
(1)
The output of a square-law device is a quantity proportional to the stimulus power of the complex wave, given by
445
where zxf/2 is the difference between the frequency of the signal and that of either masker. zero.
It is possible that the observers are detecting the signal by using the interaction between the signal and the maskers, which appears as beating or roughness when the signal is added. The case in which the signal is in
0 ø phase provides, after all, a highly overmodulated amplitude-modulated waveform, and that with the signal advanced by 00 ø a similarly overmodulated "quasifrequency modulated" one. The limits for detection based on such a beat-detector mechanism might be inferred from the relation of the detectability of beats to the frequency separation of the beating tones and their
relative amplitudes (Egan and Klumpp, 1051; Warren
and Egan, 1051). The dottedline in Fig. 5 showsthis prediction based on data obtained by Warren and Egan. The curve lies in a relation to our data which suggests that, were this explanation correct, the limiting frequency separation for the difference in detectability of the two cases would depend on the difference in amplitude of the signal and the maskers. However, the curve lies not far from our data points for the signaladvanced condition, in which the relevant interaction component is not produced at all! Thus the differences in performance cannot be attributed to temporal fluctuations in the output of Green's linear detection mechanism.
Let
three
terms
constitute
the "maskers
(2)
it is reasonable
sulting when the signal is added in the "QFM" tion is given by
alone"
condition when a = 0, but are present in all waveforms. Terms 1 and 2 show the power resulting from either masker alone; the third term is the component of the power of the simulus that results from the interaction of the masking tones to which Green attributes the particular effects of two maskers together. Similar interactions will also occur between the signal and each masker whenever the signal is added to the two-tone masking complex. These interactions, shown in the last two terms of the second equation, will produee components of half the frequency of the masker interaetion component and, moreover, of a magnitude that depends on the signal phase.
The low-frequency power components contributed by the signal-masker interactions are given by
to as-
=
+
condi-
cos'2(f/2)t]
x sin{2•rf, t- tan'•[rncos2•r(Af/2)t]}),
(5)
where, it will be remembered, zXfis the frequency separation of the maskers, f, is the signal frequency, rn is the depth of modulation, and k is chosen to keep the level of the sidebands (maskers) fixed while rn varies to determine the relative levels of the signal and maskers.
The amplitude-modulated case, in which the signal is added in the same initial phase as the maskers, produces a waveform given by
yAM(t)= k• 1+rnCOS27r(Af /2)t] sin2•rfst }.
(6)
Both the AM and QFM cases have a carrier frequency of fs and an amplitude modulation factor. That for
the AM ease, k[1 + rneos2•r(/xf/2)t],varies more widely thanthat for the QFM ease, k[1 + rn•'eos•'2•r(/Xf/2)t] •/•',
s(t)=a{cos ½[cos2rr(f• -fs)t +cos2rr(f s-f,) t]
+sin½[sin2•r(f•-fs)t+sin2•r(f, -f,)t]} .
whether
Ritsma and Engel (1064), we see that the stimulus re-
+a2sin•'(2•rfst + ½)+ 2a(sin2?rf•t)sin(2•rf, t + ½)
The first
us now consider
sume that our observers are detecting frequency changes in the phase-advanced stimulus. Following
= sin•'2•rft t + sin•'2•rfht + 2(sin2•rftt) (sin2•rfht)
+ 2a(sin27rf•t)sin(27rf•t+ qb).
On the other hand,
when½ is equal to •r/2, the contributionof this term is
(3)
except in the limiting ease as rn becomes very large, when the two factors are identical. This limiting case
This contribution clearly depends on signal phase
is our
which, in our experiments, was either 0 or •r/2. When
tor for the AM ease becomes negative periodically,
½ is 0, s(t) is given by
when rn is greater than 1, and thus produces instantaneous phase shifts of •r rad. The QFM amplitude factor
s(t)= 2a[cos2•r(/x f /2)t] ,
(4)
maskers
alone"
condition.
q'h•. modulation
does not produce a phase shift for any value of rn.
fac-
The
J. Acoust.Soc.Am., Vol. 59, No. 2, February1976 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
446
A.R. PhippsandG. B. Henning:Signalphasein tonal masking
QFM waveform does, however, in addition to the amplitude modulation factor, have a phase modulation term given by
q•(t)=-tan'lira COS27r(Af/2)t].
(7)
This term produces smooth periodic changes in the
carrier phase at a rate of Af/2 Hz. If q•(t) is not changing with time, or does so only very slowly, the stimulus has a fixed frequency fs and some
phase given by q•(t). If, on the other hand, q•(t) is changing rapidly,
frequency will be roughly approximated by a linear fre-
quency sweep from fs to a frequency determined by the maximum rate of change of q•(t)with time. The maximum rate of change of the phase of the stimulus is
27rm(Af/2), so that, as a crude approximation,the QFM producesa linear frequencysweepfrom fs Hz to + •(Af/2)] Hz andback again, followedby a sweepfrom fs Hz to Ifs- •(Af/2)] Hz andbackagaintofs Hz every 2/Af sec. Whether this frequency modulationis detected depends on the duration of the sweep. Sergeant and Harris (1962) and l•ollack (1968) have shown that the
"threshold" rate of change of frequency for unidirectional frequency sweeps is roughly inversely proportional to the duration of the sweep, for durations over 75 msec.
of the duration of the
sweeps in the QFM stimulus by noting that the inverse tangent in Eq. 7 changessignificantly only for arguments
of the functionwithin twounits of zero. At the pointwhere the masker separation Af is 10 Hz, the modulation factor • is 11; using the limits noted above and Eq. 7 we may determine that the range of modulation with a 10Hz masker separation and • = 11 is 55 Hz, and that this 55-Hz
excursion
takes
about
70 msec.
These
AM waveforms
at 4 kHz
the lower carrier
seems
so much better
than at
frequencies.
It should perhaps be noted, in passing, that the experiments that are described in Goldstein's 1967 paper also attack the problem of phase sensitivity, but from the other end of the continuum of modulation depth. In his experiments observers discriminate the just-noticeably modulated, amplitude-modulated, and quasifrequency-modulated sinusoids from carriers that are not modulated at all; our experiment, by contrast,
comparedthe detectabilityof very highlymodulated
then the stimulus will have an in-
stantaneous frequency different from rs. The change in
We can make a rough estimate
446
waveforms with the carrier-suppressed case. Goldstein found that the amplitude modulation was more detectable than the quasifrequency modulation--the reverse of our findings at the other extreme--and that the effect
was limited
than the critical Our
data
to stimuli
whose
bandwidth
was
less
bandwidth.
seem
to result
from
the interaction
of a
number of complex factors. For widely separated maskers the explanation offered by Green is appropriate, but for maskers no more than 50 Hz apart the presence of relatively long-lasting deviations of the instantaneous frequency of the waveform produced by
addingthe'signaladvanced by 90ø produces measurably better performance for which we can offer no simple explanation. ACKNOWLEDGMENTS
We should like to thank J. L. Goldstein, D. M. Green, R. J. Ritsma, J. Gi. Robson, and M. M. Taylor for their criticism of earlier versions of this paper. We are most grateful to the Director and Staff of the Applied l•sychology Unit for their gracious hospitality and tolerance.
values
imply a rate of changeof over 770 Hz/sec for 70 msec. The observers of Sergeant and Harris
detected a truly
linear sweep of 200 Hz/sec lasting 75 msec, so it seems
reasonable
that
our
observers
would
be able
Canahl, J. A. (1971). "Two- versus four-tone masking at 1000 Hz,"
to
detect the frequency modulation. On the other hand, as Af increases, the duration of the sweep falls proportionately; the rate of sweep, however, increases with the square of Af. Given the findings of l•ollack and of
SergeantandHarris thatthe"threshold"sweeprate is roughly inversely proportional to the duration of the sweep, it might be expected that the signal in the QFM condition would be relatively more detectable with increasing Af. This is not the case. A simpler interpretation would be to have the observers detecting the simple frequency change of 55 Hz; however, frequency discrimination is a strong function of the carrier frequency, so that we would expect much poorer performance with 4-kHz signals if the observers were detecting this simple frequency difference. This, is not the case.
J. Acoust.
masking in the measurement of aural harmonics by the method of best beats," J. Acoust. Soc. Am. 23, 275-286
Fletcher, H. (1940). "Auditory patterns," Rev. Mod. Phys. 12, 47-65.
Goldstein, J. L. (1967). "Auditory spectral filtering and monaural phase perception, "J.
tion with a QFM waveform for low values of Af at carrier frequencies below 4 kHz. This seems to be related to our finding no effect of signal phase with highfrequency signals, but we are unable to offer any convincing explanation for the fact that performance with
Acoust. Soc. Am. 41, 458-
479.
Green, D. M. (1965). "Masking with two tones," J. Acoust. Soc. Am. 37, 802-813.
Green, D. M.,
andSwets, J.A.
(1966).
Signal detection the-
ory and psychophysics(Wiley, New York). Pfafflin, S. M. and Mathews, M. V. (1962). "Energy detection model for monaural auditory detection," J. Acoust. Soc. Am.
34, 1842-1853.
Pollack, I. (1968). "Detectionof rate of changeof auditory frequency," J. Exp. Psychol. 77, 535-541.
Ritsma, R. J., and Engel, F. L. (1964). "Pitch of frequency modulated signals,"
Goldstein (1967) has reported audible pitch modula-
Soc. Am. 50, 471-474.
Egan, J. P., and Klumpp, R. G. (1951). "The error due to
J. Acoust. Soc. Am. 36, 1637-1644.
Sergeant, R. L., and Harris, J. D. (1962). "Sensitivity to unidirectional frequency modulation,"
J. Acoust. Soc. Am.
34, 1625-1628.
Warren, J. M., and Egan, J.P.
(1951). "On the accuracy of
the method of best beats for determining the intensity of a tone," J. Acoust. Soc. Am. 23, 111-113. Watson, C. S., Franks, J. R., and Hood, D.C. (1972).
J. Acoust.Soc.Am., Vol. 59, No. 2, February1976 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
447
,A. R. PhippsandG. B. Henning:Signalphasein tonal masking
"Detection of tones in the absence of external masking noise.
I.
Effects of signal intensity and signal frequency,"
Acoust.
Soc. Am.
J.
52, 633-643.
Zwicker, Eo (1954). "Die Verdeckung yon Schmallbandge-
447 r'•usch durch SinustJSne," Acustica 4, 415-420.
Zwicker, E., Flottorp, G., and Stevens, S.S. (1957). "Critical
band width in loudness summation,"
J. Acoust.
Soc. Am.
29, 548-557.
J. Acoust. Soc. Am., Vol. 59, No. 2, February 1976
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
G. Bruce Henning The Departmentof ExperimentalPsychology, Oxford University,Oxford OX13 UD, England (Received24 November 1974; revised2 September1975) The maskingeffectof two pure tonesof equalintensity,startedin phase,on a third pure tone placed midway in frequencybetweenthem was studiedas a functionof the frequencyseparationof the maskers for two differentstartingphasesof the signal.At large separations (50 Hz or more), the signalphasehad no effecton its detectability,but when the separationwas smaller,the maskerswere lesseffectiveat maskinga signalwhich beganin 90* phasewith respectto the maskersthan one which beganin the same phase.These resultsare consideredin terms of the energy-detectormodel frequentlyusedto describe auditory processing;thoseat small separationsare found to be inconsistentwith sucha device.It is suggestedinsteadthat deviationsin the instantaneousfrequencyof the out-of-phasesignalplus maskers complexare responsible for the improvedperformancewith suchsignalswhen the bandwidthis small. SubjectClassification:[43] 65.58, [43] 65.60, [43] 65.75.
INTRODUCTION
The present experiment is an extension of experi-
mentsby Zwieker (1954)andby Green (1965) who related the results of pure-tone masking experiments to the
concept of critical bandwidth (Fletcher, 1940; Zwieker, Flottorp, and Stevens, 1957). In Zwicker's experiment, two continuous pure tones of equal amplitude were
used to mask a narrow
band of noise centered
in
frequency between the two tones. Zwicker found that, as long as the separation of the maskers was small, the detectability of the signal remained constant at different separations. For frequency separations above a certain value, however, the masking effect of the tones fell off rapidly with increasing separation. The critical frequency difference at 1 kHz was about 200 Hz, ap-
proximately the same as Zwicker's "critical bandwidth" at that frequency.
Green's experiment was similar to Zwicker's, except that his signal was a third sinusoid with a frequency halfway between the two maskers. Green determined the detectability of his signal at three center frequencies (250 Hz, 1 kHz, and 4 kHz) for different separations of the masker frequencies.
of the two tones into those arising in each of two spectral regions. He found that for maskers close together in frequency, the degree of masking depended on the
separation of the maskers, but not on the particular frequency region involved. Moreover, in this region, the amount of masking decreased slowly with the increasing masker separation, while above some frequency difference whose value did depend on the signal frequency, the masking effect fell off much more rapidly with. increasing separation of the maskers. Green interpreted his results in terms of an energy detector con-
sistingof a square-lawdevicefollowedby an integraa time
constant
of the order
of 100 msec.
With such a device, maskers close in frequency produce fluctuations in the output of the integrator that oh-
442
The present experiment sought more or less to repeat that of Green, while investigating the effect of signal phase on detectability.
I.
PROCEDURE
Two observers (the authors)were required to detect a 200-msec burst of a sinusoidal tone.
The signal had
a linear
A two-alterna-
J. Acoust.Soc.Am., Vol. 59, No. 2, February1976
rise
and fall
time
of 25 msec.
tive temporal forced-choice technique was used; the signal was presented with equal likelihood in one of two observation intervals in each trial, and the observers were required to indicate in a subsequent 750msec
answer
interval
which
of the two observation
in-
tervals had contained the signal. Each sequence of two obserx•ation intervals
and an answer interval
lasted
3
sec, and the trials were conducted in blocks of 50. The signal was masked by two tones gated in each interval
On the basis of his results, Green divided the effects
tor with
scure the signal. Above some critical value of frequency separation, the fluctuations have fallen below the level of noise inherent in the system so that the two maskers behave independently.
with
the same
25-msec
rise
and fall
time.
The
masking tones were separated in frequency by Af Hz, 1 and were positioned at exactly +•Af and--•Af from the signal. The value of Af varied from 5 to 1500 Hz, but the signal and two maskers were always harmonics of • ,f. Each masker had the same level (73 dB SPL) throughout the experiment; in addition, continuous white noise at a spectrum level of 14 dB, low-pass filtered at 8 or 9 kHz, was present. The maskers were in sine phase at their onset; the signal was either in
sine-phase or advancedby •/2 rad (90 o). For each observer, functions were obtained relating the percentage of correct responses in 200 trials to the level of the signal in each phase condition. In all, three different
signal frequencies were used (250 Hz, 1 kHz, and 4 kHz), but the 1-kHz region was the most thoroughly explored.
Copyright¸ 1976 by the Acoustical Societyof America
442
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
443
A.R. Phippsand G. B. Henning:Signalphasein tonal masking
To achieve precise, reproducible phase relations, the maskers and signal-plus-masker waveforms were generated using the Modular One computer at the M. R. C. 's Applied Psychology Unit in Cambridge. Values of the required waveforms were calculated at discrete intervals and stored in digital form; 4000 samples for each 200-msec observation interval were read out at the appropriate rate through the 10-bit
digital-to-analogue converter (DAC), giving a total dynamic range of approximately 60 dB. The output of the DAC was led through a suitable mixing network to two pairs of TDH-39 headphones driven in phase. II.
443
ß
i
I
/x
x• x
•o
?/
60
?
x
• /
o
x
,, , ,' i i
n- 80 x
•.
x
.a,,M,.,,
oskcrs_+2.5Hz
o
ß ObserverI ß Observer2
'
RESULTS
SignalI½v½1 relativeto maskcrI½v½1
Figures 1 and 2 show the psychometric functions for the detection of a 1-kHz signal centered between maskers 5 Hz apart. Data are shown for each observer for
each phase condition. Along the abscissa of each figure is plotted the level, in decibels, of the signal relative to each masker, while the ordinate shows the percentage of correct responses obtained in 50 trials. The
signal levels for 75%correct detectionover all observations are ip.dicated by arrows on the psychometric func-
FIG. 2. Psychometric function relating performance in a twointerval forced-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
which it lies midway in frequency. Arrows indicate 75% detection levels for each observer. Signal at i kHz; maskers at ñ 2.5 Hz from this. The signal started in 90ø phase relative to the two maskers. 0 riB--73 dB SPL. Observer I is ARP; observer
2 is GBH.
tions for each observer. Results
for
the two observers
are
in reasonable
agreement at this frequency, and it is clear that the signal is more readily detected when advanced by 90 o, i.e., when the maskers and signal together form a highly over-modulated quasi-frequency-modulated waveform, rather than a highly over-modulated amplitude-modulated
one.
in about a 12-dB range of signal level, though there is considerable variability in the slope of the function. No
systematicchangeis apparent,however. Therangeof slopes is similar to that found by Watson in simple detec-
tion experimentswithout external masking (Watson, Franks, and Hood, 1972). The curves for the two obsevers follow agenerally similar path, the notable exception
Results at other frequency separations show a similar form; for both the observers the detectability of
occurring when, with maskers at +/- 750 Hz from a
the signal falls from 100% correct to chance level of performance (50% correct) as the signal level is de-
the 75%levels. These data are shownin Figs. 3 and 4,
creased.
Typically,
this transition is complete
1-kHz signal, there is a discrepancy of some 9 dB in
which also illustrate the changes in slope of the psychometric functions. The discrepancy occurs in both phase conditions, and in Green's terms is perhaps best described in terms of a slightly different "break point" betweentwo sections of the masking function for our observer 2.
IOO
Maskcrs
+ 2.5 Hz IOO
1-KHz signal;0 ø ß Observer ß Observer
I 2
•
90
.,.,
80
-41.4dB
x•
'•'
o
o
75%----->
o
70 o
•
•/xO •-2'5 dB
50 i
-15
-12
-9
-6
i
-3
x
z
•.
i
Psychometric function relating performance in a two-
which it lies midway in frequency. Arrows indicate 75% de-
o x
,
-45
Signal level relative to maskcr I½v½1 FIG. 1.
50 1
0
interval forced-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
70
o
I-KHzsignal•0 ø ß Observer I ß Observer 2
-4:2 -39 -36 -33 -30 -27 SignalI½v½1 relativeto maskcr I½v½1 (dB)
-24 m-
FIG. 3. Psychometric function relating performance in a twointerval forced-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
which it lies midway in frequency. Arrows indicate 75% detection levels for each observer. Signa1 at I kHz; maskers at
tection levels for each observer. Signal at i kHz; maskers at ñ 2.5 Hz from this. The signal and maskers were in phase at onset. 0 dB=73 dB SPL. Observer I is ARP; observer 2 is
ñ 750 Hz from this. The signal and maskers were in phase at onset. 0 dB =73rib SPL. Observer I is ARP; observer 2 is
GBH.
GBH.
.
J. Acoust. Soc. Am., Vol. 59, No. 2, February 1976
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
444
A.R. Phippsand G. B. Henning:Signalphasein tonal masking
444
Figure 5 collects the results for all frequency separations with signal frequency 1 kHz, together with the averaged data from Green's Fig. 3. Along the abscissa
[]
is plotted the frequency separation between the maskers; the ordinate shows the signal level (in decibels relative
to each masker level) correspondingto 75%correct responses.
• • o
obs. 2 - o ø
=•
,, obs.2 - 90ø
•'•-•.
ß obs. • - 90ø
ß
obs. I - o ø
-20
_•
r'- • -30
In Fig. 5, the results for both our observers are included, with the mean of the data at 1 kHz from Green's three observers indicated by the unbroken line. This experiment and Green's were performed at approximately the same SPL (77 dB per masker for Green, 73
dB here); the chief difference between the experiments is that Green's
maskers
were
continuous
while
o • -40
--E
_• •o -so o
U3
1.0
ours
were gated on with the signal, which was 76 msec long-
er than Green's signal, and had a 25-msec rise/fall time, whereas Green's had one of 12 msec. There is quite a close correspondence between our data and those
of Green over much of the range of frequency separations; the results may be profitably compared.
Above a 50-Hz masker separation, both the data for 0 ø-phase and for 90 ø-phase advanced signals coincide with those of Green. At separations below 50 Hz, there
i
i
5'0
IO
._
2.0
i
20
i
i
i
50
IOO
200
i
5OO
i
IOOO 2000
Frequency separation of maskers(Hz) FIG. 5. The data for all values of Af showing theoretical standard errors (based on assumption of a binomial distribution of responses) as vertical lines where these are larger than the physical size of the data points. The ordinate shows the signal level required to achieve 75% detection versus the frequency separations between the maskers plotted along the abscissa. The smooth curve shows the average of Green's results using two sinusoidal maskers with the signal added in random phase.
The dotted line indicates Warren and Egan's prediction of the limit for detecting beats between sinusoidal tones of different intensities.
is a marked divergence between the data from the two
phase conditions: The 0 ø-phase data are approximately coincident with Green's curve, while our observers are more sensitive to the "advanced" signals. Adding the signal leading the maskers by 90 o in phase at time zero produced a more detectable change than adding a signal initially in the same phase as the maskers. The difference increases with decreasing masker separation a•d reaches the order of 12 dB at a separation of 5 Hz.
Similar results obtain with signals at 250 Hz, but not at 4 kHz, as Table I shows. In this table, the signal levels (in decibels relative to the masker levels) for 75% correct detections are shown as a function of the signal frequency for a masker separation of 5 Hz.
IOO
III.
DISCUSSION
The results of our experiment with 1-kHz signals are clearly very similar to the corresponding ones of Green over most of the range of frequency separation of the masking tones; the phase of the signal is irrelevant as long as the separation of the maskers is sufficiently large. There is, however, another important region within.which signal phase crucially affects the detectability of all but the highest frequency signals. The region is relatively small; it is confined to conditions in which the masking tones are less than 50-Hz apart.
Let us consider the model proposed by Green (1965), who hypothesized a detection mechanism capable of accounting for the results of his experiment; the device, a filter followed by a squaring device and a short-term integrator, constitutes the energy detector frequently used to model the behavior of the ear in detecting and
o•
90
n-
80
x
o
• 750lo• •
•
•o
•.
6o
?
50
discriminating signals (Pfaffiin and Mathews, 1962; Green and Swets, 1966). In Green's formulation, the time constant of the integrator (100 msec) allows the
o
o
device to be sensitive to fluctuations in the envelope of Maskcrs + 750 Hz
/ •m / x
c• • •
o
i_KHz signal: +90 o
o
ß Observer I ß Observer 2
o o
1-
-42
-39
-36
-33
-30
-27
-24
TABLE I.
A comparison of the levels of signal relative to the
maskers required for 75% detection where the signal was at different frequencies. case
The masker separation was in every
5 Hz.
Signallevelrelativeto maskcr I½v½1 (dB) Observer
FIG. 4. Psychometric function relating performance in a twointerval force-choice detection experiment to the level of a sinusoidal signal relative to two sinusoidal maskers, between
which it lies midway in frequency. Arrows indicate 75% detection levels for each observer. Signal at 1 kHz; maskers at + 750 Hz from this. The signal and maskers were in phase at onset. 0 dB=73 dB SPL. Observer 1 =ARP; observer 2 is
Signal Frequency (Uz) 250
i
Observer
Phase (radians) 0
v/2 - 2.5
-- 13.5
1000
- 2.5
4000
- 16.0
2
Phase (radi•ns) 0
v/2
- 4.0
- 12.0
-- 17.0
- 2.5
-- 13.0
-- 15.0
- 13.0
-- 13.0
GBH.
J. Acoust. Soc. Am., Vol. 59, No. 2, February 1976
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
445
A.R. Phippsand G. B. Henning:Signalphasein tonal masking
the masking waveform, provided that they are sufficiently slow. The rate of change of the masker envelope is proportional to the difference in frequency between the maskers. The fluctuations produced at the output of the integrator, whenever sufficiently large, are assumed to obscure the presence of the signal; the component of this output resulting from the masker interaction decreases with the increasing rate, and thus also with the increasing masker separation. The amplitude of the
masker interaction term (at frequency Af Hz)decreases at a rate which Green used to predict the behavior of his observers. Signal phase, however, does not affect the component of the integrator output crucial to Green's explanation. Our results indicate that signal phase is important and, consequently, that Green's explanation is wrong. Consider the three sinusoidal components of our stimuli, having frequencies of f•, fs and fh, and phases of 0, •, and 0 at onset, corresponding respectively to the frequency and phase of the lower-frequency masker, the signal, and the higher-frequency masker. The amplitude of each masker is nominally unity, while that of
the signal has some value a, less than 1. The waveform of the total stimulus is thus given by the equation,
y( t) = sin27rf , t + a sin(27rfst+ oh)+ sin27rf ht .
(1)
The output of a square-law device is a quantity proportional to the stimulus power of the complex wave, given by
445
where zxf/2 is the difference between the frequency of the signal and that of either masker. zero.
It is possible that the observers are detecting the signal by using the interaction between the signal and the maskers, which appears as beating or roughness when the signal is added. The case in which the signal is in
0 ø phase provides, after all, a highly overmodulated amplitude-modulated waveform, and that with the signal advanced by 00 ø a similarly overmodulated "quasifrequency modulated" one. The limits for detection based on such a beat-detector mechanism might be inferred from the relation of the detectability of beats to the frequency separation of the beating tones and their
relative amplitudes (Egan and Klumpp, 1051; Warren
and Egan, 1051). The dottedline in Fig. 5 showsthis prediction based on data obtained by Warren and Egan. The curve lies in a relation to our data which suggests that, were this explanation correct, the limiting frequency separation for the difference in detectability of the two cases would depend on the difference in amplitude of the signal and the maskers. However, the curve lies not far from our data points for the signaladvanced condition, in which the relevant interaction component is not produced at all! Thus the differences in performance cannot be attributed to temporal fluctuations in the output of Green's linear detection mechanism.
Let
three
terms
constitute
the "maskers
(2)
it is reasonable
sulting when the signal is added in the "QFM" tion is given by
alone"
condition when a = 0, but are present in all waveforms. Terms 1 and 2 show the power resulting from either masker alone; the third term is the component of the power of the simulus that results from the interaction of the masking tones to which Green attributes the particular effects of two maskers together. Similar interactions will also occur between the signal and each masker whenever the signal is added to the two-tone masking complex. These interactions, shown in the last two terms of the second equation, will produee components of half the frequency of the masker interaetion component and, moreover, of a magnitude that depends on the signal phase.
The low-frequency power components contributed by the signal-masker interactions are given by
to as-
=
+
condi-
cos'2(f/2)t]
x sin{2•rf, t- tan'•[rncos2•r(Af/2)t]}),
(5)
where, it will be remembered, zXfis the frequency separation of the maskers, f, is the signal frequency, rn is the depth of modulation, and k is chosen to keep the level of the sidebands (maskers) fixed while rn varies to determine the relative levels of the signal and maskers.
The amplitude-modulated case, in which the signal is added in the same initial phase as the maskers, produces a waveform given by
yAM(t)= k• 1+rnCOS27r(Af /2)t] sin2•rfst }.
(6)
Both the AM and QFM cases have a carrier frequency of fs and an amplitude modulation factor. That for
the AM ease, k[1 + rneos2•r(/xf/2)t],varies more widely thanthat for the QFM ease, k[1 + rn•'eos•'2•r(/Xf/2)t] •/•',
s(t)=a{cos ½[cos2rr(f• -fs)t +cos2rr(f s-f,) t]
+sin½[sin2•r(f•-fs)t+sin2•r(f, -f,)t]} .
whether
Ritsma and Engel (1064), we see that the stimulus re-
+a2sin•'(2•rfst + ½)+ 2a(sin2?rf•t)sin(2•rf, t + ½)
The first
us now consider
sume that our observers are detecting frequency changes in the phase-advanced stimulus. Following
= sin•'2•rft t + sin•'2•rfht + 2(sin2•rftt) (sin2•rfht)
+ 2a(sin27rf•t)sin(27rf•t+ qb).
On the other hand,
when½ is equal to •r/2, the contributionof this term is
(3)
except in the limiting ease as rn becomes very large, when the two factors are identical. This limiting case
This contribution clearly depends on signal phase
is our
which, in our experiments, was either 0 or •r/2. When
tor for the AM ease becomes negative periodically,
½ is 0, s(t) is given by
when rn is greater than 1, and thus produces instantaneous phase shifts of •r rad. The QFM amplitude factor
s(t)= 2a[cos2•r(/x f /2)t] ,
(4)
maskers
alone"
condition.
q'h•. modulation
does not produce a phase shift for any value of rn.
fac-
The
J. Acoust.Soc.Am., Vol. 59, No. 2, February1976 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
446
A.R. PhippsandG. B. Henning:Signalphasein tonal masking
QFM waveform does, however, in addition to the amplitude modulation factor, have a phase modulation term given by
q•(t)=-tan'lira COS27r(Af/2)t].
(7)
This term produces smooth periodic changes in the
carrier phase at a rate of Af/2 Hz. If q•(t) is not changing with time, or does so only very slowly, the stimulus has a fixed frequency fs and some
phase given by q•(t). If, on the other hand, q•(t) is changing rapidly,
frequency will be roughly approximated by a linear fre-
quency sweep from fs to a frequency determined by the maximum rate of change of q•(t)with time. The maximum rate of change of the phase of the stimulus is
27rm(Af/2), so that, as a crude approximation,the QFM producesa linear frequencysweepfrom fs Hz to + •(Af/2)] Hz andback again, followedby a sweepfrom fs Hz to Ifs- •(Af/2)] Hz andbackagaintofs Hz every 2/Af sec. Whether this frequency modulationis detected depends on the duration of the sweep. Sergeant and Harris (1962) and l•ollack (1968) have shown that the
"threshold" rate of change of frequency for unidirectional frequency sweeps is roughly inversely proportional to the duration of the sweep, for durations over 75 msec.
of the duration of the
sweeps in the QFM stimulus by noting that the inverse tangent in Eq. 7 changessignificantly only for arguments
of the functionwithin twounits of zero. At the pointwhere the masker separation Af is 10 Hz, the modulation factor • is 11; using the limits noted above and Eq. 7 we may determine that the range of modulation with a 10Hz masker separation and • = 11 is 55 Hz, and that this 55-Hz
excursion
takes
about
70 msec.
These
AM waveforms
at 4 kHz
the lower carrier
seems
so much better
than at
frequencies.
It should perhaps be noted, in passing, that the experiments that are described in Goldstein's 1967 paper also attack the problem of phase sensitivity, but from the other end of the continuum of modulation depth. In his experiments observers discriminate the just-noticeably modulated, amplitude-modulated, and quasifrequency-modulated sinusoids from carriers that are not modulated at all; our experiment, by contrast,
comparedthe detectabilityof very highlymodulated
then the stimulus will have an in-
stantaneous frequency different from rs. The change in
We can make a rough estimate
446
waveforms with the carrier-suppressed case. Goldstein found that the amplitude modulation was more detectable than the quasifrequency modulation--the reverse of our findings at the other extreme--and that the effect
was limited
than the critical Our
data
to stimuli
whose
bandwidth
was
less
bandwidth.
seem
to result
from
the interaction
of a
number of complex factors. For widely separated maskers the explanation offered by Green is appropriate, but for maskers no more than 50 Hz apart the presence of relatively long-lasting deviations of the instantaneous frequency of the waveform produced by
addingthe'signaladvanced by 90ø produces measurably better performance for which we can offer no simple explanation. ACKNOWLEDGMENTS
We should like to thank J. L. Goldstein, D. M. Green, R. J. Ritsma, J. Gi. Robson, and M. M. Taylor for their criticism of earlier versions of this paper. We are most grateful to the Director and Staff of the Applied l•sychology Unit for their gracious hospitality and tolerance.
values
imply a rate of changeof over 770 Hz/sec for 70 msec. The observers of Sergeant and Harris
detected a truly
linear sweep of 200 Hz/sec lasting 75 msec, so it seems
reasonable
that
our
observers
would
be able
Canahl, J. A. (1971). "Two- versus four-tone masking at 1000 Hz,"
to
detect the frequency modulation. On the other hand, as Af increases, the duration of the sweep falls proportionately; the rate of sweep, however, increases with the square of Af. Given the findings of l•ollack and of
SergeantandHarris thatthe"threshold"sweeprate is roughly inversely proportional to the duration of the sweep, it might be expected that the signal in the QFM condition would be relatively more detectable with increasing Af. This is not the case. A simpler interpretation would be to have the observers detecting the simple frequency change of 55 Hz; however, frequency discrimination is a strong function of the carrier frequency, so that we would expect much poorer performance with 4-kHz signals if the observers were detecting this simple frequency difference. This, is not the case.
J. Acoust.
masking in the measurement of aural harmonics by the method of best beats," J. Acoust. Soc. Am. 23, 275-286
Fletcher, H. (1940). "Auditory patterns," Rev. Mod. Phys. 12, 47-65.
Goldstein, J. L. (1967). "Auditory spectral filtering and monaural phase perception, "J.
tion with a QFM waveform for low values of Af at carrier frequencies below 4 kHz. This seems to be related to our finding no effect of signal phase with highfrequency signals, but we are unable to offer any convincing explanation for the fact that performance with
Acoust. Soc. Am. 41, 458-
479.
Green, D. M. (1965). "Masking with two tones," J. Acoust. Soc. Am. 37, 802-813.
Green, D. M.,
andSwets, J.A.
(1966).
Signal detection the-
ory and psychophysics(Wiley, New York). Pfafflin, S. M. and Mathews, M. V. (1962). "Energy detection model for monaural auditory detection," J. Acoust. Soc. Am.
34, 1842-1853.
Pollack, I. (1968). "Detectionof rate of changeof auditory frequency," J. Exp. Psychol. 77, 535-541.
Ritsma, R. J., and Engel, F. L. (1964). "Pitch of frequency modulated signals,"
Goldstein (1967) has reported audible pitch modula-
Soc. Am. 50, 471-474.
Egan, J. P., and Klumpp, R. G. (1951). "The error due to
J. Acoust. Soc. Am. 36, 1637-1644.
Sergeant, R. L., and Harris, J. D. (1962). "Sensitivity to unidirectional frequency modulation,"
J. Acoust. Soc. Am.
34, 1625-1628.
Warren, J. M., and Egan, J.P.
(1951). "On the accuracy of
the method of best beats for determining the intensity of a tone," J. Acoust. Soc. Am. 23, 111-113. Watson, C. S., Franks, J. R., and Hood, D.C. (1972).
J. Acoust.Soc.Am., Vol. 59, No. 2, February1976 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
447
,A. R. PhippsandG. B. Henning:Signalphasein tonal masking
"Detection of tones in the absence of external masking noise.
I.
Effects of signal intensity and signal frequency,"
Acoust.
Soc. Am.
J.
52, 633-643.
Zwicker, Eo (1954). "Die Verdeckung yon Schmallbandge-
447 r'•usch durch SinustJSne," Acustica 4, 415-420.
Zwicker, E., Flottorp, G., and Stevens, S.S. (1957). "Critical
band width in loudness summation,"
J. Acoust.
Soc. Am.
29, 548-557.
J. Acoust. Soc. Am., Vol. 59, No. 2, February 1976
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 128.59.222.12 On: Sun, 30 Nov 2014 23:05:23
