Monaural Spectral Cues Research Articles

A localization algorithm based on head-related transfer functions

Two sound localization algorithms based on the head-related transfer function were developed. Each of them uses the interaural time delay, interaural level difference, and monaural spectral cues to estimate the location of a sound source. Given that most localization algorithms will be required to function in background noise, the localization performance of one of the algorithms was tested at signal-to-noise ratios (SNRs) from 40 to -40 dB. Stimuli included ten real-world, broadband sounds located at 5 degrees intervals in azimuth and at 0 degrees elevation. Both two- and four-microphone versions of the algorithm were implemented to localize sounds to 5 degrees precision. The two-microphone version of the algorithm exhibited less than 2 degrees mean localization error at SNRs of 20 dB and greater, and the four-microphone version committed approximately 1 degrees mean error at SNRs of 10 dB or greater. Potential enhancements and applications of the algorithm are discussed.

Binaural weighting of monaural spectral cues for sound localization

For human listeners, cues for vertical-plane localization are provided by direction-dependent pinna filtering. This study quantified listeners' weighting of the spectral cues from each ear as a function of stimulus lateral angle, interaural time difference (ITD), and interaural level difference (ILD). Subjects indicated the apparent position of headphone-presented noise bursts synthesized in virtual auditory space. The synthesis filters for the two ears either corresponded to the same location or to two different locations separated vertically by 20 deg. Weighting of each ear's spectral information was determined by a multiple regression between the elevations to which each ear's spectrum corresponded and the vertical component of listeners' responses. The apparent horizontal source location was controlled either by choosing synthesis filters corresponding to locations on or 30 deg left or right of the median plane or by attenuating or delaying the signal at one ear. For broadband stimuli, spectral weighting and apparent lateral angle were determined primarily by ITD. Only for high-pass stimuli were weighting and lateral angle determined primarily by ILD. The results suggest that the weighting of monaural spectral cues and the perceived lateral angle of a sound source depend similarly on ITD, ILD, and stimulus spectral range.

Sound Localization Under Perturbed Binaural Hearing

This paper reports on the acute effects of a monaural plug on directional hearing in the horizontal (azimuth) and vertical (elevation) planes of human listeners. Sound localization behavior was tested with rapid head-orienting responses toward brief high-pass filtered (>3 kHz; HP) and broadband (0.5-20 kHz; BB) noises, with sound levels between 30 and 60 dB, A-weighted (dBA). To deny listeners any consistent azimuth-related head-shadow cues, stimuli were randomly interleaved. A plug immediately degraded azimuth performance, as evidenced by a sound level-dependent shift ("bias") of responses contralateral to the plug, and a level-dependent change in the slope of the stimulus-response relation ("gain"). Although the azimuth bias and gain were highly correlated, they could not be predicted from the plug's acoustic attenuation. Interestingly, listeners performed best for low-intensity stimuli at their normal-hearing side. These data demonstrate that listeners rely on monaural spectral cues for sound-source azimuth localization as soon as the binaural difference cues break down. Also the elevation response components were affected by the plug: elevation gain depended on both stimulus azimuth and on sound level and, as for azimuth, localization was best for low-intensity stimuli at the hearing side. Our results show that the neural computation of elevation incorporates a binaural weighting process that relies on the perceived, rather than the actual, sound-source azimuth. It is our conjecture that sound localization ensues from a weighting of all acoustic cues for both azimuth and elevation, in which the weights may be partially determined, and rapidly updated, by the reliability of the particular cue.

Perceptual recalibration in human sound localization: Learning to remediate front-back reversals

The efficacy of a sound localization training procedure that provided listeners with auditory, visual, and proprioceptive/vestibular feedback as to the correct sound-source position was evaluated using a virtual auditory display that used nonindividualized head-related transfer functions (HRTFs). Under these degraded stimulus conditions, in which the monaural spectral cues to sound-source direction were inappropriate, localization accuracy was initially poor with frequent front-back reversals (source localized to the incorrect front-back hemifield) for five of six listeners. Short periods of training (two 30-min sessions) were found to significantly reduce the rate of front-back reversal responses for four of five listeners that showed high initial reversal rates. Reversal rates remained unchanged for all listeners in a control group that did not participate in the training procedure. Because analyses of the HRTFs used in the display demonstrated a simple and robust front-back cue related to energy in the 3-7-kHz bandwidth, it is suggested that the reductions observed in reversal rates following the training procedure resulted from improved processing of this front-back cue, which is perhaps a form of rapid perceptual recalibration. Reversal rate reductions were found to generalize to untrained source locations, and persisted at least 4 months following the training procedure.

Ventriloquism aftereffects occur in the rear hemisphere

After exposure to a consistent spatial disparity of auditory and visual stimuli, subjective localization of sound sources is usually shifted in the direction of the visual stimuli. This study investigates whether such aftereffects can be observed in humans after exposure to a conflicting bimodal stimulation in virtual reality and whether these aftereffects are confined to the trained locations. Fourteen subjects participated in an adaptation experiment, in which auditory stimuli were convolved with non-individual head-related transfer functions, delivered via headphones. First, we assessed the auditory localization of subjects in darkness. They indicated the perceived direction of a sound using an angular pointer. We then immersed the subjects in a virtual environment by means of a head-mounted display. They were asked to reproduce sequences of movements of virtual objects with a mouse click on the objects. However, we introduced a spatial disparity of 15° between the visual event and the concurrent auditory stimulation. After 20 min of exposure, we tested the subjects again in total darkness to determine whether their auditory localization system had been modified by the conflicting visual signals. We observed a shift of subjective localization towards the left in both dorsal and frontal hemifields of the subject, mainly for auditory stimuli located in the right hemispace. This result suggests that interaural difference cues and monaural spectral cues were not equally adapted, and that visual stimuli mainly influence the processing of binaural directional cues of sound localization.

The role of monaural spectral cues in modeling the precedence effect

Various evidence suggests that the precedence effect may generalize to spatial locations of sound source and echo that minimize binaural information available to the listener. In these situations, it is likely that monaural spectral cues to the direction of the source play an important role in determining the apparent direction of the source+echo composite. Here a model of directional sound localization that incorporates both binaural temporal cues and monaural spectral cues is described and evaluated. The binaural portion of the model relies on interaural cross-correlation to extract binaural cues to lateral direction. The monaural spectral portion uses a spectral correlation metric to evaluate the similarity of the incoming sound spectrum with a catalog of spectral shapes resulting from a listener’s own head-related transfer functions (HRTFs) to known source directions. The model was used to predict sound localization performance of seven human listeners in 16 spatial configurations of source and echo (presented using virtual auditory space techniques with individualized HRTFs), including six configurations where binaural information was minimized (four on the median plane). In general, precedence effects that relied primarily on spectral cue information were considerably less predictable than those that relied on binaural information. [Work supported by NIDCD.]

Localizing nearby sound sources in a classroom: Binaural room impulse responses

Binaural room impulse responses (BRIRs) were measured in a classroom for sources at different azimuths and distances (up to 1 m) relative to a manikin located in four positions in a classroom. When the listener is far from all walls, reverberant energy distorts signal magnitude and phase independently at each frequency, altering monaural spectral cues, interaural phase differences, and interaural level differences. For the tested conditions, systematic distortion (comb-filtering) from an early intense reflection is only evident when a listener is very close to a wall, and then only in the ear facing the wall. Especially for a nearby source, interaural cues grow less reliable with increasing source laterality and monaural spectral cues are less reliable in the ear farther from the sound source. Reverberation reduces the magnitude of interaural level differences at all frequencies; however, the direct-sound interaural time difference can still be recovered from the BRIRs measured in these experiments. Results suggest that bias and variability in sound localization behavior may vary systematically with listener location in a room as well as source location relative to the listener, even for nearby sources where there is relatively little reverberant energy.

Contribution of head shadow and pinna cues to chronic monaural sound localization.

Monaurally deaf people lack the binaural acoustic difference cues in sound level and timing that are needed to encode sound location in the horizontal plane (azimuth). It has been proposed that these people therefore rely on spectral pinna cues of their normal ear to localize sounds. However, the acoustic head-shadow effect (HSE) might also serve as an azimuth cue, despite its ambiguity when absolute sound levels are unknown. Here, we assess the contribution of either cue in the monaural deaf to two-dimensional (2D) sound localization. In a localization test with randomly interleaved sound levels, we show that all monaurally deaf listeners relied heavily on the HSE, whereas binaural control listeners ignore this cue. However, some monaural listeners responded partly to actual sound-source azimuth, regardless of sound level. We show that these listeners extracted azimuth information from their pinna cues. The better monaural listeners were able to localize azimuth on the basis of spectral cues, the better their ability to also localize sound-source elevation. In a subsequent localization experiment with one fixed sound level, monaural listeners rapidly adopted a strategy on the basis of the HSE. We conclude that monaural spectral cues are not sufficient for adequate 2D sound localization under unfamiliar acoustic conditions. Thus, monaural listeners strongly rely on the ambiguous HSE, which may help them to cope with familiar acoustic environments.

Separation of concurrent broadband sound sources by human listeners.

The effect of spatial separation on the ability of human listeners to resolve a pair of concurrent broadband sounds was examined. Stimuli were presented in a virtual auditory environment using individualized outer ear filter functions. Subjects were presented with two simultaneous noise bursts that were either spatially coincident or separated (horizontally or vertically), and responded as to whether they perceived one or two source locations. Testing was carried out at five reference locations on the audiovisual horizon (0 degrees, 22.5 degrees, 45 degrees, 67.5 degrees, and 90 degrees azimuth). Results from experiment 1 showed that at more lateral locations, a larger horizontal separation was required for the perception of two sounds. The reverse was true for vertical separation. Furthermore, it was observed that subjects were unable to separate stimulus pairs if they delivered the same interaural differences in time (ITD) and level (ILD). These findings suggested that the auditory system exploited differences in one or both of the binaural cues to resolve the sources, and could not use monaural spectral cues effectively for the task. In experiments 2 and 3, separation of concurrent noise sources was examined upon removal of low-frequency content (and ITDs), onset/offset ITDs, both of these in conjunction, and all ITD information. While onset and offset ITDs did not appear to play a major role, differences in ongoing ITDs were robust cues for separation under these conditions, including those in the envelopes of high-frequency channels.

Utility of Monaural Spectral Cues Is Enhanced in the Presence of Cues to Sound-Source Lateral Angle

The contention that normally binaural listeners can localize sound under monaural conditions has been challenged by Wightman and Kistler (J. Acoust. Soc. Am. 101:1050-1063, 1997), who found that listeners are almost completely unable to localize virtual sources of sound when sound is presented to only one ear. Wightman and Kistler's results raise the question of whether monaural spectral cues are used by listeners to localize sound under binaural conditions. We have examined the possibility that monaural spectral cues provide useful information regarding sound-source elevation and front-back hemifield when interaural time differences are available to specify sound-source lateral angle. The accuracy with which elevation and front-back hemifield could be determined was compared between a monaural condition and a binaural condition in which a wide-band signal was presented to the near ear and a version of the signal that had been lowpass-filtered at 2.5 kHz was presented to the far ear. It was found that accuracy was substantially greater in the latter condition, suggesting that information regarding sound-source lateral angle is required for monaural spectral cues to elevation and front-back hemifield to be correctly interpreted.

Low-Power Log-Domain CMOS Filter Bank for 2-D Sound Source Localization

This paper proposes the design of a novel current-mode front-end for the extraction of localization spectral cues from two audio signals, together with test results. The front-end consists of two parallel filter banks, envelope extraction and comparison circuitry, together with an AGC loop. The extracted cues are intended to be further processed in order to determine the source azimuth and elevation. A current-mode log-domain implementation using subthreshold MOS operation is used for micropower operation while still achieving a good bandwidth and linearity. A current-mode solution is also preferred because of the ease of implementation of certain mathematical operations. The front-end splits the input signals into different frequency bands and computes monaural and interaural spectral cues from the resulting signal envelopes for each band. The front-end has been optimized to operate at a supply voltage of 1.8 V and most blocks have been designed using a differential architecture. To our knowledge, this is the first log-domain implementation of a front-end for 2-D localization cues extraction. The design has been carried out using a standard double-poly double-metal 0.8 μm CMOS process with VT e 0.8 V. The bandpass filters which form the main core of the chip exhibit a measured dynamic range of 62 dB corresponding to 1.9% THD, while the total power dissipation is 890 μW.

Listener weighting of cues for lateral angle: the duplex theory of sound localization revisited.

The virtual auditory space technique was used to quantify the relative strengths of interaural time difference (ITD), interaural level difference (ILD), and spectral cues in determining the perceived lateral angle of wideband, low-pass, and high-pass noise bursts. Listeners reported the apparent locations of virtual targets that were presented over headphones and filtered with listeners' own directional transfer functions. The stimuli were manipulated by delaying or attenuating the signal to one ear (by up to 600 micros or 20 dB) or by altering the spectral cues at one or both ears. Listener weighting of the manipulated cues was determined by examining the resulting localization response biases. In accordance with the Duplex Theory defined for pure-tones, listeners gave high weight to ITD and low weight to ILD for low-pass stimuli, and high weight to ILD for high-pass stimuli. Most (but not all) listeners gave low weight to ITD for high-pass stimuli. This weight could be increased by amplitude-modulating the stimuli or reduced by lengthening stimulus onsets. For wideband stimuli, the ITD weight was greater than or equal to that given to ILD. Manipulations of monaural spectral cues and the interaural level spectrum had little influence on lateral angle judgements.

How Plastic Is Spatial Hearing?

The location of a sound source is derived by the auditory system from spatial cues present in the signals at the two ears. These cues include interaural timing and level differences, as well as monaural spectral cues generated by the external ear. The values of these cues vary with individual differences in the shape and dimensions of the head and external ears. We have examined the neurophysiological consequences of these intersubject variations by recording the responses of neurons in ferret primary auditory cortex to virtual sound sources mimicking the animal’s own ears or those of other ferrets. For most neurons, the structure of the spatial response fields changed significantly when acoustic cues measured from another animal were presented. This is consistent with the finding that humans localize less accurately when listening to virtual sounds from other subjects. To examine the role of experience in shaping the ability to localize sound, we have studied the behavioural consequences of altering binaural cues by chronically plugging one ear. Ferrets raised and tested with one ear plugged learned to localize as accurately as control animals, which is consistent with previous findings that the representation of auditory space in the midbrain can accommodate abnormal sensory cues during development. Adaptive changes in behaviour were also observed in adults, particularly if they were provided with regular practice in the localization task. Together, these findings suggest that the neural circuits responsible for sound localization can be recalibrated throughout life.

Plasticity in the neural coding of auditory space in the mammalian brain.

Sound localization relies on the neural processing of monaural and binaural spatial cues that arise from the way sounds interact with the head and external ears. Neurophysiological studies of animals raised with abnormal sensory inputs show that the map of auditory space in the superior colliculus is shaped during development by both auditory and visual experience. An example of this plasticity is provided by monaural occlusion during infancy, which leads to compensatory changes in auditory spatial tuning that tend to preserve the alignment between the neural representations of visual and auditory space. Adaptive changes also take place in sound localization behavior, as demonstrated by the fact that ferrets raised and tested with one ear plugged learn to localize as accurately as control animals. In both cases, these adjustments may involve greater use of monaural spectral cues provided by the other ear. Although plasticity in the auditory space map seems to be restricted to development, adult ferrets show some recovery of sound localization behavior after long-term monaural occlusion. The capacity for behavioral adaptation is, however, task dependent, because auditory spatial acuity and binaural unmasking (a measure of the spatial contribution to the "cocktail party effect") are permanently impaired by chronically plugging one ear, both in infancy but especially in adulthood. Experience-induced plasticity allows the neural circuitry underlying sound localization to be customized to individual characteristics, such as the size and shape of the head and ears, and to compensate for natural conductive hearing losses, including those associated with middle ear disease in infancy.

Altered spectral localization cues disrupt the development of the auditory space map in the superior colliculus of the ferret.

Spectral localization cues provided by the outer ear are utilized in the construction of the auditory space map in the superior colliculus (SC). The role of the outer ear in the development of this map was examined by recording from the SC of anesthetized, adult ferrets in which the pinna and concha had been removed in infancy. The acoustical consequences of this procedure were assessed by recording outer ear impulse responses via a probe-tube microphone implanted in the wall of the ear canal. Both monaural and binaural spectral cues normally show a number of asymmetric features within the horizontal plane, which allow azimuthal locations on either side of the interaural axis to be discriminated. These features were eliminated or altered by chronic pinnectomy. The responses of auditory units in the SC to noise bursts presented in the free field were examined at sound levels of approximately 10 and 25 dB above unit threshold. After bilateral pinnectomy, the representation of auditory space was severely degraded at both sound levels. In contrast to normal ferrets, many units had bilobed azimuthal response profiles, indicating that they were unable to resolve sound locations on either side of the interaural axis. There was also much less order in the distribution of best azimuths or elevations of those units that were tuned to a single direction. Some units were tuned to locations that extended much further into the hemifield ipsilateral to the recording side than the normal range of best azimuths. Unilateral removal of the outer ear, which disrupts the monaural spectral cues for one side only, had a much smaller effect on the development of the auditory representation. At supra- and near-threshold sound levels, the representation of sound azimuth in the SC on both sides of the brain was less scattered than that found after bilateral pinna removal. Nevertheless, units with bilobed responses, broader tuning, and inappropriate best azimuths were observed in both the left and right SC of ferrets in which the left pinna and concha had been removed in infancy. These data illustrate that the localization cues provided by the outer ear play a critical role in the development of the auditory space map in the SC. In contrast to other manipulations of either auditory or visual inputs, the map does not appear to adapt to the changes in spectral cues brought about by pinna removal, suggesting that residual binaural cues are, by themselves, insufficient for its normal maturation.

Monaural sound localization revisited.

Research reported during the past few decades has revealed the importance for human sound localization of the so-called "monaural spectral cues." These cues are the result of the direction-dependent filtering of incoming sound waves accomplished by the pinnae. One point of view about how these cues are extracted places great emphasis on the spectrum of the received sound at each ear individually. This leads to the suggestion that an effective way of studying the influence of these cues is to measure the ability of listeners to localize sounds when one of their ears is plugged. Numerous studies have appeared using this monaural localization paradigm. Three experiments are described here which are intended to clarify the results of the previous monaural localization studies and provide new data on how monaural spectral cues might be processed. Virtual sound sources are used in the experiments in order to manipulate and control the stimuli independently at the two ears. Two of the experiments deal with the consequences of the incomplete monauralization that may have contaminated previous work. The results suggest that even very low sound levels in the occluded ear provide access to interaural localization cues. The presence of these cues complicates the interpretation of the results of nominally monaural localization studies. The third experiment concerns the role of prior knowledge of the source spectrum, which is required if monaural cues are to be useful. The results of this last experiment demonstrate that extraction of monaural spectral cues can be severely disrupted by trial-to-trial fluctuations in the source spectrum. The general conclusion of the experiments is that, while monaural spectral cues are important, the monaural localization paradigm may not be the most appropriate way to study their role.

Monaural and binaural spectral cues created by the external ears of the pallid bat

The acoustic properties of external ears transform the spectra of incident sound in a location-dependent manner, and provide monaural and binaural spectral information used in 2-dimensional localization. Human studies suggest that binaural spectral differences, and spectral peaks and notches in monaural transfer functions, may all provide spatial information. This study examined the acoustic properties of the pallid bat ear to determine directionality, interaural intensity differences, spectral peaks and notches in transfer functions, as well as acoustic gain. The pallid bat is a gleaning bat that uses passive sound localization to find prey, and echolocation for general orientation. It is capable of very accurate passive sound localization, and the primary focus of this study was to determine the spectral cues that might support this localization acuity. Results show that the external ears of this bat create spectral maxima and minima that vary systematically with azimuth and elevation. The monaural spectral cues resemble those reported in humans and cats, and suggest that similar spectral cues are used across taxa. The ears also create robust interaural spectral differences that vary systematically with both sound azimuth and elevation. These monaural and binaural spectral cues may provide the basis for the 1° angular resolution apparent in it this bat's passive sound localization performance.

A quantitative study of auditory-evoked saccadic eye movements in two dimensions.

We investigated the properties of human saccadic eye movements evoked by acoustic stimuli in the two-dimensional frontal plane. These movements proved to be quite accurate, both in azimuth and in elevation, provided the sound source spectrum had a broad bandwidth and a sufficiently long duration. If the acoustic target was a tone, the azimuth of the saccadic end points remained equally accurate, whereas the elevation of the response was related to the frequency of the tone, rather than to the physical position of the target. Saccade elevation accuracy also declined substantially for short-duration noise bursts, although response elevation remained highly correlated with target elevation. The latencies of auditory saccades depended on the amplitude, but not on the direction of the eye movement, suggesting a polar coordinate origin of auditory saccade initiation. We also observed that the trajectories of auditory saccades were often substantially curved. Both a qualitative and a model-based analysis showed that this curvature corrected for errors in the initial direction of the saccade. The latter analysis also suggested that the kinematic properties of auditory saccades could be described by the superposition of two overlapping saccadic eye movements, hypothesized to be based on binaural difference cues and monaural spectral cues in the auditory signal, respectively. It is argued that, although the audio-oculomotor system has to operate in a feedforward way, it must nevertheless have access to an accurate representation of actual and desired eye position. Different models underlying the generation of auditory saccades are discussed.

Elevation sensitivity in the cat’s thalamo-cortical auditory system: Role of monaural spectral and binaural disparity cues

High-frequency neurons in auditory cortex (AI) and medial geniculate (MGB) of anesthetized cats are differentially sensitive to monaural and binaural directional cues present in broad-band noise. Binaural directional (BD) cells depend upon binaural stimuli for azimuth sensitivity, whereas monoaural directional (MD) cells are sensitive to the direction of monaural stimuli. In the MGB, neurons’ spatial receptive fields (SRFs) were obtained using noise bursts presented throughout the frontal hemifield and sound pressure levels that varied over an 80-dB range. BD cells were broadly tuned to elevation. Those that received excitatory input from one ear and exhibited binaural inhibition or mixed interactions had SRFs that extended throughout one lateral hemifield. Predominantly binaural cells exhibited strong binaural facilitation and had SRFs that formed a vertical band in front of the head. MD cells’ SRFs varied considerably, some were focal areas restricted in azimuth and elevation. Others consisted of multiple areas that in some cases showed level-dependent changes in location. The elevation sensitivity of MD cells was nearly identical under monaural and binaural conditions showing that it derived from monaural spectral cues. AI units showed similar response properties. [Work supported by NIDCD.]

Effects of ear plugging on single-unit azimuth sensitivity in cat primary auditory cortex. II. Azimuth tuning dependent upon binaural stimulation

1. Single-unit recordings were carried out in primary auditory cortex (AI) of barbiturate-anesthetized cats. Observations were based on a sample of 131 high-best-frequency (> 5 kHz), azimuth-sensitive neurons. These were identified by their responses to a set of noise bursts, presented in the free field, that varied in azimuth and sound-pressure level (SPL). Each azimuth-sensitive neuron responded well to some levels at certain azimuths, but did not respond well to any level at other azimuths. 2. Unilateral ear plugging was used to infer each neuron's response to monaural stimulation. Ear plugs, produced by injecting a plastic ear mold compound into the external ear, attenuated sound reaching the tympanic membrane by 25-70 dB. The azimuth tuning of a large proportion of the sample (62/131), referred to as binaural directional (BD), was completely dependent upon binaural stimulation because with one ear plugged, these cells were insensitive to azimuth (either responded well at all azimuths or failed to respond at any azimuth) or in a few cases exhibited striking changes in location of azimuth function peaks. This report describes patterns of monaural responses and binaural interactions exhibited by BD neurons and relates them to each cell's azimuth and level tuning. The response of BD cells to ear plugging is consistent with the hypothesis that they derive azimuth tuning from interaural level differences present in noise bursts. Another component of the sample consisted of monaural directional (27/131) cells that derived azimuth tuning in part or entirely from monaural spectral cues. Cells in the remaining portion of the sample (42/131) responded too unreliably to permit specific conclusions. 3. Binaural interactions were inferred by statistical comparison of a cell's responses to monaural (unilateral plug) and binaural (no plug) stimulation. A larger binaural response than either monaural response was taken as evidence for binaural facilitation. A smaller binaural than monaural response was taken as evidence for binaural inhibition. Binaural facilitation was exhibited by 65% (40/62) of the BD sample (facilitatory cells). Many of these exhibited mixed interactions, i.e., binaural facilitation occurred in response to some azimuth-level combinations, and binaural inhibition to others. Binaural inhibition in the absence of binaural facilitation occurred in 35% (22/62) of the BD sample, a majority of which were EI cells, so called because they received excitatory (E) input from one ear (excitatory ear) and inhibitory (I) input from the other (inhibitory ear). One cell that exhibited binaural inhibition received excitatory input from each ear.(ABSTRACT TRUNCATED AT 400 WORDS)