Using the interaural time difference and cross-correlation to localise short-term complex noises

The mammalian binaural cue of interaural time difference (ITD) and cross-correlation have long been used to determine the point of origin of a sound source. The ITD can be defined as the different points in time at which a sound from a single location arrives at each individual ear [1]. From this time difference, the brain can calculate the angle of the sound source in relation to the head [2]. Cross-correlation compares the similarity of each channel of a binaural waveform producing the time lag or offset required for both channels to be in phase with one another. This offset corresponds to the maximum value produced by the cross-correlation function and can be used to determine the ITD and thus the azimuthal angle θ of the original sound source. However, in indoor environments, cross-correlation has been known to have problems with both sound reflections and reverberations. Additionally, cross-correlation has difficulties with localising short-term complex noises when they occur during a longer duration waveform, i.e. in the presence of background noise. The crosscorrelation algorithm processes the entire waveform and the short-term complex noise can be ignored. This paper presents a technique using thresholding which enables higher-localisation abilities for short-term complex sounds in the midst of background noise. To determine the success of this thresholding technique, twenty-five sounds were recorded in a dynamic and echoic environment. The twenty-five sounds consist of hand-claps, finger-clicks and speech. The proposed technique was compared to the regular cross-correlation function for the same waveforms, and an average of the azimuthal angles determined for each individual sample. The sound localisation ability for all twenty-five sound samples is as follows: average of the sampled angles using cross-correlation: 44%; cross-correlation technique with thresholding: 84%. From these results, it is clear that this proposed technique is very successful for the localisation of short-term complex sounds in the midst of background noise and in a dynamic and echoic indoor environment.

Développement de la sensibilité à la localisation sonore dans le collicule supérieur du rat Long-Evans

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Spiking neuron models of the medial and lateral superior olive for sound localisation

Sound localisation is defined as the ability to identify the position of a sound source. The brain employs two cues to achieve this functionality for the horizontal plane, interaural time difference (ITD) by means of neurons in the medial superior olive (MSO) and interaural intensity difference (IID) by neurons of the lateral superior olive (LSO), both located in the superior olivary complex of the auditory pathway. This paper presents spiking neuron architectures of the MSO and LSO. An implementation of the Jeffress model using spiking neurons is presented as a representation of the MSO, while a spiking neuron architecture showing how neurons of the medial nucleus of the trapezoid body interact with LSO neurons to determine the azimuthal angle is discussed. Experimental results to support this work are presented.

Hemispheric competence for auditory spatial representation.

Sound localization relies on the analysis of interaural time and intensity differences, as well as attenuation patterns by the outer ear. We investigated the relative contributions of interaural time and intensity difference cues to sound localization by testing 60 healthy subjects: 25 with focal left and 25 with focal right hemispheric brain damage. Group and single-case behavioural analyses, as well as anatomo-clinical correlations, confirmed that deficits were more frequent and much more severe after right than left hemispheric lesions and for the processing of interaural time than intensity difference cues. For spatial processing based on interaural time difference cues, different error types were evident in the individual data. Deficits in discriminating between neighbouring positions occurred in both hemispaces after focal right hemispheric brain damage, but were restricted to the contralesional hemispace after focal left hemispheric brain damage. Alloacusis (perceptual shifts across the midline) occurred only after focal right hemispheric brain damage and was associated with minor or severe deficits in position discrimination. During spatial processing based on interaural intensity cues, deficits were less severe in the right hemispheric brain damage than left hemispheric brain damage group and no alloacusis occurred. These results, matched to anatomical data, suggest the existence of a binaural sound localization system predominantly based on interaural time difference cues and primarily supported by the right hemisphere. More generally, our data suggest that two distinct mechanisms contribute to: (i) the precise computation of spatial coordinates allowing spatial comparison within the contralateral hemispace for the left hemisphere and the whole space for the right hemisphere; and (ii) the building up of global auditory spatial representations in right temporo-parietal cortices.

Location-independent and location-linked representations of sound objects.

For the recognition of sounds to benefit perception and action, their neural representations should also encode their current spatial position and their changes in position over time. The dual-stream model of auditory processing postulates separate (albeit interacting) processing streams for sound meaning and for sound location. Using a repetition priming paradigm in conjunction with distributed source modeling of auditory evoked potentials, we determined how individual sound objects are represented within these streams. Changes in perceived location were induced by interaural intensity differences, and sound location was either held constant or shifted across initial and repeated presentations (from one hemispace to the other in the main experiment or between locations within the right hemispace in a follow-up experiment). Location-linked representations were characterized by differences in priming effects between pairs presented to the same vs. different simulated lateralizations. These effects were significant at 20-39 ms post-stimulus onset within a cluster on the posterior part of the left superior and middle temporal gyri; and at 143-162 ms within a cluster on the left inferior and middle frontal gyri. Location-independent representations were characterized by a difference between initial and repeated presentations, independently of whether or not their simulated lateralization was held constant across repetitions. This effect was significant at 42-63 ms within three clusters on the right temporo-frontal region; and at 165-215 ms in a large cluster on the left temporo-parietal convexity. Our results reveal two varieties of representations of sound objects within the ventral/What stream: one location-independent, as initially postulated in the dual-stream model, and the other location-linked.

Quantum analysis of the nondegenerate optical parametric oscillator with injected signal

In this paper we study the nondegenerate optical parametric oscillator with injected signal, both analytically and numerically. We develop a perturbation approach which allows us to find approximate analytical solutions, starting from the full equations of motion in the positive-P representation. We demonstrate the regimes of validity of our approximations via comparison with the full stochastic results. We find that, with reasonably low levels of injected signal, the system allows for demonstrations of quantum entanglement and the Einstein-Podolsky-Rosen paradox. In contrast to the normal optical parametric oscillator operating below threshold, these features are demonstrated with relatively intense fields.

The spatio-temporal brain dynamics of processing and integrating sound localization cues in humans.

Interaural intensity and time differences (IID and ITD) are two binaural auditory cues for localizing sounds in space. This study investigated the spatio-temporal brain mechanisms for processing and integrating IID and ITD cues in humans. Auditory-evoked potentials were recorded, while subjects passively listened to noise bursts lateralized with IID, ITD or both cues simultaneously, as well as a more frequent centrally presented noise. In a separate psychophysical experiment, subjects actively discriminated lateralized from centrally presented stimuli. IID and ITD cues elicited different electric field topographies starting at approximately 75 ms post-stimulus onset, indicative of the engagement of distinct cortical networks. By contrast, no performance differences were observed between IID and ITD cues during the psychophysical experiment. Subjects did, however, respond significantly faster and more accurately when both cues were presented simultaneously. This performance facilitation exceeded predictions from probability summation, suggestive of interactions in neural processing of IID and ITD cues. Supra-additive neural response interactions as well as topographic modulations were indeed observed approximately 200 ms post-stimulus for the comparison of responses to the simultaneous presentation of both cues with the mean of those to separate IID and ITD cues. Source estimations revealed differential processing of IID and ITD cues initially within superior temporal cortices and also at later stages within temporo-parietal and inferior frontal cortices. Differences were principally in terms of hemispheric lateralization. The collective psychophysical and electrophysiological results support the hypothesis that IID and ITD cues are processed by distinct, but interacting, cortical networks that can in turn facilitate auditory localization.

Four-level systems and a universal quantum gate

We discuss the possibility of implementing a universal quantum XOR gate by using two coupled quantum dots subject to external magnetic fields that are parallel and slightly different. We consider this system in two different field configurations. In the first case, parallel external fields with the intensity difference at each spin being proportional to the time-dependent interaction between the spins. A general exact solution describing this system is presented and analyzed to adjust field parameters. Then we consider parallel fields with intensity difference at each spin being constant and the interaction between the spins switching on and off adiabatically. In both cases we adjust characteristics of the external fields (their intensities and duration) in order to have the parallel pulse adequate for constructing the XOR gate. In order to provide a complete theoretical description of all the cases, we derive relations between the spin interaction, the inter-dot distance, and the external field. (C) 2008 WILEYNCH Verlag GmbH & Co. KGaA. Weinheim.

Evaluation of early tissue reactions after lumbar intertransverse process fusion using CT in a rabbit

OBJECTIVE: The objective of the study was to evaluate tissue reactions such as bone genesis, cartilage genesis and graft materials in the early phase of lumbar intertransverse process fusion in a rabbit model using computed tomography (CT) imaging with CT intensity (Hounsfield units) measurement, and to compare these data with histological results. MATERIALS AND METHODS: Lumbar intertransverse process fusion was performed on 18 rabbits. Four graft materials were used: autograft bone (n = 3); collagen membrane soaked with recombinant human bone morphogenetic protein-2 (rhBMP-2) (n = 5); granular calcium phosphate (n = 5); and granular calcium phosphate coated with rhBMP-2 (n = 5). All rabbits were euthanized 3 weeks post-operatively and lumbar spines were removed for CT imaging and histological examination. RESULTS: Computed tomography imaging demonstrated that each fusion mass component had the appropriate CT intensity range. CT also showed the different distributions and intensities of bone genesis in the fusion masses between the groups. Each component of tissue reactions was identified successfully on CT images using the CT intensity difference. Using CT color mapping, these observations could be easily visualized, and the results correlated well with histological findings. CONCLUSIONS: The use of CT intensity is an effective approach for observing and comparing early tissue reactions such as newly synthesized bone, newly synthesized cartilage, and graft materials after lumbar intertransverse process fusion in a rabbit model.

Tecnología de registro y reproducción sonora para entornos de realidad virtual

Este proyecto de fin de carrera tiene como objetivo obtener una visión detallada de los sistemas y tecnologías de grabación y reproducción utilizadas para aplicaciones de audio 3D y entornos de realidad virtual, analizando las diferentes alternativas existentes, su funcionamiento, características, detalles técnicos y sus ámbitos de aplicación. Como punto de partida se estudiará la teoría psicoacústica y la localización de fuentes sonoras en el espacio, base para el estudio de los sistemas de audio 3D. Se estudiará tanto la espacialización sonora en un espacio real y la espacialización virtual (simulación mediante procesado de información de la localización de fuentes sonoras), en los que intervienen algunos fenómenos acústicos y psicoacústicos como ITD, o diferencia de tiempo que existe entre una señal acústica que llega a los pabellones auditivos, la ILD, o diferencia de intensidad o amplitud que hay entre la señal que llega a los pabellones auditivos y la localización espacial mediante otra serie de mecanismos biaurales. Tras una visión general de la teoría psicoacústica y la espacialización sonora, se analizarán con detalle los elementos de grabación y reproducción existentes para audio 3D. Concretamente, a lo largo del proyecto se profundizará en el funcionamiento del sistema estéreo, caracterizado por el posicionamiento sonoro mediante la utilización de dos canales; del sistema biaural, caracterizado por reconstruir campos sonoros mediante el uso de las HRTF; de los sistemas multicanal, detallando gran parte de las alternativas y configuraciones existentes; del sistema Ambiophonics, caracterizado por implementar filtros de cruce; del sistema Ambisonics, y sus diferentes formatos y técnicas de codificación y decodificación; y del sistema Wavefield Synthesis, caracterizado por recrear ambientes sonoros en grandes espacios. ABSTRACT This project aims to get a detailed view of recording and reproducing systems and technologies used to 3D audio applications and virtual reality environments, analyzing the different alternatives available, their functioning, features, technical details and their different scopes of applications. As a starting point, will be studied the psychoacoustic theory and the localization of sound sources in space, basis for the 3D audio study. Will be studied both the spacialization of sound sources in real space as virtual spatialization of sound sources (simulation by information processing of localization of sound sources), in which involves some acoustic and psychoacoustic phenomena like ITD (or the Interaural time difference), the ILD, (or the Interaural Level Difference) and spatial localization by another set of binaural mechanisms. After a general overview of the psychoacoustics theory and the sound spatialization, will be analyzed in detail existing methods of recording and reproducing for 3D audio. Specifically, during the project will analyze the characteristics of the stereo systems, characterized by sound positioning using two channels; the binaural systems, characterized by reconstructing sound fields by using the HRTF; the multichannel systems, detailing many of the existing alternatives and configurations; the Ambiophonics system, which is characterized by implementing crosstalk elimination techniques; the Ambiosonics system, and its various formats and encoding and decoding techniques; and the Wavefield Synthesis system, characterized by recreate soundscapes in large spaces.

Diseño de una interfaz de representación gráfica de la base de datos de HRTF

El actual proyecto consiste en la creación de una interfaz gráfica de usuario (GUI) en entorno de MATLAB que realice una representación gráfica de la base de datos de HRTF (Head-Related Transfer Function). La función de transferencia de la cabeza es una herramienta muy útil en el estudio de la capacidad del ser humano para percibir su entorno sonoro, además de la habilidad de éste en la localización de fuentes sonoras en el espacio que le rodea. La HRTF biaural (terminología para referirse al conjunto de HRTF del oído izquierdo y del oído derecho) en sí misma, posee información de especial interés ya que las diferencias entre las HRTF de cada oído, conceden la información que nuestro sistema de audición utiliza en la percepción del campo sonoro. Por ello, la funcionalidad de la interfaz gráfica creada presenta gran provecho dentro del estudio de este campo. Las diferencias interaurales se caracterizan en amplitud y en tiempo, variando en función de la frecuencia. Mediante la transformada inversa de Fourier de la señal HRTF, se obtiene la repuesta al impulso de la cabeza, es decir, la HRIR (Head-Related Impulse Response). La cual, además de tener una gran utilidad en la creación de software o dispositivos de generación de sonido envolvente, se utiliza para obtener las diferencias ITD (Interaural Time Difference) e ILD (Interaural Time Difference), comúnmente denominados “parámetros de localización espacial”. La base de datos de HRTF contiene la información biaural de diferentes puntos de ubicación de la fuente sonora, formando una red de coordenadas esféricas que envuelve la cabeza del sujeto. Dicha red, según las medidas realizadas en la cámara anecoica de la EUITT (Escuela Universitaria de Ingeniería Técnica de Telecomunicación), presenta una precisión en elevación de 10º y en azimut de 5º. Los receptores son dos micrófonos alojados en el maniquí acústico llamado HATS (Hats and Torso Simulator) modelo 4100D de Brüel&Kjaer. Éste posee las características físicas que influyen en la percepción del entorno como son las formas del pabellón auditivo (pinna), de la cabeza, del cuello y del torso humano. Será necesario realizar los cálculos de interpolación para todos aquellos puntos no contenidos en la base de datos HRTF, este proceso es sumamente importante no solo para potenciar la capacidad de la misma sino por su utilidad para la comparación entre otras bases de datos existentes en el estudio de este ámbito. La interfaz gráfica de usuario está concebida para un manejo sencillo, claro y predecible, a la vez que interactivo. Desde el primer boceto del programa se ha tenido clara su filosofía, impuesta por las necesidades de un usuario que busca una herramienta práctica y de manejo intuitivo. Su diseño de una sola ventana reúne tanto los componentes de obtención de datos como los que hacen posible la representación gráfica de las HRTF, las HRIR y los parámetros de localización espacial, ITD e ILD. El usuario podrá ir alternando las representaciones gráficas a la vez que introduce las coordenadas de los puntos que desea visualizar, definidas por phi (elevación) y theta (azimut). Esta faceta de la interfaz es la que le otorga una gran facilidad de acceso y lectura de la información representada en ella. Además, el usuario puede introducir valores incluidos en la base de datos o valores intermedios a estos, de esta manera, se indica a la interfaz la necesidad de realizar la interpolación de los mismos. El método de interpolación escogido es el de la ponderación de la distancia inversa entre puntos. Dependiendo de los valores introducidos por el usuario se realizará una interpolación de dos o cuatro puntos, siendo éstos limítrofes al valor introducido, ya sea de phi o theta. Para añadir versatilidad a la interfaz gráfica de usuario, se ha añadido la opción de generar archivos de salida en forma de imagen de las gráficas representadas, de tal forma que el usuario pueda extraer los datos que le interese para cualquier valor de phi y theta. Se completa el presente proyecto fin de carrera con un trabajo de investigación y estudio comparativo de la función y la aplicación de las bases de datos de HRTF dentro del marco científico y de investigación. Esto ha hecho posible concentrar información relacionada a través de revistas científicas de investigación como la JAES (Journal of the Audio Engineering Society) o la ASA (Acoustical Society of America), además, del IEEE ( Institute of Electrical and Electronics Engineers) o la “Web of knowledge” entre otras. Además de realizar la búsqueda en estas fuentes, se ha optado por vías de información más comunes como Google Académico o el portal de acceso “Ingenio” a los todos los recursos electrónicos contenidos en la base de datos de la universidad. El estudio genera una ampliación en el conocimiento de la labor práctica de las HRTF. La mayoría de los estudios enfocan sus esfuerzos en mejorar la percepción del evento sonoro mediante su simulación en la escucha estéreo o multicanal. A partir de las HRTF, esto es posible mediante el análisis y el cálculo de datos como pueden ser las regresiones, siendo éstas muy útiles en la predicción de una medida basándose en la información de la actual. Otro campo de especial interés es el de la generación de sonido 3D. Mediante la base de datos HRTF es posible la simulación de una señal biaural. Se han diseñado algoritmos que son implementados en dispositivos DSP, de tal manera que por medio de retardos interaurales y de diferencias espectrales es posible llegar a un resultado óptimo de sonido envolvente, sin olvidar la importancia de los efectos de reverberación para conseguir un efecto creíble de sonido envolvente. Debido a la complejidad computacional que esto requiere, gran parte de los estudios coinciden en desarrollar sistemas más eficientes, llegando a objetivos tales como la generación de sonido 3D en tiempo real. ABSTRACT. This project involves the creation of a Graphic User Interface (GUI) in the Matlab environment which creates a graphic representation of the HRTF (Head-Related Transfer Function) database. The head transfer function is a very useful tool in the study of the capacity of human beings to perceive their sound environment, as well as their ability to localise sound sources in the area surrounding them. The binaural HRTF (terminology which refers to the HRTF group of the left and right ear) in itself possesses information of special interest seeing that the differences between the HRTF of each ear admits the information that our system of hearing uses in the perception of each sound field. For this reason, the functionality of the graphic interface created presents great benefits within the study of this field. The interaural differences are characterised in space and in time, varying depending on the frequency. By means of Fourier's transformed inverse of the HRTF signal, the response to the head impulse is obtained, in other words, the HRIR (Head-Related Impulse Response). This, as well as having a great use in the creation of software or surround sound generating devices, is used to obtain ITD differences (Interaural Time Difference) and ILD (Interaural Time Difference), commonly named “spatial localisation parameters”. The HRTF database contains the binaural information of different points of sound source location, forming a network of spherical coordinates which surround the subject's head. This network, according to the measures carried out in the anechoic chamber at the EUITT (School of Telecommunications Engineering) gives a precision in elevation of 10º and in azimuth of 5º. The receivers are two microphones placed on the acoustic mannequin called HATS (Hats and Torso Simulator) Brüel&Kjaer model 4100D. This has the physical characteristics which affect the perception of the surroundings which are the forms of the auricle (pinna), the head, neck and human torso. It will be necessary to make interpolation calculations for all those points which are not contained the HRTF database. This process is extremely important not only to strengthen the database's capacity but also for its usefulness in making comparisons with other databases that exist in the study of this field. The graphic user interface is conceived for a simple, clear and predictable use which is also interactive. Since the first outline of the program, its philosophy has been clear, based on the needs of a user who requires a practical tool with an intuitive use. Its design with only one window unites not only the components which obtain data but also those which make the graphic representation of the HRTFs possible, the hrir and the ITD and ILD spatial location parameters. The user will be able to alternate the graphic representations at the same time as entering the point coordinates that they wish to display, defined by phi (elevation) and theta (azimuth). The facet of the interface is what provides the great ease of access and reading of the information displayed on it. In addition, the user can enter values included in the database or values which are intermediate to these. It is, likewise, indicated to the interface the need to carry out the interpolation of these values. The interpolation method is the deliberation of the inverse distance between points. Depending on the values entered by the user, an interpolation of two or four points will be carried out, with these being adjacent to the entered value, whether that is phi or theta. To add versatility to the graphic user interface, the option of generating output files in the form of an image of the graphics displayed has been added. This is so that the user may extract the information that interests them for any phi and theta value. This final project is completed with a research and comparative study essay on the function and application of HRTF databases within the scientific and research framework. It has been possible to collate related information by means of scientific research magazines such as the JAES (Journal of the Audio Engineering Society), the ASA (Acoustical Society of America) as well as the IEEE (Institute of Electrical and Electronics Engineers) and the “Web of knowledge” amongst others. In addition to carrying out research with these sources, I also opted to use more common sources of information such as Academic Google and the “Ingenio” point of entry to all the electronic resources contained on the university databases. The study generates an expansion in the knowledge of the practical work of the HRTF. The majority of studies focus their efforts on improving the perception of the sound event by means of its simulation in stereo or multichannel listening. With the HRTFs, this is possible by means of analysis and calculation of data as can be the regressions. These are very useful in the prediction of a measure being based on the current information. Another field of special interest is that of the generation of 3D sound. Through HRTF databases it is possible to simulate the binaural signal. Algorithms have been designed which are implemented in DSP devices, in such a way that by means of interaural delays and wavelength differences it is possible to achieve an excellent result of surround sound, without forgetting the importance of the effects of reverberation to achieve a believable effect of surround sound. Due to the computational complexity that this requires, a great many studies agree on the development of more efficient systems which achieve objectives such as the generation of 3D sound in real time.

How do owls localize interaurally phase-ambiguous signals?

Owls and other animals, including humans, use the difference in arrival time of sounds between the ears to determine the direction of a sound source in the horizontal plane. When an interaural time difference (ITD) is conveyed by a narrowband signal such as a tone, human beings may fail to derive the direction represented by that ITD. This is because they cannot distinguish the true ITD contained in the signal from its phase equivalents that are ITD ± nT, where T is the period of the stimulus tone and n is an integer. This uncertainty is called phase-ambiguity. All ITD-sensitive neurons in birds and mammals respond to an ITD and its phase equivalents when the ITD is contained in narrowband signals. It is not known, however, if these animals show phase-ambiguity in the localization of narrowband signals. The present work shows that barn owls (Tyto alba) experience phase-ambiguity in the localization of tones delivered by earphones. We used sound-induced head-turning responses to measure the sound-source directions perceived by two owls. In both owls, head-turning angles varied as a sinusoidal function of ITD. One owl always pointed to the direction represented by the smaller of the two ITDs, whereas a second owl always chose the direction represented by the larger ITD (i.e., ITD − T).

How the owl resolves auditory coding ambiguity

The barn owl (Tyto alba) uses interaural time difference (ITD) cues to localize sounds in the horizontal plane. Low-order binaural auditory neurons with sharp frequency tuning act as narrow-band coincidence detectors; such neurons respond equally well to sounds with a particular ITD and its phase equivalents and are said to be phase ambiguous. Higher-order neurons with broad frequency tuning are unambiguously selective for single ITDs in response to broad-band sounds and show little or no response to phase equivalents. Selectivity for single ITDs is thought to arise from the convergence of parallel, narrow-band frequency channels that originate in the cochlea. ITD tuning to variable bandwidth stimuli was measured in higher-order neurons of the owl’s inferior colliculus to examine the rules that govern the relationship between frequency channel convergence and the resolution of phase ambiguity. Ambiguity decreased as stimulus bandwidth increased, reaching a minimum at 2–3 kHz. Two independent mechanisms appear to contribute to the elimination of ambiguity: one suppressive and one facilitative. The integration of information carried by parallel, distributed processing channels is a common theme of sensory processing that spans both modality and species boundaries. The principles underlying the resolution of phase ambiguity and frequency channel convergence in the owl may have implications for other sensory systems, such as electrolocation in electric fish and the computation of binocular disparity in the avian and mammalian visual systems.

Cellular mechanisms for resolving phase ambiguity in the owl's inferior colliculus

Both mammals and birds use the interaural time difference (ITD) for localization of sound in the horizontal plane. They may localize either real or phantom sound sources, when the signal consists of a narrow frequency band. This ambiguity does not occur with broadband signals. A plot of impulse rates or amplitude of excitatory postsynaptic potentials against ITDs (ITD curve) consists of peaks and troughs. In the external nucleus (ICX) of the owl's inferior colliculus, ITD curves show multiple peaks when the signal is narrow-band, such as tones. Of these peaks, one occurs at ITDi, which is independent of frequency, and others at ITDi ± T, where T is the tonal period. The ITD curve of the same neuron shows a large peak (main peak) at ITDi and no or small peaks (side peaks) at ITDi ± T, when the signal is broadband. ITD curves for postsynaptic potentials indicate that ICX neurons integrate the results of binaural cross-correlation in different frequency bands. However, the difference between the main and side peaks is small. ICX neurons further enhance this difference in the process of converting membrane potentials to impulse rates. Inhibition also appears to augment the difference between the main and side peaks.