A novel measurement method and a brief discussion of basic characteristics of measuring the phase shift angle between two sinusoidal signals of the same frequency are presented in this paper. It contains a mathematical model for using conditional averaging of a delayed signal interfered with noise to measure the phase shift angle. It also provides characteristics of conditional mean values and discusses the effect of random interferences on the accuracy of the phase shift measurement. The way to determine the variance of the conditional mean value, together with the assessment of standard and expanded uncertainty, are described. The uncertainty characteristic shows the complementary properties of the discussed angle measurement principle �� for small absolute values |��| (minimum for �� = 0) relative to the correlation principle, where the minimum measurement uncertainty is present for �� = ��/2. |

The article presents the approach to the design process of acoustic panels based on the scientific research. This approach is based on combining the technical and the design competences to develop the innovative product value for the concept of acoustic panels. The article presents the concepts of two new acoustic panels – an absorbing and scattering panel and a panel reflecting sound waves. The first part of the article presents the starting point for the presented project – the acoustic research and the inspiration for both types of presented solutions. Next, the materials possible to use were discussed, which could reproduce the natural acoustic properties of the lava and glacier caves. The next part presents consecutive stages of the product development in a modern form, ensuring the expected acoustic properties. The last part of the article presents a fully functional solution and proposes further research and development directions.

The method of a phase shift angle measurement using conditional averaging of delayed signal absolute value (CAAV) is presented in this paper. The input sinusoidal signal x(t) is without noise. White noise with normal distribution and band limited to low frequencies has been applied as disturbance of delayed sinusoidal signal z(t). Noise n(t) - N(0, σn) is added to the delayed signal - the noised and delayed signal z(t) is obtained. The phase angle shift is proportional to time location of CAAV's minimum (minimum of the characteristic of conditional averaging of delayed signal's absolute value). The phase angle shift can be determined on the basis of conditional averaging value of elaborated algorithm. The characteristics of conditional average of delayed signal's absolute value in the surrounding of the minimum of this function (the results of practical investigations and theoretical calculation) are presented. The experimental variance of characteristic CAAV in surroundings of the minimum (obtained from practical investigations and calculation) is illustrated in the paper. The algorithms of conditional averaging have been elaborated and practically realized in the LabVIEW environment.

This paper presents the results of the theoretical and practical analysis of selected features of the function of conditional average value of the absolute value of delayed signal (CAAV). The results obtained with the CAAV method have been compared with the results obtained by method of cross correlation (CCF), which is often used at the measurements of random signal time delay. The paper is divided into five sections. The first is devoted to a short introduction to the subject of the paper. The model of measured stochastic signals is described in Section 2. The fundamentals of time delay estimation using CCF and CAAV are presented in Section 3. The standard deviations of both functions in their extreme points are evaluated and compared. The results of experimental investigations are discussed in Section 4. Computer simulations were used to evaluate the performance of the CAAV and CCF methods. The signal and the noise were Gaussian random variables, produced by a pseudorandom noise generator. The experimental standard deviations of both functions for the chosen signal to noise ratio (SNR) were obtained and compared. All simulation results were averaged for 1000 independent runs. It should be noted that the experimental results were close to the theoretical values. The conclusions and final remarks were included in Section 5. The authors conclude that the CAAV method described in this paper has less standard deviation in the extreme point than CCF and can be applied to time delay measurement of random signals.

The correlation of data contained in a series of signal sample values makes the estimation of the statistical characteristics describing such a random sample difficult. The positive correlation of data increases the arithmetic mean variance in relation to the series of uncorrelated results. If the normalized autocorrelation function of the positively correlated observations and their variance are known, then the effect of the correlation can be taken into consideration in the estimation process computationally. A significant hindrance to the assessment of the estimation process appears when the autocorrelation function is unknown. This study describes an application of the conditional averaging of the positively correlated data with the Gaussian distribution for the assessment of the correlation of an observation series, and the determination of the standard uncertainty of the arithmetic mean. The method presented here can be particularly useful for high values of correlation (when the value of the normalized autocorrelation function is higher than 0.5), and for the number of data higher than 50. In the paper the results of theoretical research are presented, as well as those of the selected experiments of the processing and analysis of physical signals.

Autocorrelation of signals and measurement data makes it difficult to estimate their statistical characteristics. However, the scope of usefulness of autocorrelation functions for statistical description of signal relation is narrowed down to linear processing models. The use of the conditional expected value opens new possibilities in the description of interdependence of stochastic signals for linear and non-linear models. It is described with relatively simple mathematical models with corresponding simple algorithms of their practical implementation.

The paper presents a practical model of exponential autocorrelation of measurement data and a theoretical analysis of its impact on the process of conditional averaging of data. Optimization conditions of the process were determined to decrease the variance of a characteristic of the conditional expected value. The obtained theoretical relations were compared with some examples of the experimental results.