Costas array

While simulation (digital twins) in Architectural Acoustics has advanced significantly due to cloud computing, novel algorithms, and machine learning, progress in research and development of innovative Acoustic diffusers for applications in recording and performance arts has been limited for the past 2 decades. Recording and performance arts is and has always been interwoven with acoustics, which are primary surfaced-based (2D) and not portable (semi-permanent). While previous studies have generally examined the diffusivity of a lower order sonic crystal in an anechoic chamber, It is far removed from practical real-world applications. The author has put forward a novel higher order sonic crystal hybrid based on Costas Array-irido, to investigate the potential of being employed as a volumetric diffuser is a valid application. This proposed sonic crystal offers a level of portability and modularity that surpasses traditional surface diffuser counterparts (i.e. QRD and skyline), while also serving as an effective noise barrier. The paper details the generation of the Costas Array, showcases both theoretical predictions and experimental results related to the proposed sonic crystal's performance as a volumetric diffuser and noise barrier. Audio samples from evaluation sessions that explore different configurations, placements, and applications involving musicians from diverse genres, instrumentations, and demographics are included for interpretation.

This paper presents a study of sound absorption of slat structures. The paper stems from a need for a tool to predict the absorption coefficient for slat structures used in spaces for critical listening. For an acoustic designer, the accurate knowledge of absorption coefficient is vital in successful planning and predicting the behaviour of sound in, say a sound studio or instrument rehearsal room.

We derive the duality relation for the Hilbert series H (d m ; z) of almost symmetric numerical semigroup S (d m) combining it with its dual H d m ; z −1. On this basis we establish the bijection between the multiset of degrees of the syzygy terms and the multiset of the gaps F j , generators d i and their linear combinations. We present the relations for the sums of the Betti numbers of even and odd indices separately. We apply the duality relation to the simple case of the almost symmetric semigroups of maximal embedding dimension, and give the necessary and efficient conditions for minimal set d m to generate such semigroups.

It is well established that Schroeder diffusers may be used as surface treatment to promote diffuse sound fields in auditoria over a target frequency range. Quadratic Residue Diffusers are very effective within a design frequency bandwidth, and this frequency bandwidth may be significantly extended by a nested or fractal design. Publicly available data typically publishes diffusion coefficients separately for the parent diffuser and the child diffuser, with some ambiguity surrounding the effect the two levels have on each other, and the performance at 'crossover' frequencies. This paper uses an optimised 2D boundary element method to investigate the differences in results when the parent and child diffusers are modelled separately, and as an integrated design. It is found that the scattering properties of the child diffuser are significantly modified by the well of the parent diffuser in which it is placed. More interestingly, the excellent scattering properties of the fract...

The paper presents a number of problems related to sound reflections, and possible solutions or approximations that can be used in computer models. The problems include:-specular and diffuse reflections,-early and late reflections,-scattering due to rough structure of surfaces,-diffraction due to finite size of surfaces,-curved surfaces, convex and concave surfaces,-angle dependent absorption. Due to the wave nature of sound it is very important for the quality of a simulation model, that diffusion and diffraction effects are included in a proper way. This can lead to more reliable computer models and at the same time, good results can be obtained with a minimum of calculation time.

Helou (Media, PA) and J. Pihko (Helsinki) 1. Introduction. Given a subset A of N = {0, 1, 2,. . .} and a positive integer h, the h-representation function by A is the function which to each integer n ≥ 0 associates the number r h (A, n) of h-tuples of elements of A whose sum is equal to n. The study of such functions, their properties and their characterizations are the focus of much attention in additive number theory. In particular, they are used to study some important notions such as that of basis. The set A is called an h-basis (resp. an asymptotic h-basis) of N if every integer n ≥ 0 (resp. every sufficiently large integer n) is the sum of h elements of A. The set A is called a Sidon set if all the sums a + b, with a, b ∈ A and a ≤ b, are distinct, i.e. if r 2 (A, n) ≤ 2 for all integers n ≥ 0. An open problem due to P. Erdős, A. Sárközy and V. T. Sós [1] asks if there exists a Sidon set which is an asymptotic 3-basis of N. This problem was mistakenly presented in [3] as asking if a Sidon set can be an asymptotic 2-basis of N. Even though the negative answer to the latter question is an easy consequence of some well-known properties, it is not extant in published explicit form, and it would therefore not be without interest to give a proof using some new ideas. In this paper, we give some new properties of the 2-representation function of an infinite subset A of N, of intrinsic interest. We then apply them to give a simple proof of the fact that a Sidon set cannot be an asymptotic 2-basis of N. We then turn to the real open problem of the existence of a Sidon set which is an asymptotic 3-basis of N, and we provide a partial answer by proving that a Sidon set cannot be a 3-basis of N. We also give an algorithm for finding, if any exists, a Sidon set A such that, from a specific point on, every integer is the sum of three elements of A.

There is a considerable increase in the use of noise barriers in recent years. Noise barriers as a control noise solution can increase the insertion loss to protect receivers. This paper presents the results of an investigation about the acoustic efficiency of primitive root sequence diffuser (PRD) on an environmental single T-shape barrier design. A 2D boundary element method (BEM) is used to predict the insertion loss of the tested barriers. The results of rigid and with a different sequence diffuser coverage are also predicted for comparison. Employing PRD on the top surface of T-shape barrier has been found to improve the performance of barriers in comparison with the use of rigid and QRD coverage at the examined receiver locations. It has been found that decreasing the design frequency of PRD shifts the frequency effects towards lower frequencies, and therefore the overall A-weighted insertion loss is improved. It was also found that using wire mesh with reasonably efficient re...

The Costas Array Problem is a highly combinatorial problem linked to radar applications. We present in this paper its detailed modeling and solving by Adaptive Search, a constraint-based local search method. Experiments have been done on both sequential and parallel hardware up to several hundreds of cores. Performance evaluation of the sequential version shows results outperforming previous implementations, while the parallel version shows nearly linear speedups up to 8,192 cores.

Active technologies can enable room acoustic diffusers to operate over a wider bandwidth than passive devices, by extending the bass response. Active impedance control can be used to generate surface impedance distributions which cause wavefront dispersion, as opposed to the more normal absorptive or pressure-cancelling target functions. This paper details the development of two new types of active diffusers which are difficult, if not impossible, to make as passive wide-band structures. The first type is a maximum length sequence diffuser where the well depths are designed to be frequency dependent to avoid the critical frequencies present in the passive device, and so achieve performance over a finite-bandwidth. The second is a Bessel diffuser, which exploits concepts developed for transducer arrays to form a hybrid absorberdiffuser. Details of the designs are given, and measurements of scattering and impedance used to show that the active diffusers are operating correctly over a bandwidth of about 100Hz to 1.1kHz. Boundary element method simulation is used to show how more application-realistic arrays of these devices would behave.

The Costas Array Problem is a highly combinatorial problem linked to radar applications. We present in this paper its detailed modeling and solving by Adaptive Search, a constraint-based local search method. Experiments have been done on both sequential and parallel hardware up to several hundreds of cores. Performance evaluation of the sequential version shows results outperforming previous implementations, while the parallel version shows nearly linear speedups up to 8,192 cores.

It is well established that Schroeder diffusers may be used as surface treatment to promote diffuse sound fields in auditoria over a target frequency range. Quadratic Residue Diffusers are very effective within a design frequency bandwidth, and this frequency bandwidth may be significantly extended by a nested or fractal design. Publicly available data typically publishes diffusion coefficients separately for the parent diffuser and the child diffuser, with some ambiguity surrounding the effect the two levels have on each other, and the performance at 'crossover' frequencies. This paper uses an optimised 2D boundary element method to investigate the differences in results when the parent and child diffusers are modelled separately, and as an integrated design. It is found that the scattering properties of the child diffuser are significantly modified by the well of the parent diffuser in which it is placed. More interestingly, the excellent scattering properties of the fract...

A distinct difference configuration is a set of points in Z 2 with the property that the vectors (difference vectors) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the k-hop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of k or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the k-hop coverage of a distinct difference configuration with m points, and exploit a connection with B h sequences to construct configurations with maximal khop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application.

A two-dimensional grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many applications such as radar, sonar, physical alignment, and time-position synchronization. Rather than restricting dots to lie in a square or rectangle, as previously studied, we restrict the maximum distance between dots of the configuration; the motivation for this is a new application of such configurations to key distribution in wireless sensor networks. We consider configurations in the hexagonal grid as well as in the traditional square grid, with distances measured both in the Euclidean metric, and in the Manhattan or hexagonal metrics. We note that these configurations are confined inside maximal anticodes in the corresponding grid. We classify maximal anticodes for each diameter in each grid. We present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes. Our bounds settle (in the negative) a question of Golomb and Taylor on the existence of honeycomb arrays of arbitrarily large size. We present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various two-dimensional shapes (such as anticodes) by considering periodic configurations with distinct differences in the square grid.

With every passing decade, the issue of noise pollution has worsened in urban areas and the usefulness of noise barriers have increased. To improve the effectiveness of noise barriers in limited frequency bandwidth, a few researchers have reported that quadratic residue diffusers as noise barrier top-profiles have shown promising noise attenuation, albeit in their narrow frequency bandwidth. It has been reported for room acoustics that the frequency bandwidth of quadratic residue diffusers may significantly be extended by a nested or fractal design. Therefore, the aim of this work is to investigate the potential of fractal acoustic diffusers for noise barrier application. Upon conducting a numerical analysis of 1-D fractal diffuser as noise barrier topprofile using finite element method, it is observed that fractal diffusers outperformed T-barriers in both the shadow zone and the transition zone. Hence, fractal acoustic diffusers are promising candidates for our application as these have good diffusion properties in the integrated frequency bandwidth. If properly designed, the fractal diffuser top-edge device can be used to enhance noise attenuation over extended frequency bandwidth.

A two-dimensional grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many applications such as radar, sonar, physical alignment, and time-position synchronization. Rather than restricting dots to lie in a square or rectangle, as previously studied, we restrict the maximum distance between dots of the configuration; the motivation for this is a new application of such configurations to key distribution in wireless sensor networks. We consider configurations in the hexagonal grid as well as in the traditional square grid, with distances measured both in the Euclidean metric, and in the Manhattan or hexagonal metrics. We note that these configurations are confined inside maximal anticodes in the corresponding grid. We classify maximal anticodes for each diameter in each grid. We present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes. Our bounds settle (in the negative) a question of Golomb and Taylor on the existence of honeycomb arrays of arbitrarily large size. We present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various two-dimensional shapes (such as anticodes) by considering periodic configurations with distinct differences in the square grid.

This paper presents research on a rule-based approach to designing creative acoustic diffuser arrays. A shape grammar-influenced design method is specified that uses shape rules to recursively design arrays of quadratic residue diffusers (QRD) in ways that are neither mechanical nor deterministic.

Boundary Element Methods (BEMs) may be used to model scattering of sound by surfaces such as diffusers, accelerating prototyping of new Room Acoustics treatments. Unlike the more widely used frequency domain method, the time domain BEM is usually solved in an iterative manner so can exhibit instability, a crucial impediment to its widespread use. These instabilities are primarily associated with resonance of the cavities formed by closed surface sections, but may also be caused by discretisation or integration error corrupting physically relevant damped resonances. Previous works on time domain BEMs have focused on idealised surfaces, such as spheres and plates, and little is published on their performance for the more complex surfaces treatments typical to Room Acoustics. Consequentially, this paper will apply the method to model the transient behaviour of Schroeder Diffusers and Binary Amplitude Diffusers. Cavity resonances and integration error are addressed through use of the Combined Field Integral Equation and an adaptive contour integration scheme respectively. Thin and absorbing surface sections are implemented as required by the respective diffusers. Accuracy and stability is tested by comparison to verified frequency domain BEMs.

Let G be an additive group of order v. A k-element subset D of G is called a (v, k, λ, t)almost difference set if the expressions g − h, for g and h in D, represent t of the non-identity elements in G exactly λ times and every other non-identity element λ + 1 times. Almost difference sets are highly sought after as they can be used to produce functions with optimal nonlinearity, cyclic codes, and sequences with three-level autocorrelation. A set of positive integers A is called a Golomb ruler if the difference between two distinct elements of A are different. In this paper, we use Singer type Golomb rulers to construct new families of almost difference sets. Additionally, we constructed 2-adesigns from these almost difference sets.

When audio-frequency sound is incident near grazing on acoustically-hard surfaces with periodic sub-wavelength roughness air-borne acoustic surface waves are generated which could be used to amplify acoustic signals and, therefore, improve detection ranges of, perimeter security systems. Experimental and numerical studies using the Boundary Element Method (BEM) of the sound field generated over periodically-spaced rectangular strips also show several enhancements as a result of complex interactions between the sound field and the rough surface. Surface waves result in excess attenuation spectra with anomalous maxima greater than the 6.02 dB that would be expected from constructive interference above a smooth acoustically rigid surface. The enhancements are found to depend on the roughness spacing and can be attributed to effects due to the finite width and periodicity of the array, quarter-wavelength resonances in the gaps between elements and Bragg diffraction. Pressure maps of the...

Most conventional diffusers take the form of a surface based treatment, and as a result can only operate in hemispherical space. Placing a diffuser in the volume of a room might provide greater efficiency by allowing scattering into the whole space. A periodic cylinder array (or sonic crystal) produces periodicity lobes and uneven scattering. Introducing defects into an array, by removing or varying the size of some of the cylinders, can enhance their diffusing abilities. This paper applies number theoretic concepts to create cylinder arrays that have more even scattering. Predictions using a Boundary Element Method are compared to measurements to verify the model, and suitable metrics are adopted to evaluate performance. Arrangements with good aperiodic autocorrelation properties tend to produce the best results. At low frequency power is controlled by object size and at high frequency diffusion is dominated by lattice spacing and structural similarity. Consequently the operational bandwidth is rather small. By using sparse arrays and varying cylinder sizes, a wider bandwidth can be achieved.

Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper investigates a new type of 2D diffusers obtained by the Cymatics phenomena. Cymatics is the study of sound and vibration made visible, typically on the surface of a plate, diaphragm or membrane. Four shapes of the diffusers were designed by the Cymatic shapes and modeled by using a quadratic residue sequence. The polar response of the diffusers was measured using DIRAC software. Polar response results were generally consistent with expectations. This type of diffusers can generate a uniform polar response over the frequency range we are interested in (400Hz4000Hz). It is found that this type of acoustic diffusers can be used to maintain the acoustic energy in a room, and at the same time can treat unwanted echoes and reflections by scattering sound waves in many directions.

The appearance of band gaps in periodic media is a well known phenomenon. In the past 15 years an increasing attention was payed to sonic crystals, as the properties of such arrangements could lead to the design of innovative noise barriers. In fact, sonic crystal barriers exhibit good insulation properties at some frequencies and could be tuned in order to cause stop bands in a frequency range centred at 1 kHz, classic for road traffic noise pollution. In this paper measurements are described that were conducted over an array of cylinders arranged in a square lattice, whose Bragg band gap was centred at about 900 Hz. Measurements were conducted in accordance with EN 1793-6. Together with measurements, FE simulations were carried out in order to address and verify the procedure. In the simulations, cylinders were assumed to be infinitely rigid and the system was investigated in a 2d domain. The first hypothesis is consistent with the high contrast between the acoustic properties of air and PVC. The second one is consistent with the measurement method, as the windowing of the IRs leads to an evaluation of the attenuation due only to the BG without comprising any effect from ground reflections. Simulation and measurements are compared and discussed over a variety of cases.

The appearance of band gaps in periodic media is a well known phenomenon. In the past 15 years an increasing attention was payed to sonic crystals, as the properties of such arrangements could lead to the design of innovative noise barriers. In fact, sonic crystal barriers exhibit good insulation properties at some frequencies and could be tuned in order to cause stop bands in a frequency range centred at 1 kHz, classic for road traffic noise pollution. In this paper measurements are described that were conducted over an array of cylinders arranged in a square lattice, whose Bragg band gap was centred at about 900 Hz. Measurements were conducted in accordance with EN 1793-6. Together with measurements, FE simulations were carried out in order to address and verify the procedure. In the simulations, cylinders were assumed to be infinitely rigid and the system was investigated in a 2d domain. The first hypothesis is consistent with the high contrast between the acoustic properties of air and PVC. The second one is consistent with the measurement method, as the windowing of the IRs leads to an evaluation of the attenuation due only to the BG without comprising any effect from ground reflections. Simulation and measurements are compared and discussed over a variety of cases.

A set A is a Sidon set in an additive group G if every element of G can be written at most one way as sum of two elements of A. A particular case of two-dimensional Sidon sets are the sonar sequences, which are two-dimensional synchronization patterns. The main known constructions of sonar sequences are reminiscent of Costas arrays constructions (Welch and Golomb). Other constructions are Quadratic and Shift. In this work we present new constructions of sonar sequences, independent of the named above, using one-dimensional Sidon sets.

Abstract—A set A is a Sidon set in an additive group G if every element of G can be written at most one way as sum of two elements of A. A particular case of two–dimensional Sidon sets are the sonar sequences, which are two–dimensional synchronization patterns. The main known constructions of sonar sequences are reminiscent of Costas arrays constructions (Welch and Golomb). Other constructions are Quadratic and Shift. In this work we present new constructions of sonar sequences, independent of the named above, using one–dimensional Sidon sets. Keywords—Costas arrays, Sidon sets, sonar sequences. I.

A set of positive integers A is called a g-Golomb ruler if the difference between two distinct elements of A is repeated at most g times. This definition is a generalization of the Golomb ruler (g = 1). In this paper we construct g-Golomb ruler from Golomb ruler and we prove two theorems about extremal functions associated with this sets

Subpixel methods increase the accuracy and efficiency of image detectors, processing units, and algorithms and provide very cost-effective systems for object tracking. A recently proposed method permits micropixel and submicropixel accuracies providing certain design constraints on the target are met. In this paper, we explore the use of Costas arrays -permutation matrices with ideal auto-ambiguity properties -for the design of such targets.

A distinct difference configuration is a set of points in Z 2 with the property that the vectors (difference vectors) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the k-hop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of k or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the k-hop coverage of a distinct difference configuration with m points, and exploit a connection with B h sequences to construct configurations with maximal khop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application.

Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper investigates a new type of 2D diffusers obtained by the Cymatics phenomena. Cymatics is the study of sound and vibration made visible, typically on the surface of a plate, diaphragm or membrane. Four shapes of the diffusers were designed by the Cymatic shapes and modeled by using a quadratic residue sequence. The polar response of the diffusers was measured using DIRAC software. Polar response results were generally consistent with expectations. This type of diffusers can generate a uniform polar response over the frequency range we are interested in (400Hz-4000Hz). It is found that this type of acoustic diffusers can be used to maintain the acoustic energy in a room, and at the same time can treat unwanted echoes and reflections by scattering sound waves in many directions.

Let G be an additive group of order v. A k-element subset D of G is called a (v, k, λ, t)-almost difference set if the expressions gh, for g and h in D, represent t of the non-identity elements in G exactly λ times and every other non-identity element λ + 1 times. Almost difference sets are highly sought after as they can be used to produce functions with optimal nonlinearity, cyclic codes, and sequences with three-level autocorrelation. A set of positive integers A is called a Golomb ruler if the difference between two distinct elements of A are different. In this paper, we use Singer type Golomb rulers to construct new families of almost difference sets. Additionally, we constructed 2-adesigns from these almost difference sets.

The construction and evaluation of diffusion devices are at present often based on unsupported assumptions as to the relative performance of disparate design styles and often employs unnecessarily complicated measurement techniques. Well known, and reliable methods exist for measuring and comparing the gross acoustic properties of loudspeakers and by applying these methods to the evaluation of diffusion devices similar measurements of performance can be made with relative ease. The results obtained can allow valid direct comparison, all without undue complexity, or any risk of incoherence. The design of diffusors has evolved from implementations using curved surfaces into a predominance of alternative implementations using corrugated surfaces with the optimal dimension for the crenulations often divined from various interpretations of number theory. Traditional loudspeaker directivity and frequency response magnitude measurements demonstrate that traditional curved surface diffusors...

The Costas Array Problem is a highly combinatorial problem linked to radar applications. We present in this paper its detailed modeling and solving by Adaptive Search, a constraint-based local search method. Experiments have been done on both sequential and parallel hardware up to several hundreds of cores. Performance evaluation of the sequential version shows results outperforming previous implementations, while the parallel version shows nearly linear speedups up to 8,192 cores.

Amultiple scattering method is developed to model an array of N cylinders positioned in front of aSchroeder diffuser.R esults are compared against the more computationally intensive boundary element method, as well as existing multiple scattering methods for cylinders alone. An investigation of scattering performance from a cylinder arrangement in front of aS chroeder diffuser is also performed. The addition of cylinders is shown to offer potential benefits such as reducing the effects of periodicity in the Schroeder diffuser.

When audio-frequency sound is incident near grazing on acoustically-hard surfaces with periodic sub-wavelength roughness air-borne acoustic surface waves are generated which could be used to amplify acoustic signals and, therefore, improve detection ranges of, perimeter security systems. Experimental and numerical studies using the Boundary Element Method (BEM) of the sound field generated over periodically-spaced rectangular strips also show several enhancements as a result of complex interactions between the sound field and the rough surface. Surface waves result in excess attenuation spectra with anomalous maxima greater than the 6.02 dB that would be expected from constructive interference above a smooth acoustically rigid surface. The enhancements are found to depend on the roughness spacing and can be attributed to effects due to the finite width and periodicity of the array, quarter-wavelength resonances in the gaps between elements and Bragg diffraction. Pressure maps of the...

An ISO working group is preparing a standard for measuring the random-incidence scattering coefficient in the reverberation room [1]. This paper comments on the experiments with the realscale application of this technique to a sine-shaped surface, a one-dimensional and a twodimensional diffuser and discusses on several parameters that are related to the measurement quality and reliability.

The appearance of band gaps in periodic media is a well known phenomenon. In the past 15 years an increasing attention was payed to sonic crystals, as the properties of such arrangements could lead to the design of innovative noise barriers. In fact, sonic crystal barriers exhibit good insulation properties at some frequencies and could be tuned in order to cause stop bands in a frequency range centred at 1 kHz, classic for road traffic noise pollution. In this paper measurements are described that were conducted over an array of cylinders arranged in a square lattice, whose Bragg band gap was centred at about 900 Hz. Measurements were conducted in accordance with EN 1793-6. Together with measurements, FE simulations were carried out in order to address and verify the procedure. In the simulations, cylinders were assumed to be infinitely rigid and the system was investigated in a 2d domain. The first hypothesis is consistent with the high contrast between the acoustic properties of ...

The use of acoustic diffusers to reduce noise in urban areas has been recently numerically investigated [Acta Acustica united with Acustica, Vol. 95 (2009), p. 653668]. It was shown that a significant noise reduction can be observed by considering diffusers on the building facades. In the present study, an experimental investigation is proposed to validate last results. Measurements are carried out using a 1:10 urban street scale model, with and without acoustics diffusers, in order to evaluate the real effect of such devices, for several configurations. Results, in terms of sound attenuation and reverberation, show that a positive effect can be observed, provided that the number of diffusers is significant.

The scattering phenomenon is known to be of great importance for the acoustic quality of a performance arts space. The scattering of sound can be achieved in different ways: it can be obtained by the presence of architectural and/or decorating elements inside a room (e.g., columns, statues), by the geometry and roughness of a surface (e.g., Quadratic Residue Diffuser (QRD)) and by the diffraction effect occurring when a sound wave hits the edges of an obstacle. This article deals with the surface scattering effects and the diffusion phenomenon only related to MDF and plywood panels tested by disposing the wells both horizontally and vertically. The test results undertaken inside a semi-reverberant room and inside a large reverberant room have been compared to highlight the success and the failure of the measuring methodologies. In detail, according to the existing standards and regulations (i.e., ISO 17497—Part 2), diffusion measurements have been undertaken on a few selected types ...

When audio-frequency sound is incident near grazing on acoustically-hard surfaces with periodic sub-wavelength roughness air-borne acoustic surface waves are generated which could be used to amplify acoustic signals and, therefore, improve detection ranges of, perimeter security systems. Experimental and numerical studies using the Boundary Element Method (BEM) of the sound field generated over periodically-spaced rectangular strips also show several enhancements as a result of complex interactions between the sound field and the rough surface. Surface waves result in excess attenuation spectra with anomalous maxima greater than the 6.02 dB that would be expected from constructive interference above a smooth acoustically rigid surface. The enhancements are found to depend on the roughness spacing and can be attributed to effects due to the finite width and periodicity of the array, quarter-wavelength resonances in the gaps between elements and Bragg diffraction. Pressure maps of the...

Large surfaces of ceiling, walls and audiences of concert halls, as well as large reflecting surfaces hung over the stage, particularly influence the acoustics of the rooms interiors. The paper presents the results of simulation and experimental research of that kind of structures in a few concert halls. We have examined halls on a horseshoe and fan plans equipped, among others, with large surfaces of Schroeder diffuser or consisting of displaced equilateral triangles. Taking advantage of obtained acoustic parameters on audience surface, interesting acoustic effects were revealed. Large format acoustic structures could positively impact on the acoustic field inside the room, but can also result in negative acoustic effects. It was indicated that a sound strength G parameter was particularly helpful in identification of the influence of analyzed surfaces on the acoustics.

The scattering phenomenon is known to be of great importance for the acoustic quality of a performance arts space. The scattering of sound can be achieved in different ways: it can be obtained by the presence of architectural and/or decorating elements inside a room (e.g., columns, statues), by the geometry and roughness of a surface (e.g., Quadratic Residue Diffuser (QRD)) and by the diffraction effect occurring when a sound wave hits the edges of an obstacle. This article deals with the surface scattering effects and the diffusion phenomenon only related to MDF and plywood panels tested by disposing the wells both horizontally and vertically. The test results undertaken inside a semi-reverberant room and inside a large reverberant room have been compared to highlight the success and the failure of the measuring methodologies. In detail, according to the existing standards and regulations (i.e., ISO 17497—Part 2), diffusion measurements have been undertaken on a few selected types ...

The scattering phenomenon is known to be of great importance for the acoustic quality of a performance arts space. The scattering of sound can be achieved in different ways: it can be obtained by the presence of architectural and/or decorating elements inside a room (e.g., columns, statues), by the geometry and roughness of a surface (e.g., Quadratic Residue Diffuser (QRD)) and by the diffraction effect occurring when a sound wave hits the edges of an obstacle. This article deals with the surface scattering effects and the diffusion phenomenon only related to MDF and plywood panels tested by disposing the wells both horizontally and vertically. The test results undertaken inside a semi-reverberant room and inside a large reverberant room have been compared to highlight the success and the failure of the measuring methodologies. In detail, according to the existing standards and regulations (i.e., ISO 17497—Part 2), diffusion measurements have been undertaken on a few selected types ...

A sound diffuser is proposed based on sonic crystals, structures formed by a periodic distribution of cylindrical scatterers in a host medium, which is usually air. The diffuser is a so-called biperiodic structure, as formed by two arrays of sonic crystals with slightly different periodicities. Large diffusivity at low frequencies is achieved when the typical scale of the blocks is much larger than the periodicity of the crystals, determined by its lattice constant. An interpretation of the low frequency behavior of the diffuser is given in the homogenization limit in terms of multiple reflections and interference between the fields scattered by the different blocks. It is also shown that sonic crystal based diffusers enhance time spreading in comparison with other conventional diffusers.

Although periodic structures theory gave rise to sound diffusers almost 40 years ago, it has been only in recent years when several authors regarded the possible application of a particular kind of periodic structures, phononic crystals, in the field on room acoustics. This paper explores the possible application of periodic structures used as sound diffusers in rooms. Preliminary simulations, carried out with FDTD, shows that due to the inherent time spreading provided by a periodic structure, they can be used to reduce, or even to eliminate, pernicious effects associated with the low frequency modes of the room.

In this paper a new modified Schroeder diffuser structure is presented. The new structure m~es it possible to extend the low-frequency limit of the Schroeder diffuser so that the cutoff frequency is not directly proportional to the depth of the structure. me modified structure is atso easier to manufacture than the conventiorud Schroeder diffusers. me new structure is compared to the primitive root &R) and quadratic residue (QR) designs by numericrd simulations. These are made with finite element @M) and finite difference time domain @TD) methods and the results are compared to each other.

A new analytical theory for multiple scattering of cylindrical acoustic waves by an array of finite impedance semi-cylinders embedded in a smooth acoustically hard surface is derived by extending previous results for plane waves [Linton and Martin, J. Acoust. Soc. Am. 117 (6) 3413-3423 (2005)]. Although the computational demands of the new theory increase as the number of the semi-cylinders in the arrays and/or the frequency increases, the theory offers an improvement on analytical boss theories since the latter (i) are restricted to non-deterministic (infinite) random distributions of semi-cylinders with spacing/radii small compared to the incident wavelength and (ii) are derived only for plane waves. The influence on prediction accuracy of truncation of the infinite system of equations introduced by the new theory is explored empirically. Laboratory measurements have been made over deterministic random arrays of identical varnished wooden semi-cylinders on a glass plate. The agreement between predictions and measured relative Sound Pressure Level spectra is very good both for single deterministic random distributions and for averages representing non-deterministic random distributions. The analytical theory is found to give identical results to a Boundary Element calculation but is much faster to compute.

The Costas Array Problem is a highly combinatorial problem linked to radar applications. We present in this paper its detailed modeling and solving by Adaptive Search, a constraint-based local search method. Experiments have been done on both sequential and parallel hardware up to several hundreds of cores. Performance evaluation of the sequential version shows results outperforming previous implementations, while the parallel version shows nearly linear speedups up to 8,192 cores.

The sound scattering properties of diffusing panels are actually very difficult to measure and to predict. Furthermore, an unique, commonly accepted "diffusion coefficient" has not been defined yet. In this paper the Wave Field Synthesis approach is employed for the experimenta measurement of a physically defined diffusion coefficient. The results are in good agreemen with the numerical simulations presented in a parallel paper. 1. Precis Although many researches were conducted in the last few years, a consistent definition of a single number (the "diffusion coefficient") for stating the effectiveness of diffusing panels has not been yet obtained. In this paper, moving from the Wave Field Synthesis approach developed at the Tech. University of Delft, it is demonstrated how it is possible t characterize completely the scattering properties of a generic object by a large number of impulse response measurements taken moving the microphone at small steps along a straight line. From this characterization, by comparison with the theoretical behaviour of an absorbing/diffusing object, and after separation of the edge diffraction effect, it is possible to define objectively a surface diffusion coefficient. This new quantity is easy to measure, and ranks correctly diffusing panels of various kinds. Furthermore, this new approach is consistent with the employment of the measured diffusion coefficient in room acoustics simulation programs based on the geometrica acoustics theory, as reported in a parallel paper. The work starts with the theoretica explanation of the method, and prosecutes with experimental measurements on different panels, with validation of the results by comparison with numerical simulations.