PRINCIPAL COMPONENT ANALYSIS IN DETERMINING THE BEST SETUP FOR ACOUSTIC MEASUREMENTS IN SOUND CONTROL ROOMS

Original scientific paper Measuring process of acoustic quality parameters in sound control room in order to determine the best setup is described. Measurements of six sound control rooms impulse response have been made. The measurements are executed in accordance with the standard ISO3382. In all sound control rooms the same measurement method is used, but the measurement setups are changed. In the first scenario built-in monitor loudspeakers were used. In the second scenario, omnidirectional sound source was used. Omnidirectional measuring microphone and an artificial head were used as receivers. They were placed at the optimal listening position. Principal components analysis method is used to get the most accurate result from measured data obtained under different scenarios and measuring setups. Hence, the measuring conditions and setups which determine the value of subjective assessments of the sound control room are obtained. The results shall be used to calculate correlation between objective measurements and subjective assessments.


Introduction
Impulse response measurement method is one of the basic measurement methods in the field of objective acoustical study of the room [1].Since a linear part of transfer function between two points in the room is considered, it is assumed that principles valid for linear systems are automatically applied to acoustic room measurements.Analysis of the energy in the room is usually performed at a constant percentage bandwidth, generally an octave or one-third of octave.The problem with impulse measurement of the room is to achieve an adequate signal to noise ratio, which results in praxis with application of several ways of acoustical impulse measurements of the room.

Methods for measuring the objective parameters of acoustical quality of the room
Objective measured data are obtained by measuring the impulse response of the room, whereas measurements are executed with the use of a personal computer, i.e. the software package Easera [2,3] which is in accordance with the standard of ISO3382.The frequency range is from 63 Hz to 8 kHz, with standard octave bands.The excitation signal with sweep frequency and Maximum Length Sequence Signal -MLS is used.The rooms are excited in two scenarios.In the first scenario the installed equipment and built-in monitor loudspeakers are used, separately the left monitor speaker and separately the right monitor speaker.In the second scenario omnidirectional sound source is used, which is placed in front of the monitor loudspeakers and in front of the optimal positions provided for listening, Fig. 1.The signal from the personal computer (which is the signal source) is directly connected to the output stage of the installed electroacoustic equipment.In such a way all devices for signal processing are bypassed and their eventual impact on the signal is eliminated.Although the final analysis is done in the frequency range determined with central frequency of octave bands from 63 Hz to 8 kHz, sweep tone is generated in the frequency range 0 Hz to 24 kHz.The omnidirectional sound source is selected as a reference sound source that is used in all areas.Thus, on the one hand, the influence of different sound sources on the measurement results of the acoustic parameters when comparing the results of measurements in different areas is avoided [4].On the other hand, the use of reference omnidirectional sound source gives us the illustration of the impact of sound sources that are used in daily work in those sound control rooms on the measurement results [5,6].
The measurements were made in two ways -onechannel and binaural measurements, i.e. with one measuring microphone and with an artificial head, which were set on the position and at height in the room corresponding to the usual position for listening, i.e. the optimal listening position.As it is desired to reduce the possible measurement error to a minimum, five measurement cycles are executed for each measured parameter, and the final result is the mean value of such five values for each measured parameter.Prior to start of the five measurement cycles one pre-testing measurement is executed to check whether equipment setup is properly prepared and ready to start with the measurement process.The duration of the test signal is 5,5 s, and the sampling frequency is 48 kHz.Thus, for each measured parameter 262 144 signal samples are obtained.
The microphone is placed at the height of 1,40 m from the floor, at the exact position of the "sound engineer".Artificial head was always in the same position relative to the sound source and the microphone is placed on the medial plane, at the height of the artificial ears [7].
The known problem in measuring of acoustic parameters is repeatability.Due to measurement errors and measurement uncertainties it is sometimes difficult to get exactly the same results even with exactly the same measuring conditions.The exact repeatability is even more difficult to obtain using different types of signals and measuring conditions.Therefore, in this research measurement conditions and the measurement signals which will give the most accurate result are determined.Thus, good measurements repeatability is also obtained.This has been achieved with here shown and described measurement conditions and the applied excitation signal.Finally, the results were analysed using PCA method.
Therefore, the same measurement conditions in all rooms for all parameters are selected, as described above.The values of the following objective parameters of room acoustic quality are calculated in accordance with ISO3382 standard [8÷11]: Listed professional sound control rooms have a minimum floor area of 25,9 m 2 to a maximum of 46,20 m 2 , with a corresponding volume of at least 75,11 m 3 to a maximum of 157,08 m 3 , which is consistent with standardized sizes of the average professional sound control rooms.All rooms are appropriately acoustically treated, i.e. insulated walls to protect from outside noise, separated with a window from the studio area and are equipped with special doors that meet the needs of acoustic insulation from outside noise.In each room a mixing console is placed on the best listening position, and sound is radiated through professional loudspeaker systems [12].
Analysis of the measured objective parameters of acoustic quality of sound control room includes analysis of the results across measured frequency band.It includes the range of octave bands with central frequencies from 125 Hz to 8 kHz.With the statistical method Principal Component Analysis (PCA) measurement setup conditions are determined, for which the most accurate measurement results are obtained.
PCA is a statistical method, described in detail in [13], [14] which combines a large number of variables (results) to new, virtual variables called principal components.Those variables incorporate all existing and actually measured values, but their number is far lower than the actual.The method of calculating the principal components includes getting the data, subtracting the mean, calculating the covariance matrix, calculating the eigenvectors and eigenvalues of the covariance matrix, choosing components and forming a feature vector, and finaly, deriving the new data set [13].In this analysis, the number of principal components is limited to two (Principal Component One -PC1 and Principal Component Two -PC2) and it is found which actual measured parameters and measurement conditions have the greatest effect on the two selected (first two) components.Selecting those two principal components only the biggest impact of actual results is analysed.Also, a further increase in the number of observed principal components would increase the complexity of the analysis and at the same time, their influence on the results is not significant.
The above principle enables to determine conditions necessary to measure the acoustic properties of the room in the best way.It is assumed that every measured room meets the requirements required for analysis, and they are: all variables were measured under the same conditions, the amplitude of excitation area is such that there is a linear relationship between the variables, the number of samples is large enough to be assumed they fairly represent the corresponding measured value, all data are suitable for analysis, and no inappropriate deviations occurs in results.Mentioned inappropriate deviations in measurement results are also monitored during the measurements.
Objective parameters are measured in each room nine times with nine different conditions.For the purpose of Prior to making the PCA analysis, a statistical analysis of the results was made for each measured parameter of the sound control rooms, which includes: As this is an extremely large amount of data, this paper presents only the results of PCA analysis, which are the goal of this research.

Multichannel music control room R1
Principal component analysis of the reverberation time measured values shows that the greatest impact on the first two principal components PC1 and PC2 for the parameter EDT have measurements M3 and M9; for the parameter RT 10 have measurements M11 and M10; for the parameter RT 20 have measurements M21 and M19, while for the parameter RT 30 have measurements M36 and M32.
As in most cases the biggest impact on the first two principal components have measurements performed using an omnidirectional sound source, it can be concluded that the results of the reverberation time measurements made with omnidirectional sound source give the results that best suit their actual values.As in all cases the greatest impact in the first two principal components have measurements obtained with monitor loudspeakers excited with sweep signal, it can be concluded that this measurement conditions give results that best suit their actual values.Additionally during the calculation of the principal components related to the Clarity C, no significant impact on the measurements with omnidirectional sound source is noticed.
Principal component analysis of the Definition D values indicates that the greatest impact on the first two principal components PC1 and PC2 have measurements M4 and M5.
Principal component analysis of the interaural crosscorrelation coefficient IACC values shows that the first two principal components PC1 and PC2 for parameter IACC Early are mainly defined by measurements M3 and M1; for parameter measurements IACC Late by measurements M13 and M9, and the overall coefficient IACC Full by measurements M19 and M17.
Clearly, measurements carried out with omnidirectional sound source have a significant impact on the determination of the first two principal components for IACC coefficient.

Multichannel music control room R4
Principal component analysis of the reverberation time values shows that the greatest impact on the first two principal components PC1 and PC2 for parameter EDT have measurements M8 and M9; for the parameter RT 10 have measurements M16 and M17; for the parameter RT 20 have measurements M21 and M23, while for the parameter RT 30 have measurements M31 and M35.As in most cases the biggest impact on the first two principal components have measurements performed using built-in speakers, it can be concluded that the results of the reverberation time measurement facilitated by built-in speakers and excited with sweep tone, give results that best match their actual values.
Principal component analysis of the Clarity C values in the multichannel music control room R4, parameter C 7 indicates that the greatest impact on the first two principal components PC1 and PC2 have measurements M9 and M7; for the parameter C 50 have measurements M15 and M13; for the parameter C 80 have measurements M24 and M25, while for the parameter C 35 have measurements M34 and M35.As in all cases the greatest impact on the first two principal components have measurements facilitated by monitor loudspeakers and excited with sweep signal, it can be concluded that this measurement conditions will produce results that most closely match their actual values.Additionally, during the calculation of the principal components related to the clarity C, no significant impact of measurements done with omnidirectional sound source is noticed.
Principal component analysis of the Definition D values indicates that the greatest impact on the first two principal components PC1 and PC2 have measurements M4 and M6.
Principal component analysis of the interaural crosscorrelation coefficient IACC values shows that the first two principal components PC1 and PC2 for parameter IACC Early are mainly defined by measurements M8 and M7; for parameter by IACC Late measurements M14 and M13, and the overall coefficient IACC Full by M26 and M25.
Clearly, measurements done with built-in monitor loudspeakers have a dominant impact on the calculation of the first two principal components for IACC coefficient for sound control room R4.Principal component analysis of the reverberation time values EDT shows that the greatest impact on the first two principal components PC1 and PC2 for parameter EDT have measurements M1 and M6; for the parameter RT 10 have measurements M11 and M18; for the parameter RT 20 have measurements M26 and M27, while for the parameter RT 30 measurements M35 and M33.It is important that in the sound control room R5, a measurement executed with omnidirectional sound source has the greatest impact on the first principal component PC1 for the measured values of parameters EDT andRT 10 , while measurement executed with build-in control monitor primarily effects measurement of parameters RT 20 and RT 30 .As the second principal component PC2 is determined by measurements done with monitor speakers in all cases, it can be stated that the results of reverberation time measurements will be most accurate in cases when monitor loudspeakers are used.
Principal component analysis of the Clarity C values in the speech and music control room R5 indicates that the greatest impact on the first two principal components PC1 and PC2 for parameter C 7 have measurements M5 and M6; for the parameter C 50 have measurements M15 and M14; for the parameter C 80 have measurements M23 and M22, while for the parameter C 35 have measurements M33 and M32.
Principal component analysis of the parameter clarity C measurement results in sound control room R5 shows in all cases that the biggest impact on the first two principal components PC1 and PC2 occurred when room was excited with right-hand control monitor.Therefore, it can be concluded for room R5 that the best results are obtained with measurements performed with control monitor loudspeaker, and specifically in this case the right-hand one.
Principal component analysis of the Definition D values indicates that the greatest impact on the first two principal components PC1 and PC2 have measurements M6 and M5.
Principal component analysis of the interaural crosscorrelation coefficient IACC values shows that the first two principal components PC1 and PC2 are mainly defined for parameter IACC Early by measurements M5 and M6; for parameter measurements IACC Late by M10 and M15, and the overall coefficient IACC Full by M23 and M24.
Clearly, measurements carried out with control monitor, especially with the right-hand monitor, have the most significant effect on the calculation of the first two principal components for the IACC coefficient.Only in one case a significant impact on the principal components PC1 and PC2 have measurements with omnidirectional sound source.

Control room for audio editing R13
Principal component analysis of the reverberation time values shows that the greatest impact on the first two principal components PC1 and PC2 for parameter EDT have measurements M7 and M9; for the parameter RT 10 have measurements M11 and M10; for the parameter RT 20 have measurements M24 and M22, while for the parameter RT 30 measurements M31 and M30.
The impact on the first two principal components PC1 and PC2 in this case have the measurements carried out by omnidirectional sound source, as well as measurements with monitor loudspeakers, depending on the measured dynamics range.It is interesting that the biggest impact on measurements with omnidirectional sound source is for the parameter RT 10 , where the dynamics is the smallest.Although there is the impact on the results obtained from excitation with MLS signal, in most cases more significant is excitation with sweep tone.The principal components in the case of control room R13 in most cases are determined by measurements performed with excitation via the monitor speakers.Only the results of measurements carried out by omnidirectional sound source of the parameter C 35 have significant impact on the first two principal components PC1 and PC1.
Principal component analysis of the Definition D values indicates that the greatest impact on the first two principal components PC1 and PC2 have measurements M4 and M5.
Principal component analysis of the interaural crosscorrelation coefficient IACC values shows that the first two principal components PC1 and PC2 are mainly defined for parameter IACC Early by measurements M8 and M9; for parameter measurements IACC Late by M14 and M10, and the overall coefficient IACC Full M26 and M27.
Clearly, measurements taken with monitor loudspeakers significantly impact the calculation of the first two principal components for IACC coefficient.

Large control room of "Studio Bajsić" R11
Principal component analysis of the reverberation time values shows that the greatest impact on the first two principal components PC1 and PC2 for parameter EDT have measurements M8 and M9; for the parameter RT 10 have measurements M16 and M17; for the parameter RT 20 have measurements M21 and M26, while for the parameter RT 30 have measurements M33 and M35.Analysis and definition of the first two principal components PC1 and PC2 for control room R11 shows that in most cases a significant impact have measurements with monitor loudspeakers, mostly right-hand speaker.There is only one case with a significant impact of measurements with omnidirectional sound source.In most cases significant impact has the sweep signal.Principal component analysis of the Clarity C values in the large control room of "Studio Bajsić" R11indicates that the greatest impact on the first two principal components PC1 and PC2 for parameter C 7 have measurements M5 and M4; for the parameter C 50 have measurements M14 and M13; for the parameter C 80 have measurements M24 and M22, while for the parameter C 35 have measurements M31 and M33.
Calculating process of the principal components PC1 and PC2 for the measurement of sound control room R11 related to the parameter Clarity shows that the biggest impact on results have measurements carried out with the right-hand control monitor and in most cases with sweep tone.There is no case where measurements carried out by omnidirectional sound source have big significance for principal components PC1 and PC2.
Principal component analysis of the Definition D values indicates that the greatest impact on the first two principal components PC1 and PC2 have measurements M4 and M5.
Also in case of parameter Definition D, a significant impact on the calculation of the first two principal components PC1 and PC2 have measurements done with right-hand control monitor.
Principal component analysis of the interaural crosscorrelation coefficient IACC values shows that the first two principal components PC1 and PC2 are mainly defined for parameter IACC Early by measurements M7 and M9; for parameter measurements IACC Late by M13 and M14, and the overall coefficient IACC Full by M25 and M27.
Clearly, measurements taken with control monitor have a significant impact in the calculation of the first two principal components for IACC coefficient.Principal component analysis of the reverberation time values for control room R12 shows that the greatest impact on the first two principal components PC1 and PC2 for the parameter EDT have measurements M9 and M7; for the parameter RT 10 have measurements M12 and M15; for the parameter RT 20 have measurements M27 and M24, while for the parameter RT 30 measurements M28 and M36.

Small control room of "Studio Bajsić" R12
Calculation of the principal components PC1 and PC2 for measuring parameters of reverberation time shows that measurements with all sound sources are present, i.e. omnidirectional sound source as well as monitor loudspeakers.
Principal component analysis of the Clarity C values in the control room R12 indicates that the greatest impact on the first two principal components PC1 and PC2 for parameter C 7 have measurements M8 and M9; for the parameter C 50 have measurements M18 and M17; for the parameter C 80 have measurements M22 and M23, while for the parameter C 35 have measurements M29 and M31.In most cases significant impact in the calculation of the principal components related to the clarity parameter C of control room R12 have measurements performed with control monitor.
Principal component analysis of the Definition D values indicates that the greatest impact on the first two  Clearly, measurements taken with control monitor have in most cases a significant impact on the calculation of the first two principal components for IACC coefficient.The measurement taken with omnidirectional sound source is significant in only one case.

The final result -standardized measurement setup matrix
After detailed analysis of the measurement results of objective parameters of professional sound control room acoustical quality, as the final result a standardized matrix of measurement setup is produced.The setup matrix shows which sound source and sound source signal has to be used for the measurements that give the best results.The sound source can be either omnidirectional or built-in monitor loudspeaker, used as operational sound control monitor.The exciting signal can be the sweep signal or MLS signal.
From the standardized measurement setup matrix for professional sound control rooms should be noted that the measurement with omnidirectional sound source makes sense when measuring parameters are related to the reverberation time.The energy parameters of clarity C and definition D should be measured with operational control monitor loudspeakers which are used in the control room.

Conclusion
Sound control rooms are special rooms where acoustic quality is of special importance and it is crucial to exactly define room layout and achieve the best acoustic quality parameters.Analysis of such requirements shall facilitate in achieving such quality.This paper presents a mathematical analysis of the measurement results using Principal Component Analysis.Results of measurement of objective room acoustic quality parameters are exactly specified by the conditions under which they are measured and will be put in correlation with subjective assessment of sound control room further research.Therefore, it is extremely important to exactly determine the measurement's conditions and setup that will give the most accurate measurement results.Final results show the measurement setup for each observed parameter, separately for each sound control room.Thus, the results are obtained, which determine the value of subjective assessments of the room in the best possible way.The presented results also provide a basis for future statistical analysis and correlations between the size and shape of the room and type of sound source and/or signal with particular parameter of acoustic quality of the sound control room.This method also allows the optimization of the acoustic characteristics of the sound control rooms with adequate acoustic quality.

Figure
Figure 1Measurement setup (OSS -Omnidirectional Sound Source; ML -Monitor Loudspeaker;HATS -Head and Torso Simulator) mathematical analysis each condition of measurement is indicated by a special label, as follows:

Figure 2
Figure 2 Layout of the multichannel music control room R1

Figure 3
Figure 3 Layout of the multichannel music control room R4

3 . 3
Speech and music control room R5

Figure 5 Table 8
Figure 5 Layout of the control room for audio editing R13Table 8 Construction parameters of the control room for audio editing R13 Width [m] Depth [m] Height [m] Floor area [m 2 ] Volume [m 3 ] 5,58 4,71 2,90 25,90 75,11Principal component analysis of the Clarity C values in the control room for audio editing R13, parameter C 7 indicates that the greatest impact on the first two principal components PC1 and PC2 have measurements M7 and M8; for the parameter C 50 have measurements M15 and M13; for the parameter C 80 have measurements M25 and M26, while for the parameter C 35 have measurements M28 and M29.

Figure 6
Figure 6 Layout of the large control room of "Studio Bajsić" R11

Table 1Measurements '
conditions and labels for the statistical method of PCA Source OSS OSS OSS ML ML ML ML ML ML Position

Table 2
Construction parameters of the multichannel music control room R1

Table 3
Coefficients of principal components of the objective room quality parameters for the multichannel music control room R1

Table 4
Construction parameters of the multichannel music control room R4

Table 5 .
Coefficients of principal components of the objective room quality parameters for the multichannel music control room R4

Table 6
Construction parameters of the speech and music control room R5

Table 7
Coefficients of principal components of the of objective room quality parameters for the speech and music control room R5

Table 9
Coefficients of principal components of objective room quality parameters for the control room for audio editing R13

Table 10
Construction parameters of the large control room of "Studio Bajsić" R11

Table 11
Coefficients of principal components of the of objective room quality parameters for the large control room of "Studio Bajsić" R11

Table 12
Construction parameters of the small control room of "Studio Bajsić" R12

Table 13
Coefficients of principal components of the of objective room quality parameters for the small control room of "Studio Bajsić" R12 Principal component analysis of the interaural crosscorrelation coefficient IACC values shows that the first two principal components PC1 and PC2 are mainly defined for parameter IACC Early by measurements M8 and M9; for parameter measurements IACC Late by M11 and M14, and the overall coefficient IACC Full by M26 and M27.