Thursday, 27 May 2010

Rayleigh Duplex Theory

Duplex theory, as proposed by Lord Rayleigh, describes sound reaching the two ears as Interaural Time Differences (ITD) and Interaural Level Differences (ILD).

In the figure to the right, the path difference from the source to each ear is different, the distance from the source to the left ear is greater than the distance of the source to the right ear. The difference between these two path differences represented as time gives us the Interaural Time Difference (ITD).

The ITD is the dominant cue for frequencies at 1.5kHz or below and the ILD is more dominant for frequencies greater than 1.5kHZ. The ILD is produced due to shadowing of the head and this only occurs for greater frequencies that do not diffract around the head, creating a shadow similar to the shadow casted by light.
(image above from SternWangBrown, chapter 5, Binaural Sound Localization - Found in Links)
An experiment was conducted to verify Rayleigh's Duplex theory within an anechoic environment, having the source and binaural head a distance of 1.75 meters apart. Using four pure tones created in Csound for 125kHz, 250kHz, 500kHz and 1000kHz and the source directed at 0 degrees, 10 degrees, 30 degrees, 50 degrees, 70 degrees and 90
degrees, Rayleigh's Duplex theory for sound localization was verified.

The graph on the left is an image of the left and right binaural microphones detecting a 1000kHz pure tone single source signal approximately 1.75m away (top -left ear, bottom - right ear). As you can clearly see from this image, the two channels are out of phase with one another and that the bottom channel is delayed in comparison to the channel above. The ITD of this complete signal is 0.735milliseconds and is the maximum ITD achievable by the system since the front center of the dummy head is perpendicular to the source.

The value 0.735milliseconds could be too great a ITD, "the maximum possible ITD is about 0.66milliseconds for a typical human head size" (Computational Auditory Scene Analysis, Chapter 5, Binaural Sound Localization, DeLiang Wang and Guy J. Brown(eds.) 2005). Another paper states "a sound that is at 90 degrees to the right will create an ITD of about 0.7milliseconds" (Cochlea, Binaural Hearing, Ruth Y. Litovsky, Ph.D., Feb, 2008), showing that the differences in the average human head size have created a uncertainty in the value for the maximum possible ITD. If this value is too great, the microphones will have to be placed deeper into the dummy head to decrease the distance that they are space apart.

When comparing the binaural signal of 125kHz and 1000kHz at an angle from the source of 90 degree, the
detected signal clearly shows how the ILD differs in frequency. The 125kHz signal is the picture on the right and 1000kHz signal is the picture below on the left. When the frequency of the signal climbs above 1.5kHz, the ILD will dominate as the ITD's will be a lot smaller until they are almost negligible.

The physics behind this phenomena explains that as the frequency of the source increases, the waves will be much closer together. When the waves are much closer together, there ability to bend around objects becomes weaker. Of course, the size of the object and the frequency of the source have a diffraction relationship, but binaural perception has a standard object size, the average human head. There will be slight differences for each individual, as each individual has their own unique head shape and size, creating their own unique frequency shadow that differs the intensity at the obscured ear ever so slightly.

(picture above -

The experiment was carried out using Bandpass Noise for frequencies 125Hz to 4kHz. The results are displayed in the graph below, showing how the Interaural Time Difference decreases slightly as the center frequency is increased.

Tuesday, 25 May 2010

Csound Programs

Pure Tone Programs

Orchestra File

; 125 Hz frequency tone
;440 Hz sine wave at amplitude 10000

sr = 44100
kr = 11025
ksmps = 4
nchnls = 2

instr 1
idur = p3
a1 oscil 10000,125,1

;The number in bold is changed for each frequency

outs a1, a1


Score File

; 5 seconds score

f1 0 4096 10 1 ; use gen 10 to compute a sine wave
i1 0 5 ; run "inst 1" fom time 0 for 5 seconds
e ; end of score

Bandpass Noise Programs

;Orchestra File for Bandpass Noise
;Referenced from Clive Greated Example 15 - APSS - Edinburgh 2010

sr = 44100
kr = 11025
ksmps = 4
nchnls = 2

instr 2
icf = p5
ibw = p6
anoise rand p4
afilt reson anoise, icf, ibw
outs afilt,afilt

;Score File for BandPass Noise
;References from Clive Greated - example 15 - Edinburgh University - APSS - 2010 FM with varying harmonicity ratio

f1 0 4096 10 1
; use gen 10 to compute a sine wave

;ins st dur amp cf bw
i 2 0 3 10 125 10
i 2 6 3 25 250 20
i 2 12 3 62.5 500 40
i 2 18 3 156 1000 80
i 2 24 3 200 1500 100
i 2 30 3 391 2000 160
i 2 36 3 450 2500 200
i 2 42 3 600 3000 250
i 2 48 3 800 3500 290

i 2 54 3 976 4000 320
; end of score

Equipment notes

- Binaural Microphones
- Dummy Head
- 360 degree azimuthal angle measuring plate
- Laptop for recording
- Audacity (recording software)
- Ipod for playing tones
- (tones created using Csound)
- Dynamic Speaker
- Two stands (one for dummy head, the other for speaker)
- Mixer
- Access to Anechoic Chamber
- Two small to big jack adapters
- One big to small jack adapter
- Stereo to small jack lead
- Jack to jack lead
- Portable solid state recorder, marantz PMD660
- Soundman in ear microphones, Binaural frequency weigthing


-Quicktime pro

Sunday, 23 May 2010

Project Outline


Investigation into Rayleigh's Duplex theory and the Doppler effect using Binaural Microphones inserted into a dummy head within an anechoic environment. Tones are created in Csound and played through a loudspeaker at a set distance and set angle from the dummy head. To keep things simple, the source will only lie along the azimuth angle of the dummy head, this allows us to focus on the binaural cues that are the basis of Rayleigh's Duplex theory.

Once confirming Rayleigh's Duplex theory, an investigation into the relationship between the Doppler effect and Interaural Time Differences (ITD) will be setup using a moving source along the horizontal plane.


The recordings taken with the binaural microphones will be analysed, represented in Csound using the ILDs, ITDs and IPDs of a range of tones, played back through headphones and compared to the binaural recording, synthesizing both the Duplex theory and the Doppler effect.

Saturday, 22 May 2010


Cochlear, Binaural Hearing, Ruth Y. Litovsky Ph.D, February, 2008

(Duplex Theory, Haas Effect)

This paper gives a brief description of the binaural cues in sound localization, exploring the difference between Interaural Time Differences and Interaural Level diferences and briefly touching on intermediate frequencies that are hard to localize.

The paper extends into the auditory pathways of the left and right cochlea, how sound is introduced at the level of the superior olive complex and how ITDs and ILDs are combined in the inferior colliculus.

It also explores masking tones, unmasking tones and signal to noise ratio, allowing the listener to distinguish a voice in a noisy environment.

  1. "a sound that is 90 degrees to the right will create an ITD of about 0.7ms"
  2. "stimuli in the intermediate region fall in a gray area and may be hard to localize"


Binaural Source Localization by Joint Estimation of ILD and ITD, Matin Raspaud, Harald Viste and Gianpaolo Evangelista, senior member, IEEE, January, 2010

(Duplex Theory, Haas effect, Precedence effect, HRTF)

This paper gives a description of ITD and ILD, computes the two cues from a two-channel time-frequency representation and are combined to estimate the azimuthal angle of sources in binaural space.

A parametric model for ITD and ILD is used

An average parametric for HRIR's is used

Several experiments that validate this approach are conducted to show how models are favoured in available techniques.


Additive Versus Multiplicative Combination of Differences of Interaural Time and Intensity, Samuel H. Tao, Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1992
Additive versus multiplicative

This paper uses the position-variable model to describe the subjective lateralization of tones and bandpass noise.

Experiments include:

  • A tone that covers a wide range of frequencies that give a small ITD and no ILD.
  • A 500Hz tone over a range of ITD's and ILD's
  • Warble tones with a 500Hz center frequency over a range of different bandwidths and ILD's using one of four combinations of ITD's and IPD's
This paper references experiments conducted by Domnitz and Colburn, showing that the subjective position depends jointly on ITDs and ILDs.

Better results were obtained from the warble tones using additive intensity weighting - the predicted position with an intensity difference is a proportional offset of the ILD from the predicted position with no IID.


Introduction to Head-Related Transfer Functions (HRTF's): Representation of HRTF's in Time, Frequency and Space, Corey I.Cheng, Gregory H. Wakefield, University of Michigan, USA, April, 2001

In this paper, head related transfer functions are introduced and treated with respect to their role in the synthesis of spatial sound over headphones. It describes frequencies localized along the azimuthal plane and ambiguity around 1500Hz, where the wavelength becomes comparable to the diameter of the observers head. Head shadowing effects are explained above this frequency that give rise to interaural intensity differences

The paper notes the 'cone of confusion' from the work of Hornbostel and Wertheimer (1920), where unique spatial positions are not given by ITDS and ILDs as there is ambiguity of an infinite number of equi-distant points from the observer.

Typical HRTF measurement strategies are described, and simple applications of HRTFs to headphone-based spatialized sound synthesis are given.

By comparing and contrasting respresentations of HRTFs in the time, frequency and spatial domains, different analytic and signal processing techniques used to investigate the structure of HRTFs are highlighted.


Computational Auditory Scene Analysis, Chapter 5, Binaural Sound Localization, DeLiang Wang and Guy J. Brown (eds.) ISBN 0-471-45435-4, 2005
SternWangBrownChapter Binaural Sound Localization

This paper is useful for providing a good solid background to Binaural Sound Localization.

Physical cues and physiological mechanisms that are involved in auditory localization are explain in depth, defining the lateralization of a binaural signal as a periodic function of the ITD with a period equal to the reciprocal of the center frequency.

"If a low-frequency tone and a broadband masker are presented monaurally, the threshold SNR that is obtained will generally depend on various stimulus presented such as target duration and frequency, and the masker bandwidth" (5.4.2 - classical binaural detection)

Includes a great amount of information on the various models of Binaural perception, starting with the Jeffress hypothesis model (picture on home page), the equalization-cancellation model, cross correlation-based models of binaural interaction, Lindermann's model and Breebaart's model stating any extensions added by other researchers.

  1. "since the maximum possible ITD is about 0.66ms for a human head of typical size"
Ma, Lianxi, Junjun Yang and Jiacai Nic. Doppler Effect of Mechanical Waves and Light. Lat. Am. J. Phys. Educ. Vol. 3. No. 3. 2009. hhtp/ pp 550-552

This paper explores doppler effect of mechanical waves when the relative velocity is along the wave vector and when it is not. The geometric relationship described in this paper is necessary for explaining the frequency change of the source traveling parallel to the wave vector and the mathematics, for creating this effect in Csound.

It demonstrates the frequency ratio as a function of time and plots this result. This is necessary for predicting the small changes in frequency as the source passes the observer and can be easily plotted with respect to change in angle instead to provide a more suitable representation.


Doppler Effect

Kinsler, E. Lawrence, Austin. R. Frey, Alan. B. Coppens and James. V. Sanders. Fundamentals of Acoustics. Fourth Edition. 2000. USA. John Wiley and Sons. pp 453-455

Chapter 15, pages 453 to 455 gives a mathematical representation of doppler effect and describes briefly, the physics behind it's derivation.

Kuttruff, Heinrich. Acoustics - An Introduction. 2004. Albingdox, Oxon. Taylor and Francis. pp 74,75

Chapter 5, page 74 explains the Doppler effect as a change in frequency that occurs when either the source, observer or both are moving relative to one another.

It describes a source moving away from an observer and an observer moving towards a resting source, as expansion or contraction of the sound's frequency.
(the mathematical relationship for doppler effect was adapted from this chapter)

Wood, Alexander. Acoustics. 1940. Scotland, Glasgow. Blackie and Sons, Ltd. pp324-328

Alexander Wood defines Doppler's principal in chapter 12, pages 324 to 328, beginning with the history of it's applications, the effect of motion of the medium, motion of the source and motion of the observer.

The effect of a sound source that is traveling in a straight line, which does not pass through the observer is described mathematically and the change in frequency for this event is plotted, frequency ratio against time. (this plot is useful, frequency ratio with respect to angle instead)

Binaural Localization

Kuttruff, Heinrich. Acoustics - An Introduction. 2004. Albingdox, Oxon. Taylor and Francis. pp 252-256

Everest, Alton. F and Ken. C. Pohlmann. Master handbook of Acoustics. 2001. USA. The McGraw Hill Companies. pp 64-69