Detection of Phase Shifts in Harmonically Related,
`Tones*
`
`RICHARD C. CABOT, MICHAEL G. MINO, DOUGLASA. DORANS,IRA S. TACKEL, AND HENRYE. BREED
`
`Acoustics Research Laboratory, Rensselaer Polytechnic Institute, Troy, NY 12181
`
`The results of tests on the audibility of phase shifts in two componentoctave complexesare
`described. The tests were made via headphones with fundamental and third-harmonic signals.
`The quantitative results were compared with those of previous researchers, and a detailed
`discussion ofthe responses ofa group oflisteners is presented.
`
`Wevi’Ber
`~en6§.
`
`
`
`INTRODUCTION: Theaudibility of phase shifts in har-
`monically related tones has been a topic of discussion for
`many years. Before the advent of electronic instrumenta-
`tion, Helmholtz ran crude experiments to show that phase
`shifts were not audible. Further tests of this were made by
`Hansen and Madsen[1], Raiford and Schubert [2], Craig
`and Jeffress [3], and Mathes and Miller [4].
`Mathes and Miller [4] used sinusoidsofslightly different
`than harmonic frequency multiples. The quality or tonal
`character of the sound was judged to change with time as
`the relative phasesofthe sinusoidal signals changed. Craig
`and Jeffress [3] investigated the audibility of phase rever-
`sals of the harmonics ofa test signal. Their listeners re-
`quired extensive training sessions, and the resultant accu-
`racy of detection was only slightly better than chance.
`Raiford and Schubert [2] used a specially designed timing
`circuit to control the signal presentations. Hansen and Mad-
`sen [1] used an entirely different approachto the generation
`of a test signal, a three-component signal, generated by
`gating a sine wave.
`The testing methods used by previous experimenters do
`not appearto give the listener the most convenient method
`of comparison. Wefelt it would be more informative to
`allow thelistener complete controloverall timing ofsignal
`presentations.
`In our approach the listener controlled the
`audition intervals of both the reference and comparison
`signals. Careful note wastaken ofthe length and numberof
`audition intervals chosen bylisteners, and someinteresting
`trends were noted.
`
`
`* Presented October 31, 1975, at the 52nd Conventionofthe
`Audio Engineering Society, NewYork.
`568
`
`
`
`EQUIPMENT
`
`The apparatus used in the experimentis diagrammedin
`Fig. |. The Fourier synthesizer produces phase-locked sig-
`nals in multiples of 400 Hz. The 400-Hz and 1200-Hz
`outputs are used, with their levels monitored bya Balantine
`model 320linear dB-scale voltmeter. The 1200-Hz output
`is fed to an adjustable passive phase shifter. The phase
`difference betweeninput and outputof the phase shifter is
`monitored with a phase meter. One channel of a Crown
`DC-300-A amplifier is fed a mixture of the fundamental
`(400 Hz) and the third-harmonic (1200 Hz) signals. The
`other channel is fed with a mixture of the fundamental and
`the phase-shifted third-harmonic signals.
`The outputs of the amplifier are connected via a four-
`position switch, the relay inputselector, toa reed relay. The
`relay operationis controlled by the listener, allowing him to
`make A-—B comparisons. The signals which the listener
`received as A or B are shownin Table I for each position of
`the relay input selector. Fig. 2 shows the appearance of a
`phase-shifted and unshifted waveform andthe definition of
`the phase shift 6. The signal from therelay inputselectoris
`fed to an oscilloscope and an rms voltmeter for monitoring
`the shape and amplitude of the waveform. The output then
`goes through the feed switch to a pair of Koss ESP-9
`~ electrostatic headphones.
`level was adjusted to three
`The 400-Hz fundamental
`times the 1200-Hzthird-harmoniclevel. This relationship
`waschosen becauseit is the amplituderatio ofthe first two
`Fourier components of a square wave. The sound pressure
`level of the signal reaching the listener’s ears was 70 dB as
`computed from the manufacturer’s sensitivity specifica-
`tions. The equipmentwastested in operation with a Hewlett
`JOURNAL OF THE AUDIO ENGINEERING SOCIETY
`Sony Exhibit 1006
`Sony Exhibit 1006
`Sony v. MZ Audio
`Sony v. MZ Audio
`
`

`

`pair with the third harmonic shifted 0° and 120° waspre-
`sented to the subject for comparison. He was simultane-
`ously shown anoscilloscope presentation of the signal he
`had selected. This was intended to acquaint the subject with
`the subtlety of the differences to be detected. The subject
`wasnot allowedto see the oscilloscope during the remain-
`der of the experiment. The subjects tested were college
`students, male and female, ranging in age from 18 to 25
`years.
`
`ANALYSIS
`
`In orderto determinethe ability of the subjects to discern
`phase distortion and place a measure on the threshold of
`phase discrimination, a means of analyzing the YES and
`NOresponsesis needed. The authors chose to use a method
`first used by Blackwell [5].
`It has been found that when subjects are asked to make a
`YES-—NOdiscrimination of any test stimulus, they may
`respond YES in the absence of any actual difference. The
`subject is in effect giving a false positive response or what
`weshall term a false alarm. To obtain a measure ofthis
`tendency, stimulus pairs of identical composition (equal or
`zero phase shift in the third harmonic of both signals A and
`B) were included at random in the experiment. These pre-
`sentations are commonly known as “‘blanks’’ or ‘‘duds”’
`and a YES response to these is termed a false alarm.
`The observed YES responses may then be due to both a
`perceived difference and the random error represented by
`the false alarm rate. Denoting the probability of a false
`alarm as P;, and the probability of an observed YESre-
`sponse by Py, we may write (see [5])
`
`Po =P + PC — Pra)
`
`(1)
`
`where P is the probability of a perceived difference by a
`
`FUNDAMENTAL 40OHZ
`COMPOSITE SIGNAL
`RD HARMONIC 1200 HZ
`
`
`
`
`
`
`
`Packard spectrum analyzer and was found to contain less
`than 0.1% intermodulation and harmonic distortion. More
`importantly, the distortion content was independentof the
`relay input selectorposition or the phaseshift selected. The
`equipmentwaslocated in a room adjacentto the listener to
`avoid distractions.
`
`PROCEDURE
`
`The following procedure for gathering data was chosen
`for clarity and ease of duplication. The phaseof the adjust-
`able composite signal and the position of the relay input
`selector wereset for the first test item. The signal was then
`applied to the headphones. Thelistener was allowed to
`comparethe twosignal presentations with the A—B switch
`until satisfied that a difference was or was not perceived
`between them. Nolimit was placed on the time available or
`the number of A —B comparisons forthe listener to make his
`decision.
`His response, YES or NO, was recorded by the experi-
`menter who then disconnected the signal source from the
`headphones. The phaseof the adjustable signal as well as
`the position of the relay input selector were thenset for the
`nexttest item. The composite signal was again connected to
`the headphones. Thus nosignal was present between suc-
`cessivetrials.
`This procedure was repeated thirty times per experiment
`for each subject. The range of the phaseshift 6 was limited
`to 0°—120° in increments of 30° in the first experiment. It
`was reduced to 0°—30° in increments of 7.5° in the second
`experiment. The orderof the signal presentations wasran-
`domizedto prevent biasing of the results. Total experiment
`time ranged from eight to twenty minutesfor the subjects to
`complete one set of 30 signal pairs.
`Priorto initiating thesetoftrials foreach subject, a signal
`
`RELAY INPUT
`SELECTOR
`
`FEED SWITCH
`
`
`SIZER_|I2O00HZ) -
`
`
`
`
`CROWN DC-300A
`we SWITCH
`
` AMPLIFIER
`
`SYSTEM BLOCK DIAGRAM
`
`Fig. 1. Schematic block diagram.
`
`Table I. Function of the relay input selector.
`
`Switch
`Composite Signal Pair
`Position
`A*
`B*
`
`
`|
`2
`3
`4
`
`400 +1200 20°
`400+1200 26°
`
`400 +1200 20°
`400+1200 20°
`
`400+1200 20°
`400+1200 20°
`400+1200 20°
`400+1200 20°
`
`* Frequencies in hertz.
`
`SEPTEMBER 1976, VOLUME 24, NUMBER 7
`
`
`
`UNSHIFTED WAVEFORM
`HEADPHONESa|
`
`Q
`oO
`a
`
`
`
`EUNDAMENTAL 400HZ
`
`COMPOSITE SIGNAL
`
`3RD HARMONIC 1200 HZ
`
`SHIFTED WAVEFORM
`
`b
`
`Fig. 2. Appearance ofphase-shifted and unshifted waveform.
`a. Unshifted waveform. b. Shifted waveform.
`
`569
`
`

`

`
`
`
`
`RICHARD CABOT, MICHAEL MENO, DOUGLAS DORANS,IRA TACKEL AND HENRY BREED
`
`
`essga< -r=y—8.
`
`subject with zero false alarm rate. The data are groupedinto
`classes for each particular phase shift. Values of P») were
`computed for each class by dividing the total number of
`YES responses for all subjects in that class by the total
`number of responses.
`The values of P;, for each phase shift were computed by
`dividing the number of YES responsesto pairs of equal
`phase shift by the numberofsuch pairs. By rearranging Eq.
`(1) P may be found in terms of Py and Pra:
`
`P= Pip = Pegill = Pig).
`
`(2)
`
`The values of P, Py, and P;, are given in Table II for each
`value of phase shift. The computed values ofthe probability
`of a perceived difference are graphed asa function of6 in
`Fig. 3. The P(@) points for @ less than thirty degrees are
`circles to indicate that
`they were derived in a separate
`experiment.
`
`OBSERVATIONS AND DISCUSSION
`
`The described experimental results were obtained after
`modifications to the test procedure and equipment were
`made.
`Initially the experiment was conducted with a
`medium-power switching relay used after the relay input
`selector. The switching of the relay controlled by the sub-
`Ject caused an audibletransientin the signal perceived anda
`brief interval of silence. This was found to confuse the
`listener and makeit impossible to discriminate the intended
`stimulus better than predicted by the false alarm probability
`calculated. Whether this was due to the switchingtransient
`or the silent interval was not determined. This would seem
`to indicate that the listener’s memoryof the first presenta-
`tion is either destroyed by the transient or lost during the
`interval of silence.
`The relay was then replaced with a reed delay and the
`experiment was repeated. The problems described with the
`original
`relay were considerably reduced, as was the
`difficulty in making accurate judgments by the listener. The
`subjects, initially, had difficulty in determining whatit was
`they werelistening for. Thefirst subjects refused to believe
`that there was a difference until they were shown traces of
`the signals on an oscilloscope. After this it became standard
`practice to present the subject with a 0°— 120° phase-shifted
`pair at the beginning of the experiment and allow himto
`
`Table II. Test data.
`
`Phase
`Shift 6
`(degrees)
`
`Dectection
`Rate Py
`(%)
`
`Experiment 1, 15 Subjects
`0
`23
`30
`83
`60
`92
`90
`85
`120
`92
`
`Experiment 2, 5 Subjects
`0
`55
`7.5
`53
`15
`80.
`22.5
`83
`
`False
`Alarm
`Rate Pr,
`(%)
`
`Pp
`
`Corrected
`Rate P
`(%)
`
`23
`33
`27
`23
`27
`
`55
`52
`63
`58
`
`0
`15
`89
`81
`89
`
`0
`2
`46
`60
`
`view the signal on the oscilloscope. The oscilloscope was
`not available to be viewed for the remainderof the experi-
`ment.
`
`Thelisteners had complete control of the length of time
`each signal in the A—B pair was presented. They were told
`to operate the A—B switch as often and as long as they
`desired. A pattern seemed to develop whereby the subjects
`listened to the first signal of the pair for a comparatively
`long time, then depressed the A—B switch for a relatively
`short time andreleasedit againto listento the original. This
`wasrepeated about twice for each signalpair. This pattern
`correlates with some previous experiments in detecting
`phase shifts using similar techniques. Craig and Jeffress [3]
`presented their subjects with similar A and B signals for
`relatively long preset durations of each. They reported that
`their listeners were unable to detect a 180° phaseshift in this
`same— differenttest arrangement. Raiford and Schubert [2]
`were able to obtain reliable data by using a special timing
`arrangement. The reference waspresented fora relatively
`long time, followed by the secondsignal for a short time,
`and then the reference was presented again. The timing of
`the on-off periods was not underthe listener’s control, but
`was preset by the experimenter.. Nixon, Raiford, and
`Schubert [6] had reportedin an earlier papertheir discovery
`of the optimum timing used in their experiment and its
`usefulness in allowing phase shift detection. It is interesting
`to note that the timing chosen by ourlisteners and that
`selected by Raiford and Schubert were very similar.
`The experiment showsphase shifts of harmonic com-
`plexes to be detectable, but judging from the difficulty
`experienced by the subjects, the effect appear to be small.
`Forthe frequencies and level used, the ear is incapable of
`detecting less than about 15° of phase shift. This correlates
`well with the results of Hansen and Madsenfor the same
`frequencies and level. Considering different test methods
`used, this fact supports the reliability of both experiments.
`The experiment was performed for phase-shift increments
`of 30°, and it was foundthat a 30° shift wasstill fairly well
`recognized. The experiment wasthen repeated with phase-
`shift increments of 7.5° ranging from zero to 30°. The data
`
`
`
`x
`
`—x
`
`x
`
`¥
`
`/
`
`100--
`
`75+
`
`so+
`
`2+
`
`75
`
`+——_+—_+
`15
`225
`30
`
`—
`60
`PHASE DEGREES
`
`t
`90
`
`x
`
`—
`120
`
`Fig. 3. Computed values of the probability of a perceived
`difference.
`
`JOURNAL OF THE AUDIO ENGINEERING SOCIETY
`
`
`
`

`

`‘DETECTION OF PHASE SHIFTS IN HARMONICALLY RELATED TONES
`
`Department for many helpful suggestions on analyzing the
`data. They would also like to thank Dr. A. Bruce Carlson
`and Dr. Thomas Shannon for the loan of equipment from
`their departments.
`
`REFERENCES
`
`from the two experiments were then combinedto obtain the
`final graph. Not as manysubjects weretested for the second
`experiment because we werealready satisfied that a differ-
`ence could be reliably perceived, and wedid notfeel it was
`necessary to use as large a sample. The false alarm rate for
`the second experiment was muchhigherthanthatofthe first
`experiment. This maybeattributed to a smaller sample and
`confusion of the subject
`in attempting to make a finer:
`discrimination. The signal pairs presented were much more
`alike, and detecting a difference was more difficult. Thus
`the resulting confusion may have led to more guessing.
`
`CONCLUSIONS
`
`A measurementof the audibility of phase shifts in har-
`monic complexes has been presented. The results, both
`quantitative and qualitative, correlate well with those of
`previous researchers using both similar and very different
`experimental techniques. Although differences were de-
`tectable, they were subtle. This raises the question of its
`audibility compared to the more familiar forms of distor-
`tion.
`
`ACKNOWLEDGMENT
`
`The authors would like to express their gratitude to
`Crown International Radio and Electronics for their
`generosity in supplying equipmentused in the experiments.
`They wish to thank Dr. G. Kandel of the RPI Psychology
`
`[1] V. Hansen and E. R. Madsen, *‘On Aural Phase
`Detection: Parts | and 2,’’ J. Audio Eng. Soc., vol. 22, pp.
`10-14 (Jan./Feb. 1974); pp. 783-788 (Dec. 1974).
`[2] C. A. Raiford and E. D. Schuberts, ‘*‘Recognition of
`Phase Changes in Octave Complexes,”’ J. Acous. Soc.
`Am., vol. 50, pp. 559-567, (1971).
`[3] J. H. Craig and L. A. Jeffress, ‘‘Effect of Phase on
`the Quality of a Two Component Tone,”’ J. Acoust. Soc.
`Am., vol. 34, pp. 1752-1760 (1962).
`[4] R. C. Mathes and R. L. Miller, ‘‘Phase Effects in
`Monaural Perception,”’ J. Acoust. Soc. Am., vol. 19, pp.
`780-797 (1947).
`[5] H. R. Blackwell, ‘‘Nerval Theories of Simple Vis-
`ual Discrimination,”’ J. Opt. Soc. Am., vol. 53, pp. 129-
`160 (1963).
`[6] J. C. Nixon, C. A. Raiford, and E. D. Schubert,
`“*Technique for Investigating Monaural Phase Effects,’’ J.
`Acoust. Soc. Am., vol. 48, pp. 554-556 (1970).
`[7] J. H. Craig and L. A. Jeffress, ‘*Why Helmholtz
`Couldn’t Hear Monaural Phase Effects,’’ J. Acoust. Soc.
`Am., vol. 32, pp. 884-885 (1960).
`‘‘Effect of
`[8] R. Plomp and H. J: M. Steeneken,
`Phase on the Timbre of Complex Tones,” J. Acoust. Soc.
`Am., vol. 46, pp. 409-421 (1969).
`
`and Sigma Xi.
`
`THE AUTHORS
`
`Richard C. Cabot was born in Newark, N.J.,in 1955. He
`received the B.S. degree (cum laude) and the M. Eng.
`degree in electrical engineering from Rensselaer
`Polytechnic Institute, Troy, N.Y.,
`in 1975.
`In 1976 he
`received the M.S degree in mechanics also from Rensselaer
`Polytechnic Institute. He has completed all course re-
`quirements for a Ph.D. degreein electrical engineering and
`is currently engaged in thesis research for that degree.
`Mr. Cabotis a student memberof the Audio Engineering
`Society, S.B.E.,1.S.A., and 1.E.E.E. He is a memberof
`Tau Beta Pi and Eta Kappa Nuand an associate member
`of Sigma Xi. He is currently chairman of the Rensselaer
`Polytechnic Institute student section of the I.E.E.E. and
`vice-president of the Rensselaer Polytechnic Institute
`chapter of Eta Kappa Nu.
`
`Michael G. Mino was born in Hamburg, New York, in
`1954 and received the B.S. degree (cumlaude) in electrical
`engineering from Rensselaer Polytechnic Institute, Troy,
`N.Y.,in 1975. He received the M. Eng. degreein electrical
`engineering from Rensselaer Polytechnic Institute in 1976
`and is currently employed by Kodak Corporation in
`Rochester, N.Y.
`Mr. Mino is a memberof Tau Beta Pi and Eta Kappa Nu.
`
`Douglas A. Dorans was born in Staten Island, N.Y., in
`1954 and received the B.S. degree in civil engineering from
`Rensselaer Polytechnic Institute, Troy, N.Y., in 1976. He
`is pursuing an M. Eng. degree in civil engineering at
`Rensselaer Polytechnic Institute.
`Mr. Dorans is a memberof Chi Epsilon andis currently
`chairman of the Rensselaer Union Programming Board.
`
`Ira S. Tackel was born in 1954 and received the B.S.
`degree in biomedical engineering from Rensselaer Poly-
`technic Institute, Troy, N.Y.,
`in 1956. He is presently
`pursuing an M. Eng. degree in biomedical engineering at
`that Institute.
`
`e
`
`Henry E. Breed received the Ph.D. degree from Rens-
`selaer Polytechnic Institute, Troy, N.Y., in 1955, and has
`since been onthestaff of the Department of Physics there.
`His majorfield of activity has been physical optics, but he
`has been interested in acoustics. He has played cello in the
`Schenectady Symphony Orchestra.
`Dr. Breed is a member ofthe Audio Engineering Soci-
`ety, the Optical Society of America, the AmericanInstitute
`of Physics, the American Association of Physics Teachers,
`
`SEPTEMBER 1976, VOLUME 24, NUMBER 7
`
`