Directional Transfer Functions Research Articles

The acoustical cues to sound location in the guinea pig (Cavia porcellus)

There are three main acoustical cues to sound location, each attributable to space- and frequency-dependent filtering of the propagating sound waves by the outer ears, head, and torso: Interaural differences in time (ITD) and level (ILD) as well as monaural spectral shape cues. While the guinea pig has been a common model for studying the anatomy, physiology, and behavior of binaural and spatial hearing, extensive measurements of their available acoustical cues are lacking. Here, these cues were determined from directional transfer functions (DTFs), the directional components of the head-related transfer functions, for 11 adult guinea pigs. In the frontal hemisphere, monaural spectral notches were present for frequencies from ∼10 to 20 kHz; in general, the notch frequency increased with increasing sound source elevation and in azimuth toward the contralateral ear. The maximum ITDs calculated from low-pass filtered (2 kHz cutoff frequency) DTFs were ∼250 μs, whereas the maximum ITD measured with low-frequency tone pips was over 320 μs. A spherical head model underestimates ITD magnitude under normal conditions, but closely approximates values when the pinnae were removed. Interaural level differences (ILDs) strongly depended on location and frequency; maximum ILDs were <10 dB for frequencies <4 kHz and were as large as 40 dB for frequencies >10 kHz. Removal of the pinna reduced the depth and sharpness of spectral notches, altered the acoustical axis, and reduced the acoustical gain, ITDs, and ILDs; however, spectral shape features and acoustical gain were not completely eliminated, suggesting a substantial contribution of the head and torso in altering the sounds present at the tympanic membrane.

Vertical-plane sound localization with distorted spectral cues

For human listeners, the primary cues for localization in the vertical plane are provided by the direction-dependent filtering of the pinnae, head, and upper body. Vertical-plane localization generally is accurate for broadband sounds, but when such sounds are presented at near-threshold levels or at high levels with short durations (<20 ms), the apparent location is biased toward the horizontal plane (i.e., elevation gain <1). We tested the hypothesis that these effects result in part from distorted peripheral representations of sound spectra. Human listeners indicated the apparent position of 100-ms, 50–60 dB SPL, wideband noise-burst targets by orienting their heads. The targets were synthesized in virtual auditory space and presented over headphones. Faithfully synthesized targets were interleaved with targets for which the directional transfer function spectral notches were filled in, peaks were leveled off, or the spectral contrast of the entire profile was reduced or expanded. As notches were filled in progressively or peaks leveled progressively, elevation gain decreased in a graded manner similar to that observed as sensation level is reduced below 30 dB or, for brief sounds, increased above 45 dB. As spectral contrast was reduced, gain dropped only at the most extreme reduction (25% of normal). Spectral contrast expansion had little effect. The results are consistent with the hypothesis that loss of representation of spectral features contributes to reduced elevation gain at low and high sound levels. The results also suggest that perceived location depends on a correlation-like spectral matching process that is sensitive to the relative, rather than absolute, across-frequency shape of the spectral profile.

Directional coherence disentangles causality within the sensorimotor loop, but cannot open the loop

More and more studies indicate that corticomuscular coherence in the beta band (15–30 Hz), which expresses the functional coupling between the cortex and the muscles, originates from the interaction within the sensorimotor loop (e.g. Witham et al. 2011). The phase of the corticomuscular coherence expresses the relative time–frequency relationship and is often explained as to result from the efferent delay between the cortex and the muscles. In a recent issue of The Journal of Physiology, Witham and co-workers (2011) demonstrated that the slope of the phase of corticomuscular coherence is less negative than would be expected of pure efferent pathways and even becomes positive in some subjects (negative slopes indicate that the muscle lags the brain). This is a clear indication of a bidirectional coupling between EEG and EMG; in other words, the signals are part of a closed-loop system. However, the authors also use the phase of the directional coherence to assess the delays in the efferent and afferent pathways, which will give erroneous results in a closed-loop system, like the sensorimotor loop. The causality of signals within a closed loop is difficult to assess. For example, in the sensorimotor loop it is not obvious whether cortical activity leads muscle activity – suggesting an efferent pathway; or cortical activity lags muscle activity – suggesting an afferent pathway. In the sensorimotor loop EEG and EMG signals will contain a combination of afferent and efferent influences. As the authors demonstrate, directional coherence provides a good measure to disentangle the causal relationships of the signals within the sensorimotor loop. With directional coherence multivariate autoregressive (MVAR) modelling is used to uncover causality. MVAR modelling is a common technique which disentangles the recorded signals at a certain time instant as a weighted sum of the signals’ previous values and (unknown) external noise sources, which enter the model just before the signals (see Fig. 1). The directed coherence is calculated using the directional transfer function Hij(f) (e.g. Witham et al. eqn (3)). The directional transfer function Hij(f) is calculated, which represents: ‘the causal influence of signal j on signal i’. Figure 1 Schematic representation of the sensorimotor loop as a closed-loop system Although this is a widely accepted expression, it is a simplified expression. The precise expression would be that the direction transfer function represents the causal influence of external noise source j on signal i (Kaminski & Blinowska, 1991). In other words the directional transfer function expresses how much signal i depends on the unknown external noise source which enters the model just before signal j. The simplification on what directional transfer function represents has a tremendous effect on the understanding of the phase of the directional coherence. In Witham et al. (2011), the authors assume that the phase of the directional coherence represents the relative delay between signal i and signal j. With this assumption the slope of the phase would represent the delays in the open-loop transfer functions, i.e. the relative delay of the efferent (EEG to EMG: Heff) and afferent (EMG to EEG: Haff) pathways. However the directional transfer function is a closed-loop transfer function between noise source j and signal i. In that sense directional transfer functions allow the disentangling of the causality within a closed loop, but the phase of the directional coherence presents the relative delay between the signal within the sensorimotor loop (EEG and EMG) and the unknown external noise sources ɛ (i.e. the cortical and afferent drive). This effect contributes to the observation of Witham and co-workers that the delays measured by using the directed coherence were often larger than would be expected the known conduction delays from the cortex to muscle assesses with stimulation and peripheral nerve stimulation. In conclusion, the technique based on multivariate AR modelling – like directional coherence – decomposes signals within a closed loop as a weighted combination of external sources and the signals’ past, and allows disentangling of the causality. The phase of the directional coherence, however, describes the relative delay between the signals and the unknown external sources, and is not a direct measure of the phase of the inferred open-loop transfer function, like the efferent and afferent pathways. New techniques which are able to assess the open-loop transfer functions are highly desirable. The application of controlled external perturbations could be a promising way (Campfens et al. 2011).

Fast measurement system and super high directional resolution head-related transfer function database

Head-related transfer functions (HRTFs) describe the acoustical transmission process from a point sound source to two ears in the free field. They are vital to the researches of binaural hearing and virtual auditory display. Measurement is the most important approach to obtain HRTFs, but it is time-consuming. To accurate HRTF measurement, a computer-controlling measurement system is designed. The system consists of multiple sound sources at different elevations with a finest interval of 5° and a horizontal turntable with an azimuthal resolution of 0.1°. It is able to work in non-anechoic environment and suitable for both mannequin and human subject measurement. A practical example indicates that the system allows for measuring far-field HRTFs at 493 source directions within half an hour. By using the system, a super high directional resolution HRTF database for KEMAR mannequin is established. The database includes 3889 pairs of head-related impulse responses (HRIRs, the time domain counterpart of HRTFs) at distance of 1.0 m, elevation interval of 5° (from -45° to 90° ), and azimuthal interval of 2.5°. Each HRIR is 1024-point length at 96 kHz sampling frequency and 24-bit quantization. The database is applicable to the research on binaural hearing and virtual auditory display.

Sound pressure transformations by the head and pinnae of the adult Chinchilla ( Chinchilla lanigera)

There are three main cues to sound location: the interaural differences in time (ITD) and level (ILD) as well as the monaural spectral shape cues. These cues are generated by the spatial- and frequency-dependent filtering of propagating sound waves by the head and external ears. Although the chinchilla has been used for decades to study the anatomy, physiology, and psychophysics of audition, including binaural and spatial hearing, little is actually known about the sound pressure transformations by the head and pinnae and the resulting sound localization cues available to them. Here, we measured the directional transfer functions (DTFs), the directional components of the head-related transfer functions, for 9 adult chinchillas. The resulting localization cues were computed from the DTFs. In the frontal hemisphere, spectral notch cues were present for frequencies from ∼6–18 kHz. In general, the frequency corresponding to the notch increased with increases in source elevation as well as in azimuth towards the ipsilateral ear. The ILDs demonstrated a strong correlation with source azimuth and frequency. The maximum ILDs were <10 dB for frequencies <5 kHz, and ranged from 10–30 dB for the frequencies >5 kHz. The maximum ITDs were dependent on frequency, yielding 236 μs at 4 kHz and 336 μs at 250 Hz. Removal of the pinnae eliminated the spectral notch cues, reduced the acoustic gain and the ILDs, altered the acoustic axis, and reduced the ITDs.

Concurrent Development of the Head and Pinnae and the Acoustical Cues to Sound Location in a Precocious Species, the Chinchilla (Chinchilla lanigera)

Sounds are filtered in a spatial- and frequency-dependent manner by the head and pinna giving rise to the acoustical cues to sound source location. These spectral and temporal transformations are dependent on the physical dimensions of the head and pinna. Therefore, the magnitudes of binaural sound location cues-the interaural time (ITD) and level (ILD) differences-are hypothesized to systematically increase while the lower frequency limit of substantial ILD production is expected to decrease due to the increase in head and pinna size during development. The frequency ranges of the monaural spectral notch cues to source elevation are also expected to decrease. This hypothesis was tested here by measuring directional transfer functions (DTFs), the directional components of head-related transfer functions, and the linear dimensions of the head and pinnae for chinchillas from birth through adulthood. Dimensions of the head and pinna increased by factors of 1.8 and 2.42, respectively, reaching adult values by ~6weeks. From the DTFs, the ITDs, ILDs, and spectral shape cues were computed. Maximum ITDs increased by a factor of 1.75, from ~160μs at birth (P0-1, first postnatal day) to 280μs in adults. ILDs depended on source location and frequency exhibiting a shift in the frequency range of substantial ILD (>10dB) from higher to lower frequencies with increasing head and pinnae size. Similar trends were observed for the spectral notch frequencies which ranged from 14.7-33.4kHz at P0-1 to 5.3-19.1kHz in adults. The development of the spectral notch cues, the spatial- and frequency-dependent distributions of DTF amplitude gain, acoustic directionality, maximum gain, and the acoustic axis were systematically related to the dimensions of the head and pinnae. The dimension of the head and pinnae in the chinchilla as well as the acoustical properties associated with them are mature by ~6weeks.

Low order all-pole and all-zero models of human and cat directional transfer functions.

Directional transfer functions (DTFs), the directional components of head related transfer functions, are generally measured at finite locations in azimuth and elevation. Thus models are needed to synthesize DTFs at finer spatial resolution than the measured data to create complete virtual auditory displays. Here, minimum-phase all-pole and all-zero models were used for modeling both human and cat DTFs. For the human DTFs, model orders were chosen to achieve specific objective error criteria published in previous studies that were based on subjective listening tests. Because subjective listening tests are not always feasible in animals, objective methods must be used to assess the quality of the DTF reconstructions. Here, the same error criteria reported in subjective tests of human DTF reconstructions were used to constrain models of cat DTFs based on the assumption that if humans cannot discriminate reconstructed versus empirical DTFs for a given objective reconstruction error, then cats will not be able to either provided the reconstruction error is held below that criteria. All-pole and all-zero models of orders as low as 25 were able to model DTFs with errors comparable to previous research findings and preserve the main spectral features in both human and cat DTFs. [Work supported by NIH Grant No. R01-DC6865.]

Experimental Response of Piles in Sand under Compound Motion

This paper describes a fundamental experimental study on the vertical, horizontal, and rocking dynamic behavior of single pile foundations in granular soils. Aimed at generating an extensive experimental database with sufficient parametric variations to clarify a number of issues, multiple series of canonical small-strain forced-vibration centrifuge tests were performed on two model piles using the technique of random vibration and impact loading. Correlated well with vertical- and horizontal-centric dynamic tests within the experimental program, a novel hybrid-mode test method by means of eccentric excitation is validated and employed for the characterization of the foundation responses in general planar motion. A large set of experimental data for different length scales were generated and synthesized in the frequency domain in the form of directional force-response transfer functions. By virtue of the physical measurements, the validity and limitations of two fundamental elastodynamic pile solutions pertaining to the physical dynamic soil-foundation problem are also evaluated.

Postnatal development of sound pressure transformations by the head and pinnae of the cat: Monaural characteristics

Although there have been many anatomical, physiological, and psychophysical studies of auditory development in cat, there have been no comparable studies of the development of the sound pressured transformations by the cat head and pinnae. Because the physical dimensions of the head and pinnae determine the spectral and temporal transformations of sound, as head and pinnae size increase during development, the magnitude and frequency ranges of these transformations are hypothesized to systematically change. This hypothesis was tested by measuring directional transfer functions (DTFs), the directional components of head-related transfer functions, and the linear dimensions of the head and pinnae in cats from the onset of hearing ( approximately 1.5 weeks) through adulthood. Head and pinnae dimensions increased by factors of approximately 2 and approximately 2.5, respectively, reaching adult values by approximately 23 and approximately 16 weeks, respectively. The development of the spectral notch cues to source location, the spatial- and frequency-dependent distributions of DTF amplitude gain (acoustic directionality), maximum gain, and the acoustic axis, and the resonance frequency and associated gain of the ear canal and concha were systematically related to the dimensions of the head and pinnae. These monaural acoustical properties of the head and pinnae in the cat are mature by 16 weeks.

The acoustical cues to sound location in the rat: Measurements of directional transfer functions

The acoustical cues for sound location are generated by spatial- and frequency-dependent filtering of propagating sound waves by the head and external ears. Although rats have been a common model system for anatomy, physiology, and psychophysics of localization, there have been few studies of the acoustical cues available to rats. Here, directional transfer functions (DTFs), the directional components of the head-related transfer functions, were measured in six adult rats. The cues to location were computed from the DTFs. In the frontal hemisphere, spectral notches were present for frequencies from approximately 16 to 30 kHz; in general, the frequency corresponding to the notch increased with increases in source elevation and in azimuth toward the ipsilateral ear. The maximum high-frequency envelope-based interaural time differences (ITDs) were 130 mus, whereas low-frequency (<3.5 kHz) fine-structure ITDs were 160 mus; both types of ITDs were larger than predicted from spherical head models. Interaural level differences (ILDs) strongly depended on location and frequency. Maximum ILDs were <10 dB for frequencies <8 kHz and were as large as 20-40 dB for frequencies >20 kHz. Removal of the pinna eliminated the spectral notches, reduced the acoustic gain and ILDs, altered the acoustical axis, and reduced the ITDs.

Are there systematic movements of poles/zeros with sound source location for pole/zero models of acoustic directional transfer functions?

Humans and animals locate sound sources using three main acoustical cues: Interaural time (ITD) and level (ILD) differences and monaural spectral shape cues. The cues are generated by the spatial‐ and frequency‐dependent filtering of the propagating sound waves by the torso, head, and external ears. These acoustic transformations can be captured in measurements of the directional transfer functions (DTFs), the directional components of the head related transfer functions (HRTFs). A set of DTFs can be used to create a virtual auditory environment by presenting over headphones arbitrary sounds filtered with DTFs. DTFs are generally measured at finite locations in azimuth and elevation, so models are needed to synthesize DTFs for source locations not measured. Here, we investigated the use of different pole/zero models with different orders to model DTFs measured in humans and cats. With models that successfully characterized the DTFs with little error, we examined the systematic movements of the poles/zeros in the unit circle with changes in source azimuth and elevation. The ultimate goal of this research is to find a simple relationship between the movements of the poles/zeros with source location. [NIH Grant No. R01‐DC6865.]

The acoustics and psychoacoustics of sound localization in the cat

Cats are a common model system for the anatomy, physiology, and psychophysics of sound localization. There are three main cues to location: Interaural differences in time (ITD) and level (ILD) and monaural spectral shape. Here, the cues were derived from measurements of directional transfer functions, the directional components of head‐related transfer functions. In the frontal hemisphere, spectral notches were present for frequencies from ∼8–16 kHz; the notch frequency increased with increases in source elevation and in azimuth towards the ipsilateral ear. The maximum ITDs were ∼380 s. Maximum ILDs depended on source azimuth and frequency, but were as large as 35 dB at some frequencies. For the psychophysics of localization, cats were trained using operant conditioning to indicate the apparent locations of sounds via gaze shift (combined eye and head movements); eye and head position were measured using the search coil technique. Auditory targets consisted of noise bursts of varying duration, intensities, and spectral content. Localization of long duration, moderately intense, and broadband targets were accurate and precise, but deteriorated for sounds that were short‐duration, narrow‐band, or that were very intense or faint. Cat sound localization capabilities are in many ways similar to humans. [NIH grants DC006865 and DC02840.]

Frequency scaling reduces individual differences in external‐ear transfer functions in developing cats

There are three cues to sound location: Interaural differences in time and level and monaural spectral shape cues. The ultimate magnitudes of these cues depend largely on the linear dimensions of head and pinnae. During development, the increasing interaural distance associated with a growing head and pinnae result in cues that change substantially and continuously until maturation is complete. These experiments examined whether the intersubject differences in the directional transfer functions (DTFs), the directional components of the head‐related transfer functions, of cats during development could be reduced by scaling one set of DTFs on a log‐frequency axis. Measurements were made of both the physical dimensions of the head and pinnae and the DTFs of cats aged 4 weeks to adulthood. For each pair of subjects, an optimal frequency scaling factor was computed that minimized the differences in the DTFs. In many cases, the optimal factors for pairs of subjects were proportional to the ratios of the measured physical dimensions of the head and pinnae in those subjects. Although there were still considerable differences in the DTFs even after scaling, these data support frequency scaling as a potential method of modeling the development of the DTFs in cats. [Work supported by NIH Grant DC006865.]

Reducing individual differences in the external-ear transfer functions of the Mongolian gerbil

This study examines individual differences in the directional transfer functions (DTFs), the directional components of head-related transfer functions of gerbils, and seeks a method for reducing these differences. The difference between the DTFs of a given animal pair was quantified by the intersubject spectral difference (ISSD), which is the variance in the difference spectra of DTFs for frequencies between 5 and 45 kHz and for 361 source directions. An attempt was made to reduce the ISSD by scaling the DTFs of one animal in frequency and/or rotating the DTFs along the source coordinate sphere. The ISSD was reduced by a median of 12% after optimal frequency scaling alone, by a median of 19% after optimal spatial rotation alone, and by a median of 36% after simultaneous frequency scaling and spatial rotation. The optimal scaling factor (OSF) and the optimal coordinate rotation (OCR) correlated strongly with differences in head width and pinna angles (i.e., pinna inclination around the vertical and front-back axes), respectively. Thus, linear equations were derived to estimate the OSF and OCR from these anatomical measurements. The ISSD could be reduced by a median of 22% based on the estimated OSF and OCR.

Influence of the Antennas on the Ultra-Wideband Transmission

Spectrum is presently one of the most valuable goods worldwide as the demand is permanently increasing and it can be traded only locally. Since the United States Federal Communications Commission (FCC) has opened the spectrum from to , that is, a bandwidth of , for unlicensed use with up to EIRP, numerous applications in communications and sensor areas are showing up. Like all wireless devices, these have an antenna as an integral part of the air interface. The antennas are modeled as linear time-invariant (LTI) systems with a transfer function. The measurement of the antenna's frequency-dependent directional transfer function is described. Quality measures for the antennas like the peak value of the transient response, its width and ringing, as well as the transient gain are discussed. The application of these quality measures is shown for measurements of different UWB antennas.

Multi Frequency Solution of Chatter Stability for Low Immersion Milling

Finish milling is usually required in the peripheral milling of thin aircraft webs with long end mills, where the structures are flexible and radial depths of cut are small. The spindle speed and depth of cut must be selected optimally to avoid both forced and chatter vibrations, which in turn enables production of the parts within specified tolerances. Recent articles show that stability pockets differ at certain speeds when the radial immersion in milling is low and the machining process is highly intermittent. This paper presents a stability theory which predicts chatter stability lobes that are not covered by classical chatter theories in which the coupling between the spindle speed and process stability are neglected. The dynamics of low radial immersion milling are formulated as an eigenvalue problem, where harmonics of the tooth spacing angle and spread of the transfer function with the harmonics of the tooth passing frequencies are considered. It is shown that the stability lobes are accurately predicted with the presented method. This paper details the physics involved when the tooth passing frequencies alter the effective transfer function of the structure in the stability solution. The products of the harmonics of the directional coefficients and transfer functions of the structure are evaluated at the natural mode under the influence of tooth passing frequency harmonics in order to obtain the exact locations of chatter stability lobes.

Development of the sound localization cues in cats

Cats are a common model for developmental studies of the psychophysical and physiological mechanisms of sound localization. Yet, there are few studies on the development of the acoustical cues to location in cats. The magnitude of the three main cues, interaural differences in time (ITDs) and level (ILDs), and monaural spectral shape cues, vary with location in adults. However, the increasing interaural distance associated with a growing head and pinnae during development will result in cues that change continuously until maturation is complete. Here, we report measurements, in cats aged 1 week to adulthood, of the physical dimensions of the head and pinnae and the localization cues, computed from measurements of directional transfer functions. At 1 week, ILD depended little on azimuth for frequencies &amp;lt;6–7 kHz, maximum ITD was 175 μs, and for sources varying in elevation, a prominent spectral notch was located at higher frequencies than in the older cats. As cats develop, the spectral cues and the frequencies at which ILDs become substantial (&amp;gt;10 dB) shift to lower frequencies, and the maximum ITD increases to nearly 370 μs. Changes in the cues are correlated with the increasing size of the head and pinnae. [Work supported by NIDCD DC05122.]

Vertical-plane sound localization probed with ripple-spectrum noise.

Ripple-spectrum stimuli were used to investigate the scale of spectral detail used by listeners in interpreting spectral cues for vertical-plane localization. In three experiments, free-field localization judgments were obtained for 250-ms, 0.6-16-kHz noise bursts with log-ripple spectra that varied in ripple density, peak-to-trough depth, and phase. When ripple density was varied and depth was held constant at 40 dB, listeners' localization error rates increased most (relative to rates for flat-spectrum targets) for densities of 0.5-2 ripples/oct. When depth was varied and density was held constant at 1 ripple/oct, localization accuracy was degraded only for ripple depths > or = 20 dB. When phase was varied and density was held constant at 1 ripple/oct and depth at 40 dB, three of five listeners made errors at consistent locations unrelated to the ripple phase, whereas two listeners made errors at locations systematically modulated by ripple phase. Although the reported upper limit for ripple discrimination is 10 ripples/oct [Supin et al., J. Acoust. Soc. Am. 106, 2800-2804 (1999)], present results indicate that details finer than 2 ripples/oct or coarser than 0.5 ripples/oct do not strongly influence processing of spectral cues for sound localization. The low spectral-frequency limit suggests that broad-scale spectral variation is discounted, even though components at this scale are among those contributing the most to the shapes of directional transfer functions.

Modeling individual differences in ferret external ear transfer functions.

Individual variations in head and outer ear size, as well as growth of these structures during development, can markedly alter the values of the binaural and monaural cues which form the basis for auditory localization. This study investigated individual differences in the directional component of the head-related transfer function of both adult and juvenile ferrets. In line with previous studies in humans and cats, intersubject spectral differences were found to be reduced by scaling one of the directional transfer functions on a log-frequency axis. The optimal scale factor correlated most highly with pinna cavity height. Optimal frequency scaling reduced interear spectral difference equally well for adult-juvenile comparisons as for comparisons between pairs of adult ears. This illustrates that the developmental changes in localization cue values should be at least partly predictable on the basis of the expected growth rate of the outer ear structures. Predictions of interaural time differences (ITDs) were also derived from the physical dimensions of the head. ITDs were found to be poorly fitted by the spherical head model, while much better predictions could be derived from a model based on von Mises spherical basis functions. Together, these findings show how more accurate estimates of spatial cue values can be made from knowledge of the dimensions of the head and outer ears, and may facilitate the generation of virtual acoustic space stimuli in the absence of acoustical measurements from individual subjects.

Contribution of spectral cues to human sound localization.

The contribution of spectral cues to human sound localization was investigated by removing cues in 1/2-, 1- or 2-octave bands in the frequency range above 4 kHz. Localization responses were given by placing an acoustic pointer at the same apparent position as a virtual target. The pointer was generated by filtering a 100-ms harmonic complex with equalized head-related transfer functions (HRTFs). Listeners controlled the pointer via a hand-held stick that rotated about a fixed point. In the baseline condition, the target, a 200-ms noise burst, was filtered with the same HRTFs as the pointer. In other conditions, the spectral information within a certain frequency band was removed by replacing the directional transfer function within this band with the average transfer of this band. Analysis of the data showed that removing cues in 1/2-octave bands did not affect localization, whereas for the 2-octave band correct localization was virtually impossible. The results obtained for the 1-octave bands indicate that up-down cues are located mainly in the 6-12-kHz band, and front-back cues in the 8-16-kHz band. The interindividual spread in response patterns suggests that different listeners use different localization cues. The response patterns in the median plane can be predicted using a model based on spectral comparison of directional transfer functions for target and response directions.