**3. Subjective evaluation of room acoustic quality parameters**

For the purposes of subjective acoustic quality evaluation, we examined the following parameters:


12. Distortion;

214 Stochastic Modeling and Control

mathematics:

can be relaxed.

parameters:

1. Noise volume; 2. Intimacy, Presence;

7. Echo Disturbance; 8. Speech Intelligibility;

10. Sound stage imaging;

5. Tonal Reproduction, Timbre; 6. Sound Definition, Clarity;

9. Spectral Uniformity, Balance;

3. Loudness; 4. Reverberance;

11. Dynamics;

independently of the other components.

quality were made, and at the end their mutual correlation is shown. Why? Because possible

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

In linear acoustics, an echo is the convolution of the original sound with a function

 In artificial reverberation (digital signal processing, pro audio), convolution is used to map the impulse response of a real room on a digital audio signal (Krhen, 1994). In electrical engineering, the convolution of one function (the input signal) with a second function (the impulse response) gives the output of a linear time-invariant system (LTI). At any given moment, the output is an accumulated effect of all the prior values of the input function, with the most recent values typically having the most influence (expressed as a multiplicative factor). The impulse response function provides

that factor as a function of the elapsed time since each input value occurred.

In statistics, as noted above, a weighted moving average is a convolution.

random variables is the convolution of their individual distributions."

**3. Subjective evaluation of room acoustic quality parameters** 

 In digital signal processing and image processing applications (Pap, Kosić & Fajt, 2006), the entire input function is often available for computing every sample of the output function. In that case, the constraint that each output is the effect of only prior inputs

Convolution amplifies or attenuates each frequency component of the input

In probability theory, the probability distribution of the sum of two independent

For the purposes of subjective acoustic quality evaluation, we examined the following

convolution problems. See visual explanation of convolution and its applications.

Some of convolution applications are cited bellow. Citation from:

http://www.answers.com/topic/convolution (2012/12/31):

representing the various objects that are reflecting it.


**Figure 1.** Visual explanation of convolution - according to: http://www.answers.com/topic/convolution (2011/12/31)

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 listener's music memory on test results.

For this purpose, a group of subjects first heard a music test pattern, and the evaluation process began 1 minute after the end of the test pattern – Measurement Type A.

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 – Measurement Type B.

#### 216 Stochastic Modeling and Control

It is interesting to note that for Room 1, for all parameters except for (3) at least one subject had given the worst score when they did test with the impact of musical memory, while in Type B test, only 4 parameters are not given the worst score.

Stochastic Based Simulations and Measurements of Some Objective Parameters of Acoustic Quality: Subjective Evaluation of Room Acoustic Quality with Acoustics Optimization in Multimedia Classroom … 217

**Figure 3.** The feedback difference depending on musical memory (Meas.Type A – Meas.Type B) – Positive value: better result without memory effect; Negative value: better result with memory effect





1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18


0,00%




0,00%










0,61%

Room 1 Room 2


relatively large dispersion of results (Table 1).

Meas.Type B: 23/33 (69.7%).

1,72%

7,88%


0,61%

0,61%







0,00%

**Rating value**

2,00%

4,00%

6,00%

8,00%

10,00%







0,61%


3,03%

(11/18 – 61%).

B: 4.09 / 4.18.

In this evaluation, 8/18 (44.4%) of the parameter (Meas.Type A) and 10/18 (55.5%) parameters (Meas.Type B) also received the best value. This clearly points to a very large dispersion of results, and points (and confirms) the problem that always exists in the subjective assessment of acoustical quality parameters. Standard deviation shows us also the

**Parameter**

In the most cases, individual results are significantly below average: Room 1 – Meas.Type A: 26/33 (78.8%); Meas.Type B: 23/33 (69.7%) and Room 2 – Meas.Type A: 18/33 (54.5%) ;

Musical memory definitely has an impact on making assessments about the acoustical quality, and we can see (Fig. 2) that the results are in the most cases better with memory effect. This is especially outlined in the Room 2 (16/18 – 88.8%), compared with Room 1

When we compare the subjective assessment of the average acoustic impression (18) with an average value of all parameters, we can see that these values are in Room 1 acoustically untreated room: Meas.Type A: 2.48 / 2.98; Meas.Type B: 2.45 / 3.06 much more different than in Room 2 - acoustically treated room: Meas.Type A: 3.97 / 4.03; Meas.Type

**Figure 2.** Feedback results for Room 1 / Measurement Type A – Minimum, Maximum and Average Value


**Table 1.** Standard deviation for all feedback results

216 Stochastic Modeling and Control

3,24 3,27

3,09

3,33

2,70

2,48

3,30

2,70 2,76

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 **Parameter**

3,06

3,27

2,97 3,03 3,15

2,82 2,76 2,76

2,48

Value

0,00

1,00

2,00

3,00

**Rating value**

4,00

5,00

It is interesting to note that for Room 1, for all parameters except for (3) at least one subject had given the worst score when they did test with the impact of musical memory, while in

**Figure 2.** Feedback results for Room 1 / Measurement Type A – Minimum, Maximum and Average

*Parameter 1 2 3 4 5 6 7 8 9*  σRoom 1, Type A 1.07 0.83 0.93 1.03 0.83 0.93 1.22 0.80 0.74 σRoom 1, Type B 0.99 0.61 0.83 1.02 0.81 0.78 0.99 0.86 0.57 σRoom 2, Type A 0.98 0.58 0.55 0.88 0.59 0.58 0.36 0.69 0.65 σRoom 2, Type B 0.64 0.72 0.55 0.85 0.46 0.59 0.17 0.55 0.46 *Parameter 10 11 12 13 14 15 16 17 18*  σRoom 1, Type A 1.13 0.75 1.29 0.80 1.02 0.87 1.02 0.85 0.78 σRoom 1, Type B 1.02 0.71 1.03 0.72 0.91 0.95 1.15 0.77 0.82 σRoom 2, Type A 0.70 0.64 0.73 0.72 0.74 0.90 0.59 0.86 0.67 σRoom 2, Type B 0.90 0.67 0.53 0.66 0.65 0.89 0.52 0.80 0.67

**Table 1.** Standard deviation for all feedback results

Type B test, only 4 parameters are not given the worst score.

**Figure 3.** The feedback difference depending on musical memory (Meas.Type A – Meas.Type B) – Positive value: better result without memory effect; Negative value: better result with memory effect

In this evaluation, 8/18 (44.4%) of the parameter (Meas.Type A) and 10/18 (55.5%) parameters (Meas.Type B) also received the best value. This clearly points to a very large dispersion of results, and points (and confirms) the problem that always exists in the subjective assessment of acoustical quality parameters. Standard deviation shows us also the relatively large dispersion of results (Table 1).

In the most cases, individual results are significantly below average: Room 1 – Meas.Type A: 26/33 (78.8%); Meas.Type B: 23/33 (69.7%) and Room 2 – Meas.Type A: 18/33 (54.5%) ; Meas.Type B: 23/33 (69.7%).

Musical memory definitely has an impact on making assessments about the acoustical quality, and we can see (Fig. 2) that the results are in the most cases better with memory effect. This is especially outlined in the Room 2 (16/18 – 88.8%), compared with Room 1 (11/18 – 61%).

When we compare the subjective assessment of the average acoustic impression (18) with an average value of all parameters, we can see that these values are in Room 1 acoustically untreated room: Meas.Type A: 2.48 / 2.98; Meas.Type B: 2.45 / 3.06 much more different than in Room 2 - acoustically treated room: Meas.Type A: 3.97 / 4.03; Meas.Type B: 4.09 / 4.18.
