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ON THE PERCEPTION
OF PHASE DIFFERENCES
IN ACOUSTIC SIGNALS
ON THE PERCEPTION OF PHASE DIFFERENCES
IN ACOUSTIC SIGNALS
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BIBLIOTHEEK TU Delft P 1950 4197ON THE PERCEPTION
OF PHASE DIFFERENCES
IN ACOUSTIC SIGNALS
PROEFSCHRIFT
ter verkrijging van de graad van doctor in de technische wetenschappen
aan de Technische Hogeschoo! Delft, op gezag van de rector magnificus
dr. ir. H. van Bekkum, hoogleraar in de afdeling der scheikundige
tech-nologie, voor een commissie aangewezen door het college van dekanen
te verdedigen op woensdag 7 aprii 1976 te 14.00 uur
door
THEODORUS JOHANNES FRANCISCUS BUUNEN
natuurkundig ingenieur, geboren te Utrecht
Dit proefschrift is goedgekeurd door de promotoren
Prof. dr. G. van den Brink
Aan mijn ouders
Aan Tine
De resultaten van het in dit proefschrift beschreven onderzoek zijn
grotendeels reeds elders gepubliceerd of zullen gepubliceerd worden. De
gegevens hierover zijn aan het eind van dit voorwoord te vinden.
Het tot stand komen van dit proefschrift is mede mogelijk gemaakt
door de inspanningen van anderen. Het zal duidelijk zijn dat de
mede-auteurs van bovengenoemde publikaties, te weten dr.ir. F.A. Bilsen, prof.
dr. G. v.d. Brink, ir. J.M. Festen, dr. J.H. ten Kate en ir. J. Raatgever
hierbij een belangrijke rol hebben gespeeld. Ir. T. Eland en D. van
Val-kenburg hebben deelgenomen aan de luisterproeven. De dialoog met dr. M.
Rodenburg is belangrijk geweest voor de experimenten betreffende
"omhul-lende detektie". De apparatuur die beschikbaar was bestond gedeeltelijk
uit eigenbouw apparaten die in de loop der tijd zijn vervaardigd door
K. Bel, J. Faase, E.E.E. Frietman en W. Willems. Voor sotnmige metingen
is gebruik gemaakt van de hybriede rekenmachine van het Rekencentrum van
de T.H. Delft. Dr. R. Bathgate heeft korrekties aangebracht bij de
verta-ling in het Engels. Het type werk is verzorgd door C.E.M. Buunen-op de
Weegh en M. Mulder-van Nouhuys.
Allen die hebben bijgedragen ben ik dank verschuldigd.
Buunen, T.J.F., Festen, J.M., Bilsen, F.A. and van den Brink, G., (1974) "Phase effects in a three-component signal", J.Acoust.Soc.Am.55, 297-303
Buunen, T.J.F. and Bilsen, F.A., (1974) "Subjective phase effects and combination tones", in Models and Faats in Hearing, Eds E. Zwicker and E. Terhardt, pp 344-352.
Buunen, T.J.F., (1975) "Two hypotheses on monaural phase effects", Acustica 34, 98-105.
Buunen, T.J.F., (1975) "Dynamic properties of the auditory system in relation to masking by non-stationary signals", Publikatie ^ , van het Nederlands Akoestisch Genootschap, 49-57.
Buunen, T.J.F., ten Kate, J.H., Raatgever, J. and Bilsen, F.A., (1976) "A combined psychophysical and electrophysiological study on the role of combination tones for the perception of phase changes", submitted for publication in J.Acoust.Soc.Am.
CONTENTS
INTRODUCTION 1 Chapter 1 CONDITIONS FOR THE AUDIBILITY OF PHASE CHANGES 6
1.1 Literature 6 1.2 The, audibility of phase changes in three-component signals 8
1.2.1 Signal, method and apparatus 8
1.2.2 The audibility range as a function of L 10
1.2.3 The audibility range as a function of f 12
1.3 The audibility of phase changes in broadband signals 13
1.4 Conclusions 14
Chapter 2 THE NATURE OF SUBJECTIVE PHASE EFFECTS 15
2.1 Literature 15
2.1.1 Phase effects in three-component signals 15
2.1.2 Phase effects in broadband signals 16
2.2 The prominence of residue pitch in a three-component signal 17
2.2.1 Qualitative observations 17
2.2.2 Signal, method and apparatus 18
2.2.3 The prominence of residue pitch as a function of 9 20
2.3 The audibility of separate harmonics in broadband signals 22
2.4 Conclusions 23 Chapter 3 MECHANISMS FOR THE EXPLANATION OF PHASE EFFECTS 24
3.1 Time structure detection 24
3.1.1 Envelope detection and fine-structure detection 24
3.1.2 Envelope changes as a function of phase in a
three-oomponent signal 25
3.1.3 The audibility of differences between signals with
identical envelopes 28
3.2 Auditory nonlinearity 31
3.2.1 Combination tones 31
3.2.2 A phase dependent internal spectrum 32
3.3 Conclusions 34 Chapter 4 COMBINATION TONES AND THE AUDIBILITY REGION OF PHASE
CHANGES 35 4.1 The boundaries of the audibility region 35
4.1.1 The lower boundary 35
4.1.2 The upper boundary 37
4.2.1 The relation between psychophysical and
electrophysio-logical experiments 39
4.2.2 Animal preparation and acoustic system 40
4.2.3 Signal, method and apparatus 41
4.2.4 The detectability of CT's as a function of L and f 45
4.3 Detection of CT's in a forward masking experiment 53
4.3.1 Signal, method and apparatus 53
4.3.2 The detectability of CT's as a function of L 54
4.4 Conclusions 58
Chapter 5 INTERACTION OF COMBINATION TONES AND ACOUSTIC
COMPONENTS 60 5.1 Estimation of the internal spectrum by means of
cancel-lation experiments 60
5.1.1 Signal, method and apparatus 60
5.1.2 The internal spectrum as a function of B 61
5.1.3 Relation between the internal spectrum and the prominence
of residue pitch 64
5.2 The interaction of CT's and acoustic components measured in
a forward masking experiment 65
5.2.1 Verification of the results of the cancellation
experiments 65
5.2.2 Vector addition of a CT and an acoustic component 67
5.3 The interaction of CT's and acoustic components measured in
an electrophysiological experiment 69 5.4 Reinterpretation of de Boer's phase rule 70
5.5 Conclusions 71 Chapter 6 ENVELOPE DETECTION AND THE AUDIBILITY OF PHASE CHANGES 73
6.1 A model for envelope detection 73 6.2 Envelope detection for amplitude modulated tones 74
6.2.1 Signal, method and apparatus 74
6.2.2 The threshold of envelope detection as a function of f , 76
6.3 Envelope detection and the masking by modulated noise 78
6.3.1 Literature 78
6.3.2 Signal, method and apparatus 79
6.3.3 The effect of f .on the masked threshold 81
6.3.4 Relation between the masking by modulated noise and
models for the processing of amplitude Variations 84
6.4 Envelope detection and the audibility region of phase
changes 87 6.5 Conclusions ' 89
SUMMARY AND GENERAL CONCLUSIONS 91
INTRODUCTION
This thesis describes investigations on the auditory system arising from some problems about the audibility of phase changes in acoustic signals. In this introduction we will try to place the work against the back-ground of auditory research in general, and will briefly indicate the methods of investigation used.
Auditory research in general may have one of two goals. The first
is to describe the functioning of the auditory system by using a model
that simulates the signal processing without being realistic with
respect to the physiological structure. Such research will yield a set
of parameters of the ear that can be used e.g. in technological
applications. An example of work of this kind is the measurement of the
sensitivity of the ear to sinusoidal signals as a function of frequency.
The knowledge gained from these experiments may be helpful e.g. for the
design of transducers like loudspeakers and microphones in communication
equipment. Another example is the investigation of the integration time
of the auditory system in order to measure subjective attributes (e.g.
loudness or nuisance value) of sounds whose amplitude varies with time.
This type of research generally has a very specific, well defined goal.
However, it has the disadvantage that the results, formulated in a
"black-box model", are of very limited application: A different model
must be designed for each attribute of auditory sensation.
A more generally applicable model can only be obtained if
physiological data about the auditory system are also taken into account.
This brings us to the second goal of auditory research, to "know how the
auditory system works". The model that results from this type of
research will have to be compatible with all the black-box models. It
will be clear that this fundamental knowledge about the functioning of
the auditory system will not only have technical implications as do the
black-box models. For instance, it will give more insight into the
information processing in the nervous system in general. It also
provides a guide for the diagnosis of auditory complaints. It is obvious
cannot be strictly ascribed to one of the two classes described before.
The results of an experiment may be used for a black-box model even
though they were obtained in an experiment aimed at increasing
fundamental knowledge, and conversely it is often useful for the
under-standing of a system to describe experimental results in terms of a
black-box model. The distinction thus lies not in the nature of the
experiments but in the intention of the worker. The experiments
des-cribed in this thesis were intended to increase fundamental knowledge
of the auditory system.
The basic subject of this study is the audibility of phase changes
in acoustic signals. The reason why this topic is of interest for the
theory of hearing can only be understood with reference to former and
current theories about signal processing by the auditory system.
Therefore a very brief introduction into this theory will be given here.
It is commonly accepted that the peripheral auditory system
performs a frequency analysis of an acoustic signal. Clear evidence for
this is found e.g. in the masking of one sound by another (Wegel and
Lane, 1924). From this point of view the peripheral auditory system can
be represented by a set of bandpass filters with a form that is still a
subject of research. The output of the bandpass filters is coded in one
way or another to give pulsed electrical signals ("spikes") which can be
observed in the cells and fibres of the auditory nervous system. One of
the main objectives of auditory research is to determine which
proper-ties of the output of the bandpass filters are coded in the spike trains.
Electrophysiological measurements have demonstrated that the number
of spikes per second is related to the level of the acoustic signal. It
has also been demonstrated that the interval between successive spikes
is related to the periodicity of the signal (Kiang et al., 1965). It is
now important to know whether a change in the time structure of an
acoustic signal but not in the power at the output of the bandpass
filters changes the sensation evoked by the signal. If this was the case
it would show that time-structure information is not only preserved in
the spike trains on the auditory pathway but is also used to bring about
an aspect of the subjective sensation. It will be clear that
investi-gation of this problem is no easy matter, as it requires an acoustic
signal whose time structure can be changed without affecting its power
spectrum. In order to obtain a signal that fulfils this condition,
phase changes between components in an acoustic signal have to be
intro-duced .
Such reasoning was already applied a century ago by von Helmholtz
(1954) who investigated whether changes in the phases of the first 8
harmonics of 120 Hz were audible. Since then the audibility of phase
changes in acoustic signals, which will be called "subjective phase
effects" from now on, has been a permanent subject of investigation
mainly in view of the fundamental question as to which parameters of a
sound are coded in spike trains in the peripheral auditory system and
decoded in the central auditory system. This has also been the main
motive for the work described in this thesis. The main question is
whether the audibility of phase changes in acoustic signals justifies
the conclusion that parameters other than the output power of the
peri-pheral bandpass filters are coded and used in the auditory system.
It is self-evident that the sensation of a sound cannot be fully
described by its power spectrum alone, because the frequency analysis
performed by the auditory system is non-ideal ("short-time frequency
analysis"). This can be demonstrated by modulating the amplitude of a
pure tone with a 1 Hz sinusoid. The power spectrum of the resulting
signal consists of three components with frequency separations of 1 H z .
The sensation is that of a pure tone with a slowly changing loudness.
The detection of time structure by the ear in this case comes down to
the detection of amplitude changes. A distinction between those signals
in which amplitude changes are audible as such, because of the
short-time analysis by the ear, and those in which amplitude modulation is
manifest as changes in the power spectrum, is clearly crucial for the
explanation of the audibility of phase changes, since phase changes
affect the time structure of the signal.
The expression "phase changes in acoustic signals" used throughout
this work, should not be interpreted too broadly. In the first place
only signals presented to one ear (monaurally) have been investigated.
Phase changes between signals at different ears may lead to phenomena
like lateralization and binaurally masked level differences (Blauert,
1974) which are not considered here. The second limitation on the field
spectrum consisting of discrete components are studied. This rules out
signals with a continuous frequency spectrum like white noise sent
through a phase shifting network as described e.g. by Cramer and Huggins
(1958). It also excludes signals that have a transient character, like
Huffmann sequences (signals with a flat frequency spectrum but with well
defined phase jumps; Patterson and Green, 1970).
In view of the above limitations the sim^plest signal to use for the
investigation of phase effects is one consisting of two discrete
frequency components. Changes in the phase of one component relative to
the other are easily detectable in such signals. A vast amount of
literature has been published on this topic. The use of octave complexes,
with a ratio of 1:2 between the frequencies of the two components, is
very common. One of the most recent papers is by Lamore (1975) who found
that the pitch and loudness of the higher frequency component depended
on the phase relation between the components. The main problem
encoun-tered in attempts to explain these effects is the question, whether the
auditory system is coding and using information about the time structure
of the signal. The research performed on phase effects in two-component
signals has not yet led to unanimous conclusions and new hypotheses are
still being made.One of the controversial topics is the influence of the
distortion introduced by the ear. It has been demonstrated that the
signal processing by the auditory system cannot always be described by
a linear transformation. It was emphasized already in Helmholtz's time
that distortions like the sum and difference tones of two components
may give rise to a phase-dependent interaction between either these
distortion products themselves or between distortion products and
acoustic components. The problem has not yet been solved (see e.g.
Clack et al., 1972 and Lamore, 1975).
Phase effects in three-component signals have not received as much
attention in the literature as phase effects in two-component signals.
Most of the experiments described in this thesis deal with phase
effects in three-component signals; in some cases more complex signals
such as a periodic pulse have also been studied. It appears from
literature that phase changes in three-component signals are audible
(Mathes and Miller, 1947) but the origin of these phase effects is not
of time-structure detection and nonlinearities still appears to lie
at the root of the problem.
Two different experimental approaches have been used during this
study. The first is the psychophysical method in which a specific sound
is presented to an observer who is asked to adjust e.g. the threshold
of hearing for that signal, or to adjust a reference signal in such a
way that e.g. its pitch or its loudness is equal to that of the signal
under investigation. He may also be asked whether two signals are equal
or not. These psychophysical experiments were performed by several
observers. The number of observers used to investigate a certain effect
was usually rather small in the experiments reported here. Data on many
observers are only useful if one is interested in e.g. the mean
auditory threshold for normal observers. For the purposes of our
experiments it is often sufficient to know that a certain threshold or
effect exists. Knowledge about the mean value of the threshold for a
large number of observers seldom adds essential information about the
hearing mechanisms involved. As a consequence of a limited number of
observers used, the comparison of results of different types of
experiments will have to be made for one and the same observer.
The second experimental method of studying the hearing system is
to follow the signals from the peripheral processing in the cochlea to
the central processes on the cortex. This is commonly done by inserting
a micro-electrode into the auditory nerve centres of an animal. These
experiments are called electrophysiological experiments. In the
experiments described below both techniques have been applied for one
and the same problem, the perception of phase changes in complex
CHAPTER 1. CONDITIONS FOR THE AUDIBILITY OF PHASE CHANGES
This chapter reviews some of the existing literature on phase effects. It appears from the work cited that phase changes are only audible if the separation between the frequency components of the signal is small enough. Measurements on this audibility range for phase changes are presented.
1.1. Literature
The audibility of phase changes has been a subject of research
since 1830. A limited amount of literature on this subject was published
before 1950. Thereafter the number of papers increases. We need not give
a complete historical survey of the literature here because a recent
review may be found elsewhere (Plomp and Steeneken, 1969). However, a
selected number of publications will be discussed to provide a
back-ground for the items dealt with in this study.
One of the first discussions of the audibility of phase changes in
a complex signal was started about a century ago by Helmholtz (1954).
He investigated a signal consisting of 8 successive harmonics of 120 Hz,
the amplitude and phase of each tone being separately variable, and
concluded that phase changes are not audible in this stimulus. He could
not investigate higher harmonics so he left the question open as regards
these "unmusical" sounds. Other observers did hear phase effects and the
discussions about the audibility of phase changes have nearly always
been concentrated on the role of distortion in the apparatus or the ear
itself.
The audibility of phase changes in signals consisting of three
frequency components was investigated by Mathes and Miller (1947). They
concluded that phase changes of the central component (i.e. the
component with the middle frequency) are easily detectable provided the
frequency separation between the components does not exceed a certain
fraction of the central frequency. Experiments with three-component
signals by de Boer (1956) gave qualitatively the same results although
his results differ quantitatively from those of Mathes and Miller.
Goldstein (1967a) confirmed the statements about the limited audibility
of phase changes and repeated experiments first performed by Zwicker
(1952) on the subjective difference between AM (amplitude-modulated) and
QFM (quasi-frequency-modulated) signals which differ only with respect
to the phase of the central component. The nature of these phase effects
has been described as a change in "roughness", "harshness", "timbre" and
in the prominence of a "basic pitch" or "residue pitch". These
subjec-tive qualities will be discussed more thoroughly in chapter 2.
The fact that phase changes are audible at all confirms that the
frequency resolution in the auditory system must be subject to
limitations. Phase effects can only occur if there is interaction
be-tween the frequency components of the signal, also after the frequency
analysis performed by the basilar membrane. This reasoning led Zwicker
(1952) and Goldstein (1967a) to estimate this frequency resolution
(the "critical band") from the maximum frequency separations between the
components for which phase effects still occur.
The limited frequency separation between the components is not the
only condition to be fulfilled if phase changes are to be heard. There
is also a restraint on the value of the phase changes. De Boer (1956,
1961) has reported that no subjective effects occur for phase changes
in a multi-component signal which obey his "phase rule". This empirical
rule states that the subjective quality of a sound is unchanged if the
phases of the components are shifted by a constant amount and/or amounts
that are linearly dependent on the frequency of the components.
Experimental evidence was obtained from psychophysical experiments with
steady-state signals whose components (3, 5 or 7 in total) had equal
frequency spacing. De Boer's phase rule has consequences for the number
of phase permutations of a complex sound that give different sensations.
It can be shown mathematically that the number of variables is reduced
by two, because of the two arbitrary constants in the phase rule (see
section 3.1 below). This implies that in a three-component signal with
three variable phases, all phase changes resulting in different
sensation can be expressed in terms of one variable phase.
Phase effects in more complex sounds (i.e. sounds with more
frequency components) have been studied by Licklider (1957). He
limited audibility in terms of a minimum separation between components.
Schroeder (1959) also observed phase effects in signals containing up
to 31 harmonics. His comments on the subjective nature of phase effects
are especially interesting and will be discussed more extensively in
chapter 2. However, he does not mention any limits for the frequency
separation required to give phase effects. Bilsen (1968) compared a
low-pass filtered periodic pulse and periodic noise filtered in the
same way. The only difference between these signals is the phase
relation between their frequency components. The results indicate a
limited audibility of phase effects in broadband signals, since no
phase effects occurred if only lower-order harmonics passed through the
low-pass filter. A common aspect of all experiments on phase effects is
that they show that these effects exist not only for high levels but
also for relatively low absolute levels of the signal.
The above mentioned authors explained phase effects on the
assumption that the time structure of the signal determines an aspect
of the sensation and changes of the phases alter the time structure of
the signal. They further assumed that the nonlinearity of the auditory
system does not play an important role because phase effects also occur
at low sensation levels. The limited audibility of the phase changes
as a function of the frequency separation of the components has been
ascribed to the frequency analysing properties of the ear, since the
complex time structure of the signal is not represented in the movements
of the basilar membrane at large frequency separations. De Boer's phase
rule is a very strong argument for the theory of time-structure
detec-tion because it can be demonstrated that phase changes obeying this
phase rule give no changes in the envelope of the signal (de Boer,
1956). The conclusion might easily be that phase changes that preserve
the envelope are inaudible . It will be shown (in section 3.2) however
that this "inverse" of the phase rule is only valid for small frequency
separations between the components, say up to 30-60 Hz.
1.2. The audibility of phase changes in three-component signals
1.2«1.
Signal, method and apparatus
frequency component in a three-component signal are audible depending
on the frequency separation Af of these components. Mathes and Miller
(1947) found no phase effects if the frequency separation was more than
40% of the signals central frequency for a signal with a power spectrum
equal to that of a 100% SAM (sinusoidally-amplitude-modulated) pure tone.
It is thus possible to define an audibility range for phase effects in
terms of the values of Af for which they are audible. The maximum and
minimum values of Af for which subjective phase effects occur will be
called the upper and lower limit of the audibility range. The upper
limit of the audibility range was measured by e.g. de Boer (1956) for a
limited number of carrier frequencies and for a level difference of
-6 dB between the central component and the sidebands. As regards its
power spectrum, this signal is equivalent to an SAM pure tone with a
modulation depth of 100%. In the present study the audibility range of
phase effects for this type of signals has been measured over a wider
range of carrier frequencies and values of the level difference L,
between the central frequency component and the sidebands.
The stimuli used in the present experiments on the audibility
range were generated as follows: Two sinusoids of frequency f and f ,
(=Af) were multiplied in a four-quadrant multiplier with a carrier
suppression of more than 50 dB. The resulting signal consists of two
frequency components f -Af and f +Af. If a component with frequency
f'=f +2 Hz is added, the signal can be described as a three-component c c
signal, the central component of which has a continuously changing
phase. This signal evokes a clearly audible beat with a repetition rate
of 4 Hz, provided Af is relatively small. The fact that this repetition
rate is twice the frequency difference between f and f implies that c c
the beats cannot be due to incomplete suppression of f . As the value
of Af is raised the beats become less pronounced and finally disappear.
The method used here to measure a limit of the audibility range
for phase changes is an adjustment procedure. The observer was seated
in an acoustically insulated booth, where he received the
three-compo-nent signal with continuously changing phase of the central compothree-compo-nent
monaurally via a Telephonies TDH-39 headphone. He was asked to increase
Af from a value for which phase changes were audible, until no phase
value until phase effects were just distinguishable. The mean of these
two values represents his estimate of the upper limit of the audibility
range. Distortion products were at least 55 dB lower than f at the c
input of the headphone.
1.2.2. The audibility range of phase changes as a function of L
The audibility range of phase changes was measured for several
values of the level L of the sidebands in the three-component signal
relative to the level of the central component. The adjustment
proce-dure used has b e e n , described in the previous section. The observers
measured the audibility range for discrete values of L, starting at -6
dB and decreasing in steps of 5 dB. For high values of L , only an upper
limit to the audibility range was found. When Af was decreased from the
maximum value in this case, the beat remained audible until Af was of
the order of the repetition rate (4 H z ) . For low values of L, the
observers also measured a value of Af below which phase changes were
inaudible. Each upper and lower limit was measured at least four times
in different experimental sessions. The spread of the results was about
O.lAf. The mean values found by two observers at f =2000 Hz are c
presented in Fig.1,1.a and Fig.l.l.b.
dB
Fig.l.1.a.
The audibility region of phase changes indicated as a hatched area. The filled circles are the datapoints from which the audibility region has been derived.
0 008 016 024 Af/. >
The audibility region is defined as the hatched area. Phase changes are
audible within this region. The boundaries of the audibility region are
Fig.1.l.b.
The same as in Fig.1.a, for a different observer.
obtained by graphical interpolation between the experimental points. The
same measurem.ents were performed for f =100
observer. The results are shown in Fig.1.2,
same measurem.ents were performed for f =1000 Hz and f =4000 Hz by one
da
0 t^ =1000 Hz 45dB SL 008 AtA dB 0 35dBSL 0.08 Af/f; 016 — > 016 024 Fig.1.2.The audibility region of phase changes for two values of f for one observer.
A common aspect of all experimental results is that phase effects do
not occur for values of Af larger than 18-28% of the central frequency,
depending on the observer and the value of f . The average of these
values corresponds reasonably well with the value of 20% given by
de Boer (1956) for a signal with a power spectrum equal to that of
an SAM pure tone.
The form of these audibility regions differs from what could be
expected on the hypothesis of time-structure detection, which predicts
weaker interaction of the frequency components for large frequency
separations, owing to the ears frequency resolution. Thus, if the
changes in the time structure caused by phase changes, become less
pronounced (as is the case with decreasing values of L ) , we would
expect no phase effects to occur for small values of L and large
frequency separations. The results of our measurements show on the
contrary, that the phase effects vanish at small frequency separations
as L is decreased. This result demonstrates that time-structure
detection and frequency analysis by the auditory system alone cannot
account for the form of the audibility region for phase changes.
1.2.3.
The audibility of phase changes as a function of f
The audibility range for three-component signals as defined in
1.2.1. has also been measured with varying values of f in order to
investigate whether the audibility of phase changes depends on the
frequency range of the signal. The level of f was 30 dB SL for each
observer. The levels of all three components were equal in this
experi-ment, which corresponds to L=0 dB. The results are given in Fig.1.3.
Fig.1.3.
The audibility range of phase changes for three observers as a function of f . Phase changes are audible for values of Af/f below the
data-. c
p o i n t s .
D o b s T B o obs JR A obsTE Af/ 05 25 Goldstein(1967a) P . - - 0 - - Q . 10 20 40 8D kHz fr > 12The audibility appears to be fairly independent of the frequency range.
Similar results were obtained by Goldstein (1967a) for a
three-component signal with L=-6 dB.He measured the maximum frequency
separation between the components for which a difference between an AM
and a QFM signal was audible.His results are given in Fig.1.3 as a
dotted curve.
1.3. The audibility of phase changes in broadband signals
There are very few reports in the literature of a limited
audibility range of phase changes in broadband signals.As mentioned in
section 1.1, Bilsen (1968) measured the audibility of the difference
between low-pass filtered periodic pulses and periodic noise.The
frequency components of a periodic pulse are all in cosine phase while
the phase relations are random for periodic noise.Bilsen's experiments
were not aimed at deciding precisely which of the higher components
gives the phase information.This may be ths component nearest to the
cut-off frequency,or one of the other higher components since the
high-frequency slope of the low-pass filter was only 35 dB/oct.
Therefore, an experiment was devised to investigate the audibility
range of phase changes in a periodic pulse. One of the components of the
signal was given an adjustable phase.This was realised by cancelling the
original component with a phase-lock generator(HP-3203A) which gives a
supression of at least 60 dB. A component of the same frequency and
adjustable phase is subsequently added by means of a second phase-lock
generator. The observer could manipulate the phase at will. By changing
the harmonic number of the component we investigated for which harmonic
number a phase change of the component was audible. The level of the
periodic pulse was chosen such that the level of the harmonic under
investigation was always 40 dB SL. The whole procedure was repeated for
several values of the pulse repetition rate, thus giving data on the
audibility range of phase changes in a broadband signal. As this
experiment was performed by one observer only,the results have to be
used with caution. The results are plotted in Fig.1.4 together with
those of Bilsen (1968). For our results f is the frequency of the
component for which a phase change was audible and Af is the periodicity
Fig.l.4.
The audibility range of phase changes in broadband signals as a function of the frequency region. The mean of our datapoints of Fig. 1.3 is also plotted.
25 .5 rO 2fl 4.0 8.0 kHz fc >
of the low-pass filter. The agreement is reasonably good. The mean of the audibility ranges found in section 1.2.2 for three-component signals has also been plotted in this figure.
1.4. Conclusions
The measurements on the audibility region of phase changes as a function of the sideband level L have demonstrated that an explanation based solely on time-structure detection is hardly tenable. The
measurements on the audibility range as a function of the frequency f do not help us in the search for an alternative explanation for the phase effects. The resolution of the frequency analysis,responsible for the limited audibility,can be estimated from these results. It appears to be proportional to the frequency region because the audibility range is approximately a constant fraction of the central frequency. This conclusion confirms statements by other investigators (e.g. Zwicker,1967) about the constant relative bandwidth of the auditory "bandpass filters". It is not surprising that the data on the limited audibility of phase changes agree reasonably well with the "critical band" as the latter is a rough estimate of the frequency resolution of the auditory system. However, our data are not in agreement with the conclusion of earlier workers in this field, that time-structure detection is the reason for
the ear's phase sensitivity.
^k
.05
_.^._
periodic three-co periodicfc^-*~~
pulse (obsTB) mponent signal noise/pulse (Bilsen^^^^.
1968) ^ 1 14CHAPTER 2. THE NATURE OF SUBJECTIVE PHASE EFFECTS
The foregoing chapter concentrated on the mere audibility of phase changes. Conditions were found which have to be fulfilled if phase changes were to be audible as a change in the sensation evoked by a complex signal. In this chapter the nature of phase effects will be discussed by describing the aspects of the sensation that vary when a phase change in a complex signal is heard.The phase dependence of the prominence of the residue pitch is quantified.
2.1 . Literature
2.1.1.
Phase effects in three-component signals
Mathes and Miller (1947) described phase effects in a three-component
signal as a change in the "roughness" or "harshness" of the sound as a
whole. Terhardt (1967) measured the change in roughness for one specific
phase change.The second effect reported by Mathes and Miller was a
change in the prominence of a "basic pitch". A doubling or tripling of
this basic pitch has also been found. Goldstein (1967a) described the
subjective differences between AM and QFM sounds. For modulation
frequencies larger than 20 Hz he described AM as being "buzzier" than
QFM. An increase in the modulation frequency reduced the "buzziness" and
both sounds became tonal musical complexes. Ritsma and Engel (1964) found
a pitch variation as a function of phase. These pitch differences were
differences in the "residue pitch" or "basic pitch",
Residue pitch is a low pitch,roughly corresponding to that of a
pure tone with a frequency equal to that of the common (but absent)
fundamental of the complex (Schouten,1940). This fundamental is not
present in the power spectrum of the acoustic signal, nor is it
generated by nonlinear effects (Licklider,1954). For a survey of the
literature on residue pitch the reader is referred to articles by
Schouten (1970) and Ritsma (1970). The influence of the phase in a
three-component signal on the residue pitch was measured by Ritsma and
corresponding to changes in the "time structure" of the signal. In this
case "time structure" means the position of pronounced peaks within the
envelope of the signal and not the change in the envelope itself. The
doubling and tripling of pitch as reported by Mathes and Miller was not
found by these authors. However, the results of Ritsma and Engel were not
confirmed by Patterson (1973) who repeated their experiment. Experiments
by Vightman (1973) did not show any influence of phase on the value of
the residue either. Licklider (1955) noticed that the possibility of
hearing the residue pitch at all in a five-component signal depends on
the phase relation between the components. Bilsen (1973) found that the
masking of the residue pitch of a three-component signal by white noise
depends on the phase relation of the components if Af/f <0.12.
2.1.2. Phase effects in broadband signals
The most prominent change in the subjective quality of a sound due
to phase changes is called a change in timbre in almost every paper on
phase effects. We have not tried to define the term "timbre" sofar; in
general we will follow the definition given in the American Standards
Association (1960), which reads: "Timbre is that attribute of auditory
sensation in terms of which a listener can judge that two sounds,
similarly presented and having the same loudness and pitch, are
dissimilar". Plomp (1970) argued that this definition is a negative one,
since every aspect of sensation that is not pitch nor loudness nor
duration must then be timbre. Stating that a phase effect in a stationary
signal is a change in timbre would thus mean that the effect may be
anything except a change in pitch or loudness.
Licklider (1957) reported that a change of phase in a 16-harmonic
complex sound gives rise to changes in timbre and changes in pitch.
Schroeder (1959) made more explicit statements about the nature of phase
effects in signals containing up to 31 harmonics. He reported that
changes in timbre related to the peak factor of the signal could be
heard, as could distinct tones caused by manipulation of the phase,
Another interesting statement by this author is that little or no
subjective change is produced by a variation of the phase which leaves
the envelope of the stimulus unchanged,
Very limited progress has been made in the quantitative measurement
of timbre changes. The difficulties encountered in measuring a change in
timbre may be due to the negative definition of this concept. Plomp and
Steeneken (1969) have used a promising approach, the "multi-dimensional
scaling method", which can be used for comparing the timbres of sounds
with different phase configurations. It has proved possible in this way
to express the effects of phase changes in a sound in terms of an
equivalent change in the slope of the amplitude spectrum.
The variations in the pitch of a complex tone as a function of
phase has been investigated by Patterson (1973) for 6- and 12-component
signals. These experiments were repeated by Wightman (1973). A change in
the phase relation of the components from cosine to random phase did not
have any effect on the pitch of the stimulus as a whole. The experiments
were performed by comparing the test signal with a reference stimulus.
Their results do not support the results of Licklider (1957). A common
aspect of all investigations on phase effects is that the explanation is
mainly based on the assumption that the time structure of a stimulus is
detected by the auditory system.
2.2. The prominence of residue pitch in a three-component signal
2.2.1.
Qualitative observations
Our own observations on phase effects in three-component signals
have confirmed the statements in the literature about the changing
roughness of a sound as a function of phase. This is certainly the case
for small frequency separations between the components, say up to 100 H z .
The changing roughness was less apparent for frequeny separations
approaching the boundaries of the audibility region as found in section
1.2.1. The change may then be described as one in "timbre" or "tonality".
It appears from this that a different subjective criterion is used in
assessing phase changes for small and large frequency separations. For
small separations the roughness difference is very apparent, while for
large separations it is a matter of different "tonalities". Some
indication of the existence of the two different criteria may be found
e.g. in a paper by Goldstein (1967a), who reported that as the frequency
separation increased an AM and a QFM signal were initially very
It might be possible that the frequency separation where the judgement
changes from "dissimilar" to "similar, but still different", is caused
by a change in the subjective criterion.
We observed no obvious pitch changes in the residue pitch although
the prominence of the residue pitch does depend on the phase in a
three-component signal. No doubling or tripling of residue pitch could be
observed. However, at low values of the frequency separation between the
components,say Af=30 Hz, the periodicity of the "rattle" is doubled if
the signal is changed from AM to QFM. The only effect of phase on the
residue pitch was concerned with the prominence of the latter. Therefore
a series of experiments was devised to measure the prominence of residue
pitch as a function of the phase 6 in a three-component signal,
2.2.2. Signal, method and apparatus
The pitch of a stimulus consisting of three components may be
ambiguous. The same stimulus can lead to a residue-pitch sensation as
well as to a pitch sensation that corresponds to the frequency content
of the signal. If the same stimulus is presented to an observer N times,
in between other stimuli, then the fraction of the N responses
corres-ponding to residue-pitch perception is assumed to be a measure of the
prominence of this residue pitch. An estimate of this fraction, which is
subject-dependent, can be obtained by the following method. Stimuli are
presented in pairs to an observer according to the time diagram of
Fig.2.1.
Fig.2.1,
Timing diagram of the stimu-lus presentation used in the experiments on the prominence time > °f ^^^ residue pitch
Stimulus 1 consists of 9f , lOf and llf and stimulus 2 consists of o o 0
8g , 9g and lOg ; g being slightly higher (5% or 10%) than f , see
Fig.2.2.
The observer is asked to report which one of the two stimuli has the
higher pitch. If he finds stimulus 1 higher than stimulus 2 there are
several possible ways this judgement could have been reached. The most
obvious one is that his judgement is based on a correlate of the spectral
centres of gravity of both signals. But as the residue pitch itself
, fie --Kb,
, fie .
s t i
st2 frequency
-9'o 10fo 11'o
8 g , 9g^10g^
F i g . 2 . 2
Power spectrum of the signals used to measure the prominence of the residue pitch. The dashed lines represent the pitch of the absent fundamental.
is ambiguous (Schouten et al.,1962) the observer's judgement might also
be based on a residue pitch in stimulus 1, not corresponding to f and
slightly higher than a residue pitch in stimulus 2. If the observer
judges stimulus 2 higher than stimulus 1, then this is only possible
if he heard one of the residue pitches in stimulus 1. The frequency of
occurrence of this response,which has been called the "correct" response
in this study, is assumed to be a measure of the "prominence" of the
residue pitch. This method does not tell us anything about the perception
of stimulus 2, which is merely used as a reference. This stimulus
confi-guration is analogous to those used by Patterson (1969) and Smoorenburg
(1971). Pairs of stimuli were presented in a random order and in
alteration with other stimuli. The percentage of "correct" responses is
comparable with the "performance" used by Houtsma and Goldstein (1972),
The signals were generated with a hybrid computer (AD-4,IBM 1800)
and recorded with a tape recorder (Ampex FR-1800). Distortion products
and noise were always more than 45 dB below the signal level. The phase
relation of the components in stimulus 1 was varied; it was kept constant
in stimulus 2 in order to have a constant reference. The tape was played
back and the signals were presented monotically (via a Grason-Stadler
earphone type TDH-39) to the observer who was seated in an acoustically
insulated room. The sensation level was 40 dB SL on the average unless
stated otherwise. The same tape was played a number of times to get
about 80 presentations for each phase relation. Two types of reference
stimuli (g =1.05f and g =1.10f ) were used in a random order on the O O o o
same tape, in order to make the pitch changes less monotonous.
A three-component signal with amplitudes A, B and C, phases p , p .
carried out with a combination of the 9th, 10th and 11th harmonics of
200 Hz. Only the phase 6 (=p„-(p.+p-)/2) was varied during the experiment.
By definition we took 6=0 for all three components in cosine phase.
While the following topic is not really vital for a proper
under-standing of the results presented below, it should be realized that "de
Boer's phase rule" permits such a reduction of the number of phase
permutations to be investigated. This can be shown as follows. Let the
frequencies of the components be f -Af,f and f +Af and their phases
p., p . and p. respectively. The phase rule states that a phase change
equal to a+bf, where f is the frequency of the components, does not
change the sensation. Because a and b are arbitrary constants they may
be chosen such that the following relations hold:
Pj+a+b(f^-Af)=0 (2.1)
p +a+b(f^+Af)=0 (2.2)
In this case the phase of the central component changes from p„ to
p -(p +p-)/2. This implies that an arbitrary phase permutation is
equi-valent to one in which the phases of the sidebands are zero and the phase
of the central component is given by 9 which is equal to p -(p +p-)/2.
Thus, only phase variations for which 0<A6<180° involve a perceptive
change and have to be examined. In other words, it does not matter which
phase (p,, p~ or p.) is changed as long as 6 has the desired value.
2.2.3. The prominence of residue pitch as a function of 9
The results for a sensation level of 40 dB are given in Fig.2.3 for
three observers. As described in the previous section, each measured
point represents the percentage of "correct" responses for one particular
phase angle 9. Inspection of Fig,2,3 shows that one value of 6 is least
favourable for hearing the residue pitch of the stimulus; however the
value of 9 in question varies from observer to observer.
Results for 30 and 50 dB SL are shown in Fig.2,4 for one observer.
It may be noted that the minimum in the curve becomes less pronounced
and shifts towards higher 6 with increasing intensity. It may further be
concluded that the envelope of the external time structure cannot be
related directly to the prominence of the residue pitch, since the
minimum would be expected to be at 6=90 in that case. It would be
looses
% 100 if) (/)150
in 01 A i A = o = A fi 5% 10%•
\
k
0—S
? B 8 1
obs.TB 40dBSL Fig.2.3. Fraction of "correct" responses as a function of 9 for three obser-vers. The sensation level of the signal is 40 dB above threshold. The smooth curve is made by eye as a best fit to the datapoints. The 5%- and 10% points are obtained with a reference stimulus whose absentfundamen-tal g was 5% resp. 10% higher than f . 60 120 180" % 100 t/1
Iso
UI "o 01 i-o 0 A = 5% o = . o > ^< A ^ A . 10%h-7H
obsJF 40dBSL>
I/'
°/
/
> o o 5 i o A Ir\J
N
o i A 0 60 120 180"difficult to explain the difference between the different observers and
the level dependence on this assumption.
Measurements carried out at f =400 Hz gave analogous results, which
have not been plotted because they give no additional qualitative
infor-mation. In this case the prominence of the residue pitch is diminished
and the minimum is found at a value of 9 different from that for
f =200 Hz. o
1^8f—a—«—a—8—a—fi—a—SH-*
Fig.2.4.
Fraction "correct" responses as a function „ of 9 for levels of 30 •'SO and 50 dB SL. The o—o—I smooth curve is a best
fit made by eye to the measured points.
2,3. The audibility of separate harmonics in broadband signals
If the phases of harmonics above the fifth are varied in a periodic
pulse, changes in timbre are clearly audible. A phase shift of a
harmo-nic above the 10th-15th also makes it easier for an observer to "pick"
this harmonic out. Plomp (1966) showed that an observer can identify the
individual harmonics in a periodic pulse up to the 10th. Observations
during the measurements of section 1.3. however, have shown that if e.g.
the 15th harmonic is shifted in phase by 90 then this harmonic is also
very easily audible. This qualitative finding confirms Schroeder's
(1959) results. It can be explained by the same reasoning as given by
Duifhuis (1972) to account for the audibility of a high harmonic in a
periodic pulse although the harmonic itself is removed from the signal.
Due to the limited bandwidth of the frequency analysis of the ear, the
harmonic is observable in the short-time frequency spectrum of the
signal. Cancellation of a component of the acoustic signal is equivalent
to the addition of a component with equal amplitude but opposite phase.
Duifhuis argued that this component becomes audible if the bandwidth of
the bandpass filters comprises several harmonics of the signal.
A phase change of p in a component of amplitude D is equivalent
to the addition of a component with the same frequency, an amplitude
equal to D/2-2cos (p) and a phase of p/2+90 . This component will be
audible by analogy to the situation described by Duifhuis. Duifhuis
(1972) gave a more detailed description of this effect.
An alternative explanation of the effect is given by Schroeder
(1975). His reasoning is based on changes in the long term spectrum due
to phase changes in the signal. A disadvantage of this explanation is
that the limited frequency selectivity of the ear and its short-time
analysis are not explicitly required for the effect. It is obvious
however that these must play a role because the underlying phase effect
is the same for the 15th harmonic of 200 Hz as for the 50th harmonic
of 10 Hz. In the latter case it is useless to consider the long-term
spectrum of the signal. For this reason the explanation as given by
Duifhuis (1972) is preferred because it also covers those cases where
time-structure detection clearly occurs.
2.4. Conclusions
In general, phase changes in an acoustic signal appear to affect
the roughness of a sound, the prominence of the residue pitch, the
timbre (roughness is not included in the term timbre, here) and the
possibility of picking a harmonic out of a broadband signal.
The measurements described in this chapter quantify the dependence
of the prominence of residue pitch on the phase 6. Further experiments
on the actual values of the "residue pitch" as a function of phase have
not been performed, mainly because no pitch change was found in an
exploratory experiment with the signals used in the previous
measure-ments.
Explanation of phase effects is made difficult by the fact that
the subjective effects cannot all be accounted for by one and the same
mechanism. For instance the roughness of a sound and its residue pitch
cannot be detected by the same mechanism because roughness is audible
in signals where residue pitch is absent. Consequently more than one
CHAPTER 3. MECHANISMS FOR THE EXPLANATION OF PHASE EFFECTS
Two possible mechanisms for monaural phase effects are discussed in this chapter, viz. time-structure detection by the auditory system and interaction of combination tones and acoustic frequency components within the ear. The experimental evidence indicates that both mechanisms contribute to the audibility of phase changes.
3.1. Time-structure detection
3.1.1.
Envelope detection and fine-structure detection
The audibility of phase changes is frequently ascribed to the
capability of the ear to code and detect changes in the time structure
of the signal, since this is the only clue to explain phase effects in
a linear system (Mathes and Miller, 1947, de Boer, 1956 and Goldstein,
1967a). Two kinds of time-structure detection may be distinguished.
The first is "fine-structure detection". This implies the detection of
prominent peaks in the time function of the acoustic signal (Schouten
et al., 1962). Such a mechanism has been frequently invoked to explain
the residue pitch. The inverse of the time interval between two
promi-nent peaks of the signal is supposed to be equal to the frequency of a
sinusoid with the same pitch as the residue pitch. According to this
argument, detection of the fine structure would result in an audible
phase effect because the time function of the signal is profoundly
changed by a phase variation. Recent investigations, however, have
pro-duced some evidence against an explanation of residue pitch in terms of
time-structure detection. Terhardt (1972) has summed up some of these
arguments. Furthermore, Houtsm-a and Goldstein (1972) have shown that
monotic interaction of frequency components is not necessary for the
perception of residue pitch. Consequently, it is improbable that phase
effects are caused by fine structure-detection since the measurements
of chapter 2 have demonstrated that the prominence of the residue pitch
changes as a function of phase. Besides, de Boer (1956) has shown that
phase changes resulting in a different fine structure but a constant
envelope are not audible. This eliminates fine-structure detection as a
major source of phase effects in three-component signals. It does not
imply, however, that the fine structure of a signal cannot be coded by
the auditory system at all. It has been shown in the literature that
fine-structure detection is a predominant factor in the localization of
a sound source for signal frequencies up to 1500 Hz (see e.g. Blauert,
1974).
The second meaning of the term "time-structure detection" is
detec-tion of the envelope of a signal by the auditory system. The sensitivity
of the ear to envelope changes can be readily demonstrated by modulating
a pure tone of e.g. 2000 Hz with a sinusoid of 10 Hz. The instantaneous
amplitude variations are then audible. It is obvious that variations of
the envelope due to changes of the phases in a three-component signal
will also be audible if the frequency Af is of the order of 10 H z . It
will become increasingly difficult to detect the changes in the envelope
if the value of Af increases. Thus, for small values of Af envelope
detection is apparently an important source of phase effects. The shape
of the envelope of a three-component signal as a function of phase is
therefore studied in greater detail in the next section,
3.1.2. Envelope changes as a function of phase in a three-component
signal
A three-component signal with frequency components at equal
separations Af can be written as:
S(t)=Acos((io -Au)t+p.)+Bcos(u t+P2)+Ccos ( ((o^+Au) t+p„) (3.1)
where S(t) is the instantaneous value of the acoustic signal,
(J) =2IIf , A(jj=2nAf and A, B and C are amplitudes. The envelope of
the signal is given by:
E(t) = |Aexp(j((jj^-Au)t+jpj)+Bexp(ju^t+jp2)+Cexp(j(a)^+Aa))t+jp2)| (3.2)
E(t)=|Aexp(j(-Au)t+Pj))+Bexp(jp2)+Cexp(j(Aojt+P2))| (3.3)
The three terms of equation(3.3)may each be represented as a phasor in
a complex plane (see Fig.3.1). The varying amplitude of the envelope is
represented by the length of the resultant E which varies as its tip
travels round the ellipse (see Goldstein, 1967a). Obviously, this
length does not depend on a rotation of the coordinate axes in the
Fig.3.1.
Phasor diagram to illus-trate the time dependence of the envelope E(t) of a three-component signal given in equation(3.3) .
determined by the values of A, B and C and by the phase 9 where
9=p.-(p.+p,)/2, The invariance of the envelope for constant 0
corres-ponds to the inaudibility of phase changes under these conditions as
formulated in the phase rule of de Boer (1956),
In order to illustrate the type of envelope changes that occur as
a function of 9, Fig.3.2 gives the phasor diagrams, the spectra and the
envelopes of an AM and a QFM signal. For both signals A=B/2=C but 9=0
for AM and 6=90 for QFM sounds. The envelope of the QFM signal shows
twice the periodicity of the AM case. This doubling is audible as a
doubling of the tempo of the "rattle" or the "roughness" for small values
of Af. The changes in the envelope due to phase changes will be smaller
if A and C are small compared to B. This is the case for decreasing
values of L in the experiments on the audibility region in section 1.2.
de Boer (1956) showed that arbitrary changes in the phases p , p„
and p in a three-component signal leaves the envelope intact if Ae=0°.
However, this does not imply that the envelope is always changed if 9
is varied. Consider for instance a three-component signal with L=-6 dB
and change the phase 9 from +60 to -60 . The phasor diagram.s of Fig,3,3
show that in this case too the envelope is unaffected. This may be
generalized to all signals with equal amplitudes of the highest and the
lowest frequency component. A phase change from 6=9, to 9=-9 does not
affect the envelope. Closer consideration of the effect of such a
symmetrical change in 9 reveals that the change results in a reversal of
AMsignal ENVELOPE SPECTRUM PHASOR DIAGRAM
Im
9 = 0°
Re
QFM signal ENVELOPE SPECTRUM PHASOR DIAGRAM
Im
9=90"
Re
Fig.3.2. The envelopes of AM and QFM sounds, as derived from the phasor diagrams. In this case the ellipse of Fig.3.1 has become a straight line because A=C.
Fig.3.3.
Phasor diagrams showing that the time dependence of E, as
its tip travels along the dashed line, is the same for 9=+6, and 9=-e..
the envelope in time. Such a reversal does not affect the envelope if
the sidebands in a three-component signal are equal, because of the
symmetry of the envelope in that condition. These signals are suitable
for investigation of whether the audibility of a phase change is indeed
due to a change in the envelope, as might be concluded from de Boer's
phase rule. In other words, an experiment can be performed to
investi-gate whether de Boer's phase rule justifies the conclusion that the
envelope. If the subjective character of a sound is completely
deter-mined by the envelope of the acoustic signal and its frequency spectrum,
then we may expect that "symmetrical" phase changes, not obeying the
phase rule but leaving the envelope intact, will be inaudible. This will
certainly be the case for very small frequency separations between the
components of the complex (large period of the envelope) but it is not
self-evident for larger values of Af.
3.1.3.
The audibility of differences between signals with identical
envelopes
Three-component signals with a centre frequency f and a frequency
separation Af were used in a psychophysical experiment on the audibility
of a difference between two signals for which the values of 6 were
opposite. The level of the sidebands was 6 dB below the level of the
central frequency component. The signals were generated with the set-up
given in Fig.3.4. sine generator program. generator phase lock generator •c Af ^Sl nhncD shift
'\
?
X
^c -01 phase shift-|-tnree-comp signal e=+9i
+
three comp e i n o o l Q - Q. -"•J-"-" " " 1 Fig.3.4. Block diagram of the experimental set-up for inves-tigation ofdifferences between signals with
opposite values of
The observer was seated in an acoustically isolated booth and
manipula-ted a switch to select one of the two stationary signals. He also had
two push-buttons at his disposal to indicate whether the signals sounded
equal or different. He listened to the signals as long as he wanted. In
one experimental session 6 different values of Af were investigated viz.
Af=8, 16, 3 2 , 64, 128 and 256 H z . The frequency of a programmable
oscillator (Krone Kite 4131 R) was set by a DEC Lab-8E computer at one
of the randomly chosen possible values of Af. The observer's choices
were also registrated by this computer. Each value of Af was selected
6 times in one session. The reliability of the responses has been checked
by presenting not only the two signals with opposite phase but also
two completely identical signals. The results for these "reliability
signals" indicate whether the observer is biased in calling the two
signals different. Three different values of f were used, f =1000, c c
2000 and 4000 H z . Each observer made 5 complete runs for every value of
f . In all signals the level of the central frequency component has been
chosen at approximately 50 dB SL and 9=60 or 9=-60 . The results are
given in Fig.3.5 for three observers. The scores for the 5 sessions have
been added to give a total of 30 presentations for every value of Af.
The "reliability check" was performed 10 times for every value of Af.
The results do not show any appreciable bias of the observers. The
occasions on which two identical signals were judged different were so
rare that they can be ascribed to mistakes. A similar measurement was
carried out for 6=30 and f =2000 Hz in order to show that the results c
are not specific for 6=60 . The results for this signal and with two
observers are also given in Fig.3.5.
The data show that two signals with opposite phase 6 are
indistin-guishable if the frequency separation Af is smaller than 30 Hz.
Consequently, the sensation evoked by these signals is determined by the
frequency spectrum and the envelope only. There are two possible
expla-nations for the subjective difference between the signals if Af is
larger than 30 Hz. The first is that apparently the observed phase
effects are not due to envelope detection by the ear but to some other
mechanism based on nonlinear signal processing as elaborated in the next
section. Alternatively, the envelope, as coded in the action potentials
of the nerves, may not be the same as the envelope of the acoustic
signal. This reasoning is inspired by the finding, confirmed by all
observers independently that for e.g. f =1000 Hz and Af=64 Hz, a
dis-tinct difference in roughness is audible between the signals with
oppo-site values of 6. The roughness of a sound is apparently not uniquely
determined by the envelope of the acoustical signal but by some
30 20 10' 0 f^=1000Hz,9=60 obsJR yA
/
\
/ ^
« r - / - - 9 " ^ " ° " " ' ° f^=1000Hz,9z60 nl ObsTB 16 64 255 f^=1000Hz,9 = 60 ObsFB 64 256 15 64 256H2 30 20-lOj 0 fc=2000Hz,9=60 obsJR f^=2000H2,9=50 ObsTB 16 64 255 f^=2000Hz,9=60 O b s F B 15 64 2 5 5 H z f|,=4000Hz,9=50 obs J.R 30 20 10' 0 f^=4000Hz,9=60 ObsTB 16 64 255 fj.=4000Hz,9 = 6 0 -,1 O b s F B 256 30" 20 10 f^=2000Hz,9=30 ObsJR Fig.3.5. 256 f^=2000Hz,9=30 ObsTB 255Results of the experiment on the audibility of a d i f -ference between signals with opposite values of 6. The abscissa is the frequency separation A f . The number of times an observer judged the two signals to be differ-ent is the ordinate. The dashed lines represdiffer-ent the results of the "reliability" signals (see t e x t ) .
