The paper presents an innovative approach for the index assessment of the acoustic properties of churches. A new formula for an approximate single number index to assess selected acoustic parameters of church interiors, such as reverberation time (RT), speech intelligibility index (RASTI) and music clarity index (C80), is presented in the paper. The formula is created by means of the Singular Value Decomposition (SVD) method. An innovative approach for calculating the weights of partial indices is shown by solving the problem of redundant information, i.e., the system of overdetermined linear equations, using a computed pseudoinverse matrix. The new procedures for calculating the values of three partial indices and the single number index to assess selected acoustic parameters are presented. The proposed method was verified by measurements in several selected churches.
A new approach to acoustic quality assessment of churches during simulation tests is proposed in the article. The numerical global index, based on four partial indices: reverberation, speech intelligibility, music sound index and a proposed new one - sound strength index, assesses the acoustic parameters of the model of the tested church in a complex manner.
The global single number index was obtained from 17 simulations of acoustic adaptation options of the investigated church's interior. The equation of the approximate global index has been obtained by means of singular vectors, obtained from Singular Value Decomposition (SVD) of the Index Observation Matrix of Simulation Variants (IOMSV). The weights of four partial indices and a universal equation of the global index have been calculated using the SVD technique to solve the problem of correlated acoustical parameters. The global index may be a helpful tool during simulation tests of acoustic quality assessment of churches. The proposed final equation of the global index does not require knowledge of the SVD technique and the values of acoustic parameters preferred for churches. Therefore the methodology proposed is easily applicable.
In parallel with research conducted using conventional methods, a uniform index method for assessing the acoustic quality of Roman Catholic churches has been developed. The latest version of the index method has been created using the index observation matrix of 12 churches which have been rated by means of the single number global index.
Assessments of the acoustic quality of any Roman Catholic church, using two calculation models: the Global Acoustic Properties Index (GAP) and the Global Index (GI), are shown in the article. The verification was performed on the example of one church, showing the way of calculating global indices to assess the acoustic quality of a new facility. The next stages in the development of the index method for assessing the acoustic quality of churches were taking into account the audience, using simulation tests and determining the spatial distribution of the single number GAP index in an examined church. An attempt to use the GAP and GI calculation models to assess the acoustic properties of some churches is also shown in the article.
Multiple input multiple output (MIMO) is a multiple antenna technology used extensively in wireless communication systems. With the ever increasing demand in high data rates, MIMO system is the necessity of wireless communication. In MIMO wireless communication system, where the multiple antennas are placed on base station and mobile station, the major problem is the constant power of base station, which has to be allocated to data streams optimally. This problem is referred as a power allocation problem. In this research, singular value decomposition (SVD) is used to decouple the MIMO system in the presence of channel state information (CSI) at the base station and forms parallel channels between base station and mobile station. This practice parallel channel ensures the simultaneous transmission of parallel data streams between base station and mobile station. Along with this, water filling algorithm is used in this research to allocate power to each data stream optimally. Further the relationship between the channel capacity of MIMO wireless system and the number of antennas at the base station and the mobile station is derived mathematically. The performance comparison of channel capacity for MIMO systems, both in the presence and absence of CSI is done. Finally, the effect of channel correlation because of antennas at the base stations and the mobile stations in the MIMO systems is also measured.
Spectrophotometry is an analytical technique of increasing importance for the food industry, applied i.a. in the quantitative assessment of the composition of mixtures. Since the absorbance data acquired by means of a spectrophotometer are highly correlated, the problem of calibration of a spectrophotometric analyzer is, as a rule, numerically ill-conditioned, and advanced data-processing methods must be frequently applied to attain an acceptable level of measurement uncertainty. This paper contains a description of four algorithms for calibration of spectrophotometric analyzers, based on the singular value decomposition (SVD) of matrices, as well as the results of their comparison - in terms of measurement uncertainty and computational complexity - with a reference algorithm based on the estimator of ordinary least squares. The comparison is carried out using an extensive collection of semi-synthetic data representative of trinary mixtures of edible oils. The results of that comparison show the superiority of an algorithm of calibration based on the truncated SVD combined with a signal-to-noise ratio used as a criterion for the selection of regularisation parameters - with respect to other SVD-based algorithms of calibration.
In the paper, an extended analysis of the polarization properties of a liquid crystal cell with a biconically tapered single-mode telecommunication optical fiber was presented. These properties are a result of a sample geometry and used LC materials. They were analyzed by using two theoretical models based on the matrix decomposition methods, i.e., polar and singular-value one. By measuring Mueller matrices, information about losses, depolarization, dichroism and birefringence was obtained. In the experiment two types of tested samples filled with well-known 6CHBT and E7 liquid crystals were prepared and all optical parameters were shown as the voltage dependence. The tested samples have dichroic properties and for both models calculated PDL is similar and it increases from 2.6 to 6.6 dB for E7 and from 0.4 to 2.7 dB for 6CHBT with voltage changes within the range of 40 – 190 V. Optical losses simultaneously decrease from 30 dB to 27 dB and from 36 dB to 28 dB, respectively. The birefringence properties cannot be directly comparable due to differences between both applied models but voltage fluctuations of these parameters are not significant. These results confirm expected dichroic properties of designed device and complete knowledge about its working principles. Moreover, presented analysis validates usefulness of the singular-value decomposition model applied to dichroic optical fiber elements.