932 resultados para Generalized impulse response functions
Resumo:
Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.
Resumo:
The capability to detect combustion in a diesel engine has the potential of being an important control feature to meet increasingly stringent emission regulations, develop alternative combustion strategies, and use of biofuels. In this dissertation, block mounted accelerometers were investigated as potential feedback sensors for detecting combustion characteristics in a high-speed, high pressure common rail (HPCR), 1.9L diesel engine. Accelerometers were positioned in multiple placements and orientations on the engine, and engine testing was conducted under motored, single and pilot-main injection conditions. Engine tests were conducted at varying injection timings, engine loads, and engine speeds to observe the resulting time and frequency domain changes of the cylinder pressure and accelerometer signals. The frequency content of the cylinder pressure based signals and the accelerometer signals between 0.5 kHz and 6 kHz indicated a strong correlation with coherence values of nearly 1. The accelerometers were used to produce estimated combustion signals using the Frequency Response Functions (FRF) measured from the frequency domain characteristics of the cylinder pressure signals and the response of the accelerometers attached to the engine block. When compared to the actual combustion signals, the estimated combustion signals produced from the accelerometer response had Root Mean Square Errors (RMSE) between 7% and 25% of the actual signals peak value. Weighting the FRF’s from multiple test conditions along their frequency axis with the coherent output power reduced the median RMSE of the estimated combustion signals and the 95th percentile of RMSE produced from each test condition. The RMSE’s of the magnitude based combustion metrics including peak cylinder pressure, MPG, peak ROHR, and work estimated from the combustion signals produced by the accelerometer responses were between 15% and 50% of their actual value. The MPG measured from the estimated pressure gradient shared a direct relationship to the actual MPG. The location based combustion metrics such as the location of peak values and burn durations were capable of RMSE measurements as low as 0.9°. Overall, accelerometer based combustion sensing system was capable of detecting combustion and providing feedback regarding the in cylinder combustion process
Resumo:
To assess if tree age may modulate the main climatic drivers of radial growth, two relict Pinus nigra subsp. salzmannii populations (Maria, most xeric site; Magina, least xeric site) were sampled in southern Spain near the limits of the species range. Tree-ring width residual chronologies for two age groups (mature trees, age <= 100 years (minimum 40 years); old trees, age > 100 years) were built to evaluate their responses to climate by relating them to monthly precipitation and temperature and a drought index (DRI) using correlation and response functions. We found that drought is the main driver of growth of relict P. nigra populations, but differences between sites and age classes were also observed. First, growth in the most xeric site depends on the drought severity during the previous autumn and the spring of the year of tree-ring formation, whereas in the relatively more mesic site growth is mainly enhanced by warm and wet conditions in spring. Second, growth of mature trees responded more to drought severity than that of old trees. Our findings indicate that drought severity will mainly affect growth of relict P. nigra populations dominated by mature trees in xeric sites. This conclusion may also apply to similar mountain Mediterranean conifer relicts.
Resumo:
Indoor localization systems become more interesting for researchers because of the attractiveness of business cases in various application fields. A WiFi-based passive localization system can provide user location information to third-party providers of positioning services. However, indoor localization techniques are prone to multipath and Non-Line Of Sight (NLOS) propagation, which lead to significant performance degradation. To overcome these problems, we provide a passive localization system for WiFi targets with several improved algorithms for localization. Through Software Defined Radio (SDR) techniques, we extract Channel Impulse Response (CIR) information at the physical layer. CIR is later adopted to mitigate the multipath fading problem. We propose to use a Nonlinear Regression (NLR) method to relate the filtered power information to propagation distances, which significantly improves the ranging accuracy compared to the commonly used log-distance path loss model. To mitigate the influence of ranging errors, a new trilateration algorithm is designed as well by combining Weighted Centroid and Constrained Weighted Least Square (WC-CWLS) algorithms. Experiment results show that our algorithm is robust against ranging errors and outperforms the linear least square algorithm and weighted centroid algorithm.
Resumo:
Long-term electrocardiogram (ECG) often suffers from relevant noise. Baseline wander in particular is pronounced in ECG recordings using dry or esophageal electrodes, which are dedicated for prolonged registration. While analog high-pass filters introduce phase distortions, reliable offline filtering of the baseline wander implies a computational burden that has to be put in relation to the increase in signal-to-baseline ratio (SBR). Here we present a graphics processor unit (GPU) based parallelization method to speed up offline baseline wander filter algorithms, namely the wavelet, finite, and infinite impulse response, moving mean, and moving median filter. Individual filter parameters were optimized with respect to the SBR increase based on ECGs from the Physionet database superimposed to auto-regressive modeled, real baseline wander. A Monte-Carlo simulation showed that for low input SBR the moving median filter outperforms any other method but negatively affects ECG wave detection. In contrast, the infinite impulse response filter is preferred in case of high input SBR. However, the parallelized wavelet filter is processed 500 and 4 times faster than these two algorithms on the GPU, respectively, and offers superior baseline wander suppression in low SBR situations. Using a signal segment of 64 mega samples that is filtered as entire unit, wavelet filtering of a 7-day high-resolution ECG is computed within less than 3 seconds. Taking the high filtering speed into account, the GPU wavelet filter is the most efficient method to remove baseline wander present in long-term ECGs, with which computational burden can be strongly reduced.
Resumo:
Investigations have shown that the analysis results of ground level enhancements (GLEs) based on neutron monitor (NM) data for a selected event can differ considerably depending the procedure used. This may have significant consequences e.g. for the assessment of radiation doses at flight altitudes. The reasons for the spread of the GLE parameters deduced from NM data can be manifold and are at present unclear. They include differences in specific properties of the various analysis procedures (e.g. NM response functions, different ways in taking into account the dynamics of the Earth’s magnetospheric field), different characterisations of the solar particle flux near Earth as well as the specific selection of NM stations used for the analysis. In the present paper we quantitatively investigate this problem for a time interval during the maximum phase of the GLE on 13 December 2006. We present and discuss the changes in the resulting GLE parameters when using different NM response functions, different model representations of the Earth’s magnetospheric field as well as different assumptions for the solar particle spectrum and pitch angle distribution near Earth. The results of the study are expected to yield a basis for the reduction in the spread of the GLE parameters deduced from NM data.
Resumo:
This paper explores the dynamic linkages that portray different facets of the joint probability distribution of stock market returns in NAFTA (i.e., Canada, Mexico, and the US). Our examination of interactions of the NAFTA stock markets considers three issues. First, we examine the long-run relationship between the three markets, using cointegration techniques. Second, we evaluate the dynamic relationships between the three markets, using impulse-response analysis. Finally, we explore the volatility transmission process between the three markets, using a variety of multivariate GARCH models. Our results also exhibit significant volatility transmission between the second moments of the NAFTA stock markets, albeit not homogenous. The magnitude and trend of the conditional correlations indicate that in the last few years, the Mexican stock market exhibited a tendency toward increased integration with the US market. Finally, we do note that evidence exists that the Peso and Asian financial crises as well as the stock-market crash in the US affect the return and volatility time-series relationships.
Resumo:
We combine phytoplankton occurrence data for 119 species from the continuous plankton recorder with climatological environmental variables in the North Atlantic to obtain ecological response functions of each species using the MaxEnt statistical method. These response functions describe how the probability of occurrence of each species changes as a function of environmental conditions and can be reduced to a simple description of phytoplankton realized niches using the mean and standard deviation of each environmental variable, weighted by its response function. Although there was substantial variation in the realized niche among species within groups, the envelope of the realized niches of North Atlantic diatoms and dinoflagellates are mostly separate in niche space.
Resumo:
Indoor multpropagation channel is modeled by the Kaiser electromagnetic wavelet. A method for channel characterization is proposed by modeling all the reflections of indoor propagation in a kernel function instead of its impulse response. This led us to consider a fractal modulation scheme in which Kaiser wavelets substitute the traditional sinusoidal carrier.
Resumo:
In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redun-dancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.
Resumo:
A system for simultaneous 2D estimation of rectangular room and transceiver localization is proposed. The system is based on two radio transceivers, both capable of full duplex operations (simultaneous transmission and reception). This property enables measurements of channel impulse response (CIR) at the same place the signal is transmitted (generated), commonly known as self-to-self CIR. Another novelty of the proposed system is the spatial CIR discrimination that is possible with the receiver antenna design which consists of eight sectorized antennas with 45° aperture in the horizontal plane and total coverage equal to the isotropic one. The dimensions of a rectangular room are reconstructed directly from spatial radio impulse responses by extracting the information regarding round trip time (RTT). Using radar approach estimation of walls and corners positions is derived. Tests using measured data were performed, and the simulation results confirm the feasibility of the approach.
Resumo:
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.
Resumo:
El objetivo de este Proyecto Fin de Carrera es el estudio y simulación de la sonorización de una sala de cine mediante la utilización del sistema DOLBY ATMOS. Para ello, se simulará la sala 6 del complejo de cines Kinépolis de Madrid utilizando el programa de simulación electroacústica EASE en el que se dispondrá el sistema de sonido DOLBY ATMOS. Primero se procederá a realizar el modelo geométrico en el programa EASE, a partir de los planos de la instalación y medidas realizadas en el recinto. Este programa de simulación permite obtener los parámetros acústicos y electroacústicos necesarios para realizar el estudio de la sala. Luego se diseñará el sistema de sonido de acuerdo a las disposiciones del sistema DOLBY ATMOS, mediante la ubicación de sistemas de altavoces de cine existentes en el mercado, siempre intentando mantener el uso de la sala de forma convencional como DOLBY DIGITAL y cumpliendo los requisitos de uniformidad y ángulos de apuntamiento recomendados por DOLBY. A continuación, una vez dispuestos los altavoces, se procederá a su configuración, realizando una ecualización y ajuste de nivel de manera individual para cada una de las fuentes sonoras, tanto de los altavoces de pantalla, altavoces de surround de pared y techo y los altavoces de subgraves. Como resultado de todo ello, se comprobarán parámetros como la inteligibilidad, respuesta impulsiva, respuesta en frecuencia y tiempo de reverberación en diferentes puntos de escucha, comparando los resultados obtenidos entre ellos. También se realizará una configuración compatible con el sistema de sonido 7.1, realizando su correspondiente configuración, ecualización, ajuste y aplicando los retardos necesarios. Una vez esté todo configurado, será dar un presupuesto de lo que supondría la reformar de un cine convencional a un sistema DOLBY ATMOS, teniendo en cuenta el número de altavoces disponibles en la sala actual, los modelos utilizados, amplificadores y mano de obra. También se realizará un diagrama de conexionado del sistema de sonido utilizado en el proyecto, incluyendo todos los parámetros necesarios de la configuración. Por último se comprobará la viabilidad técnica y económica del sistema diseñado, viendo cuál es la opción que más se adecua a cada necesidad y sugiriendo soluciones a los posibles problemas que se puedan encontrar. ABSTRACT. The main aim of this Project is the study and simulation of the sound of a movie theater by using DOLBY ATMOS system. It is going to be simulated the movie theatre 6 at Kinepolis cinema complex in Madrid using the simulation program EASE according to the sound system DOLBY ATMOS. First of all we proceed to conduct the geometric pattern in the EASE program, from installation drawings and measurements made on the premises. This simulation program allows getting the acoustic and electroacoustic parameters necessary for the study of the theatre. Then the sound system designed according to the suggestions of ATMOS DOLBY, by locating theater speaker systems on the market, always trying to keep the use of the room for DOLBY DIGITAL conventional and meeting the requirements of uniformity and pointing angles DOLBY recommended. Then, once the speakers are prepared, you can proceed to configure, make equalization and level setting individually for each of the sound sources, both screen speakers, surround speakers (wall and ceiling) and subwoofer. As a result, parameters are checked as intelligibility, impulse response, frequency response and reverberation time in different listening points, comparing the results between each other. There will also be configured to support 7.1 sound system, making the corresponding settings, equalization, level setting and applying the necessary delays. Once everything is configured, it will give an estimate of what would be the reform of a conventional film DOLBY ATMOS system, taking into account the number of speakers available in the current room, the models used, amplifiers and labor. Also there will be a wiring diagram of the sound system used in this project, including all of the configuration parameters needed. Finally, check the technical and economic feasibility of the designed system, seeing what is the option that best suits to each need and suggesting possible solutions to problems you might find during the process.
Resumo:
Hollow heart is a problem quite specific to seedless watermelon, affecting to all varieties. Percentage of fruits affected range from nil to up to more than 50% of the fruits. The acoustic impulse response of 158 watermelons was measured using a prepolarized free-field microphone. After carrying out a fast Fourier transformation on the time signal of the generated sound several acoustic parameters were evaluated. Values of spectral density were significantly different between 'good watermelons' and 'hollow heart watermelons'.
Resumo:
Scaling is becoming an increasingly important topic in the earth and environmental sciences as researchers attempt to understand complex natural systems through the lens of an ever-increasing set of methods and scales. The guest editors introduce the papers in this issue’s special section and present an overview of some of the work being done. Scaling remains one of the most challenging topics in earth and environmental sciences, forming a basis for our understanding of process development across the multiple scales that make up the subsurface environment. Tremendous progress has been made in discovery, explanation, and applications of scaling. And yet much more needs to be done and is being done as part of the modern quest to quantify, analyze, and manage the complexity of natural systems. Understanding and succinct representation of scaling properties can unveil underlying relationships between system structure and response functions, improve parameterization of natural variability and heterogeneity, and help us address societal needs by effectively merging knowledge acquired at different scales.