**1. Introduction**

210 Stochastic Modeling and Control

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This chapter offers an original scientific research about stochastic based simulations and measurements of some objective parameters of acoustic quality and subjective evaluation of room acoustic quality, with acoustics optimization in multimedia classroom, complete scientific analysis, and application. The organisation of this chapter is very simple. After a short introduction that is an overview of completed research there are two main chapter parts with some definitions and explanations on the main subjects and research done. The conclusion to this research is contained in the final chapter segment, before the cited references.

According to http://www.answers.com/topic/convolution (2011/12/31), stochastic control methodology (SCM) is applied in a variety of fields including the computing, communications and acoustics optimization in multimedia environment. Also, SCT as a branch of control theory (CT) that deals with systems which involve random variables/signals and which occurrence can only be described in probabilistic terms attempts to predict and minimize the effect of these random signals through the optimization of controller design for acoustics optimization in multimedia room. Such deviations occur when random noise and disturbance processes are present in a control system, so that the system does not follow its prescribed course but deviates from the latter by a randomly

© 2012 Šimović et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Šimović et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 212 Stochastic Modeling and Control

varying amount. In contrast to deterministic signals, random signals cannot be described as given functions of time such as a step, a ramp, or a sine wave. The exact function is unknown to the system designer; only some of its average properties are known. A random signal may be generated by one of nature's processes, for instance, wind or multimedia wave-induced forces and moments on a antenna or a multimedia room. Alternatively, it may be generated by human intelligence, for instance, the contour to be followed by a duplicating machine. Outstanding experimental fact about nature's random processes is that these signals are very closely "Gaussian" that is a mathematical concept which describes one or more signals, i1, i2, …, in having the following properties: The amplitude of each signal is normally distributed and the joint distribution function of any number of signals at the same or different times taken from the set is a multivariate normal distribution. This experimental fact is not surprising in view of the fact that a random process of nature is usually the sum total of the effects of a large number of independent contributing factors. For instance, an ocean-wave height at any particular time and place is the sum of wind-generated waves at previous times over a large area. The underlying mechanism that generates a random process can usually be described in physical or mathematical terms. For instance, the underlying mechanism that generates shot-effect noise is thermionic emission. If the generating mechanism does not change with time, any measured average property of the random process is independent of the time of measurement aside from statistical fluctuations, and the random process is called stationary. If the generating mechanism does change, the random process is called nonstationary. Random noise is a type of noise comprised of transient disturbances which occur at random times; its instantaneous magnitudes are specified only by probability distribution functions which give the fraction of the total time that the magnitude lies within a specified range. Random noise represents: in mathematics a form of random stochastic process arising in control theory, or in physics noise characterized by a large number of overlapping transient disturbances occurring at random, such as thermal noise and shot noise, also known as fluctuation noise.

Stochastic Based Simulations and Measurements of Some Objective Parameters of Acoustic Quality: Subjective Evaluation of Room Acoustic Quality with Acoustics Optimization in Multimedia Classroom … 213

concerning the relevance of making judgments about the subjective assessment of quality of space based on objective measurements of the room acoustic quality rating which is at the end always subjective and influenced by convolution, where information about the statistical correlation of subjective assessments and objective measurements of room acoustic quality is shown. In the first part of this work the results of statistical analysis of two acoustically differently treated spaces subjective testing are shown. The number of test participants was 33, of which 8 had musical education. The musical sample duration was 16.5 min. The loudness level has been calibrated, i.e. it was identical in both rooms. Eighteen parameters were evaluated in two ways: with and without the impact of musical memory. These results were compared with hypothetical results based on the experience of the authors. The comparison of subjective judgment and objective measuring results is shown. The possibility of making judgments about the subjective assessment of quality of space based on objective measurements is also given. At the end, information about the statistical correlation (Žužul, Šimović & Leinert-Novosel, 2008) of subjective assessments and objective measurements (Kosić, 2008) of room acoustic quality is shown (Krhen, 1994). Room acoustics is a characteristic of a room in which sound is well transferred and well received (heard), i.e., sound depending on type (speech or music, that is, type of music) and purpose (listening or recording). The development of acoustics – acoustic science, and especially its subcategories, architectural acoustics, is founded on defining objective parameters of spatial room acoustic quality and finding new methods (von zur Gathen & Gerhard, 2003) of their measuring and identifying their relationship with subjective parameters of spatial acoustic quality obtained through subjective testing (Everest & Pohlmann, 2009). That is why the task of this simulation research was to make an estimate, a simulation and measurement of the acoustics of a representative multimedia classroom (classroom at the Department of Electroacoustics, Faculty of Electrical Engineering and Computing, FER). The main idea of the second part of this chapter is that it offers an original scientific discussion with a conclusion concerning the relevance of making a prediction, stochastic based simulations and measurements of (some objective parameters of) acoustic (quality) in a sample multimedia classroom (classroom at the Department of Electroacoustics, Faculty of Electrical Engineering and Computing, or FER). Measurements and simulations of some objective parameters of acoustic quality were conducted in order to determine whether the representative multimedia classroom was acoustic or not, and if not, what measures (with stochastic optimization) should be taken in order for the mentioned room to meet optimal

Subjective rating of acoustic quality is always the most important result which must be as high as possible, and it depends on several factors, such as: training of the listener, familiarity with the topic, musical memory and even the expectations of the listener. These ratings, however, always affect the same parameters, which were assessed in our studies. The statistical based analysis of these results has been made. On the other hand, objective parameters are much easier to measure. Measurements of objective parameters of acoustic

conditions for being acoustic.

**2. Introduction to analysis** 

The room acoustics for multimedia room is complex problem which has to be take in consideration while designing the one, because it consists of several parts, like: analysing and calculating of acoustical parameters, measuring the real condition, simulating on computer, finding the cause and giving the solution for possible problems. Calculating and measuring methods, as well as their results, have to be analised and shown. At the end some proposals to obtain better conditions have to be given, and the simulation with proposed actions have to be made, to find out if those proposals solved the problem found out in the real room (Domitrović, Fajt & Krhen, 2009).

The room acoustic quality rating is at the end always subjective and influenced by stochastic (Simovic & Jr. Simovic, 2010) convolution (Uludag, 1998; Sobolev, 2001). The only question is how sharp is the criteria which should be met, what is the purpose of space and how important is the quality of listening for the listeners. With regard to this, judgment process is extremely complex (Fajt, 2000). On the other hand, it is possible to do objective measurement relatively easily and quickly. Following the above stated, the main idea of the first part of this chapter is that it offers an original scientific discussion with a conclusion concerning the relevance of making judgments about the subjective assessment of quality of space based on objective measurements of the room acoustic quality rating which is at the end always subjective and influenced by convolution, where information about the statistical correlation of subjective assessments and objective measurements of room acoustic quality is shown. In the first part of this work the results of statistical analysis of two acoustically differently treated spaces subjective testing are shown. The number of test participants was 33, of which 8 had musical education. The musical sample duration was 16.5 min. The loudness level has been calibrated, i.e. it was identical in both rooms. Eighteen parameters were evaluated in two ways: with and without the impact of musical memory. These results were compared with hypothetical results based on the experience of the authors. The comparison of subjective judgment and objective measuring results is shown. The possibility of making judgments about the subjective assessment of quality of space based on objective measurements is also given. At the end, information about the statistical correlation (Žužul, Šimović & Leinert-Novosel, 2008) of subjective assessments and objective measurements (Kosić, 2008) of room acoustic quality is shown (Krhen, 1994). Room acoustics is a characteristic of a room in which sound is well transferred and well received (heard), i.e., sound depending on type (speech or music, that is, type of music) and purpose (listening or recording). The development of acoustics – acoustic science, and especially its subcategories, architectural acoustics, is founded on defining objective parameters of spatial room acoustic quality and finding new methods (von zur Gathen & Gerhard, 2003) of their measuring and identifying their relationship with subjective parameters of spatial acoustic quality obtained through subjective testing (Everest & Pohlmann, 2009). That is why the task of this simulation research was to make an estimate, a simulation and measurement of the acoustics of a representative multimedia classroom (classroom at the Department of Electroacoustics, Faculty of Electrical Engineering and Computing, FER). The main idea of the second part of this chapter is that it offers an original scientific discussion with a conclusion concerning the relevance of making a prediction, stochastic based simulations and measurements of (some objective parameters of) acoustic (quality) in a sample multimedia classroom (classroom at the Department of Electroacoustics, Faculty of Electrical Engineering and Computing, or FER). Measurements and simulations of some objective parameters of acoustic quality were conducted in order to determine whether the representative multimedia classroom was acoustic or not, and if not, what measures (with stochastic optimization) should be taken in order for the mentioned room to meet optimal conditions for being acoustic.

## **2. Introduction to analysis**

212 Stochastic Modeling and Control

varying amount. In contrast to deterministic signals, random signals cannot be described as given functions of time such as a step, a ramp, or a sine wave. The exact function is unknown to the system designer; only some of its average properties are known. A random signal may be generated by one of nature's processes, for instance, wind or multimedia wave-induced forces and moments on a antenna or a multimedia room. Alternatively, it may be generated by human intelligence, for instance, the contour to be followed by a duplicating machine. Outstanding experimental fact about nature's random processes is that these signals are very closely "Gaussian" that is a mathematical concept which describes one or more signals, i1, i2, …, in having the following properties: The amplitude of each signal is normally distributed and the joint distribution function of any number of signals at the same or different times taken from the set is a multivariate normal distribution. This experimental fact is not surprising in view of the fact that a random process of nature is usually the sum total of the effects of a large number of independent contributing factors. For instance, an ocean-wave height at any particular time and place is the sum of wind-generated waves at previous times over a large area. The underlying mechanism that generates a random process can usually be described in physical or mathematical terms. For instance, the underlying mechanism that generates shot-effect noise is thermionic emission. If the generating mechanism does not change with time, any measured average property of the random process is independent of the time of measurement aside from statistical fluctuations, and the random process is called stationary. If the generating mechanism does change, the random process is called nonstationary. Random noise is a type of noise comprised of transient disturbances which occur at random times; its instantaneous magnitudes are specified only by probability distribution functions which give the fraction of the total time that the magnitude lies within a specified range. Random noise represents: in mathematics a form of random stochastic process arising in control theory, or in physics noise characterized by a large number of overlapping transient disturbances occurring at

random, such as thermal noise and shot noise, also known as fluctuation noise.

real room (Domitrović, Fajt & Krhen, 2009).

The room acoustics for multimedia room is complex problem which has to be take in consideration while designing the one, because it consists of several parts, like: analysing and calculating of acoustical parameters, measuring the real condition, simulating on computer, finding the cause and giving the solution for possible problems. Calculating and measuring methods, as well as their results, have to be analised and shown. At the end some proposals to obtain better conditions have to be given, and the simulation with proposed actions have to be made, to find out if those proposals solved the problem found out in the

The room acoustic quality rating is at the end always subjective and influenced by stochastic (Simovic & Jr. Simovic, 2010) convolution (Uludag, 1998; Sobolev, 2001). The only question is how sharp is the criteria which should be met, what is the purpose of space and how important is the quality of listening for the listeners. With regard to this, judgment process is extremely complex (Fajt, 2000). On the other hand, it is possible to do objective measurement relatively easily and quickly. Following the above stated, the main idea of the first part of this chapter is that it offers an original scientific discussion with a conclusion

Subjective rating of acoustic quality is always the most important result which must be as high as possible, and it depends on several factors, such as: training of the listener, familiarity with the topic, musical memory and even the expectations of the listener. These ratings, however, always affect the same parameters, which were assessed in our studies. The statistical based analysis of these results has been made. On the other hand, objective parameters are much easier to measure. Measurements of objective parameters of acoustic

#### 214 Stochastic Modeling and Control

quality were made, and at the end their mutual correlation is shown. Why? Because possible convolution problems. See visual explanation of convolution and its applications.

Stochastic Based Simulations and Measurements of Some Objective Parameters of Acoustic Quality: Subjective Evaluation of Room Acoustic Quality with Acoustics Optimization in Multimedia Classroom … 215

**Figure 1.** Visual explanation of convolution - according to: http://www.answers.com/topic/convolution

One room was acoustically untreated (Room 1), while the other was acoustically treated as a listening room (Room 2). All subjects evaluated parameter values as numeric values in the range from 1 to 5. In each room two tests were made. The goal was to determine the effect of

For this purpose, a group of subjects first heard a music test pattern, and the evaluation

After that a 15 min pause was done, and subsequently after the pause the following test started in which subjects entered their ratings during the test sample listening –

process began 1 minute after the end of the test pattern – Measurement Type A.

12. Distortion;

14. Brilliance;

16. Resonance;

g(τ)→g( − τ).

the τ-axis.

(2011/12/31)

shown here) is the

convolution of functions f and g. If f(t) is a unit impulse, the result of this process is simply g(t), which is therefore called the impulse response.

Measurement Type B.

listener's music memory on test results.

13. Stability of performance;

17. Ambience Reproduction, Diffusion; 18. Overall Acoustic Impression.

15. Bass reproduction;

Express each function in terms of a dummy variable τ. Reflect one of the functions:

Add a time-offset, t, which allows g(t − τ) to slide along

Start t at -∞ and slide it all the way to +∞. Wherever the two functions intersect, find the integral of their product. In other words, compute a sliding, weighted-average of function f(τ), where the weighting function is g( − τ). The resulting waveform (not

Some of convolution applications are cited bellow. Citation from: http://www.answers.com/topic/convolution (2012/12/31):

"Convolution and related operations are found in many applications of engineering and mathematics:

