The radiation of sound waves from partially lined duct is treated by using the mode-matching method in conjunction with the Wiener-Hopf technique. The solution is obtained by modification of the Wiener-Hopf technique and involves an infinite series of unknowns which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the problem parameters, whereby the effects of these parameters on the sound diffraction are studied. A perfect agreement is observed when the results of radiated field are compared numerically with a similar work existing in the literature.
Gabor Wigner Transform (GWT) is a composition of two time-frequency planes (Gabor Transform (GT) and Wigner Distribution (WD)), and hence GWT takes the advantages of both transforms (high resolution of WD and cross-terms free GT). In multi-component signal analysis where GWT fails to extract auto-components, the marriage of signal processing and image processing techniques proved their potential to extract autocomponents. The proposed algorithm maintained the resolution of auto-components. This work also shows that the Fractional Fourier Transform (FRFT) domain is a powerful tool for signal analysis. Performance analysis of modified fractional GWT reveals that it provides a solution of cross-terms of WD and blurring of GT.
Nowadays a geometrical surface structure is usually evaluated with the use of Fourier transform. This type of transform allows for accurate analysis of harmonic components of surface profiles. Due to its fundamentals, Fourier transform is particularly efficient when evaluating periodic signals. Wavelets are the small waves that are oscillatory and limited in the range. Wavelets are special type of sets of basis functions that are useful in the description of function spaces. They are particularly useful for the description of non-continuous and irregular functions that appear most often as responses of real physical systems. Bases of wavelet functions are usually well located in the frequency and in the time domain. In the case of periodic signals, the Fourier transform is still extremely useful. It allows to obtain accurate information on the analyzed surface. Wavelet analysis does not provide as accurate information about the measured surface as the Fourier transform, but it is a useful tool for detection of irregularities of the profile. Therefore, wavelet analysis is the better way to detect scratches or cracks that sometimes occur on the surface. The paper presents the fundamentals of both types of transform. It presents also the comparison of an evaluation of the roundness profile by Fourier and wavelet transforms.
This study proposes a surface profile and roughness measurement system for a fibre-optic interconnect based on optical interferometry. On the principle of Fizeau interferometer, an interference fringe is formed on the fibre end-face of the fibre-optic interconnect, and the fringe pattern is analysed using the Fast Fourier transform method to reconstruct the surface profile. However, as the obtained surface profile contains some amount of tilt, a rule for estimating this tilt value is developed in this paper. The actual fibre end-face surface profile is obtained by subtracting the estimated tilt amount from the surface profile, as calculated by the Fast Fourier transform method, and the corresponding surface roughness can be determined. The proposed system is characterized by non-contact measurement, and the sample is not coated with a reflector during measurement. According to the experimental results, the difference between the roughness measurement result of an Atomic Force Microscope (AFM) and the measurement result of this system is less than 3 nm.
In this paper the method of fast impedance spectroscopy of technical objects with high impedance (|Zx| ≥1 GΩ) is evaluated by means of simulation and a practical experiment. The method is based on excitation of an object with a sinc signal and sampling the response signals proportional to current flowing through and voltage across the measured impedance. The object’s impedance spectrum is obtained with the use of continuous Fourier transform on the basis of linear approximations between samples in two acquisition sections, connected with the duration of the sinc signal. The method is first evaluated in MATLAB by means of simulation. An influence of the sinc signal duration and the number of samples on impedance modulus and argument measurement errors is explored. The method is then practically verified in a constructed laboratory impedance spectroscopy measurement system. The obtained acceleration of impedance spectroscopy in the low frequency range (below 1 Hz) and the decrease of the number of acquired samples enable to recommend the worked out method for implementation in portable impedance analyzers destined for operation in the field.
Signal analysis performed during surface texture measurement frequently involves applying the Fourier transform. The method is particularly useful for assessing roundness and cylindrical profiles. Since the wavelet transform is becoming a common tool for signal analysis in many metrological applications, it is vital to evaluate its suitability for surface texture profiles. The research presented in this paper focused on signal decomposition and reconstruction during roundness profile measurement and the effect of these processes on the changes in selected roundness profile parameters. The calculations were carried out on a sample of 100 roundness profiles for 12 different forms of mother wavelets using MATLAB. The use of Spearman's rank correlation coefficients allowed us to evaluate the relationship between the two chosen criteria for selecting the optimal mother wavelet.
It is assumed in the paper that the signals in the enclosure in a transient period are similar to a noise induced by vehicles, tracks, cars, etc. passing by. The components of such signals usually points out specific dynamic processes running during the observation or measurements. In order to choose the best method of analysis of these phenomena, an acoustic field in a closed space with a sound source inside is created. Acoustic modes of this space influence the sound field. Analytically, the modal analyses describe the above mentioned phenomena. The experimental measurements were conducted in the room that might comprise the closed space with known boundary conditions and the sound source Brüel & Kjær Omni-directional type 4292 inside. To record sound signals before the field's steady state was reached, the microphone type 4349 and the 4-channel frontend 3590 had been used. The obtained signals have been analysed by using two approaches, i.e. Fourier and the wavelet analysis, with the emphasis on their efficiency and the capability to recognise important details of the signal. The results obtained for the enclosure might lead to the formulation of a methodology for an extended investigation of a rail track or vehicles dynamics.
A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f) algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency). The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.
The main objective of this paper is to produce an applications-oriented review covering infrared techniques and devices. At the beginning infrared systems fundamentals are presented with emphasis on thermal emission, scene radiation and contrast, cooling techniques, and optics. Special attention is focused on night vision and thermal imaging concepts. Next section concentrates shortly on selected infrared systems and is arranged in order to increase complexity; from image intensifier systems, thermal imaging systems, to space-based systems. In this section are also described active and passive smart weapon seekers. Finally, other important infrared techniques and devices are shortly described, among them being: non-contact thermometers, radiometers, LIDAR, and infrared gas sensors.
This paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.
This paper deals with the amplitude estimation in the frequency domain of low-level sine waves, i.e. sine waves spanning a small number of quantization steps of an analog-to-digital converter. This is a quite common condition for high-speed low-resolution converters. A digitized sine wave is transformed into the frequency domain through the discrete Fourier transform. The error in the amplitude estimate is treated as a random variable since the offset and the phase of the sine wave are usually unknown. Therefore, the estimate is characterized by its standard deviation. The proposed model evaluates properly such a standard deviation by treating the quantization with a Fourier series approach. On the other hand, it is shown that the conventional noise model of quantization would lead to a large underestimation of the error standard deviation. The effects of measurement parameters, such as the number of samples and a kind of the time window, are also investigated. Finally, a threshold for the additive noise is provided as the boundary for validity of the two quantization models
Power systems that are highly loaded, especially by a stochastic supply of renewables and the presence of storages, require dynamic measurements for their optimal control. Phasor measurement units (PMUs) can be used to capture electrical parameters of a power system. Standards on the PMU dynamic performance have been modified to incorporate their new dynamic mode of operation. This paper examines the PMU dynamic performance and proposes essential algorithms for measurement accuracy verification. Measurements of dynamic input signals, which vary in amplitude or frequency, were taken during automated tests of two PMUs. The test results are presented and expounded with further recommendation for the performance requirements. This paper also presents and examines applied testing procedures with relevance to the specifications of the IEEE Standard for Synchrophasor C37.118.1™-2011 and its amendment C37.118.1a™-2014.
The article presents the detection of gases using an infrared imaging Fourier-transform spectrometer (IFTS). The Telops company has developed the IFTS instrument HyperCam, which is offered as a short- or long-wave infrared device. The principle of HyperCam operation and methodology of gas detection has been shown in the paper, as well as theoretical evaluation of gas detection possibility. Calculations of the optical path between the IFTS device, cloud of gases and background have been also discussed. The variation of a signal reaching the IFTS caused by the presence of a gas has been calculated and compared with the reference signal obtained without the presence of a gas in IFTS's field of view. Verification of the theoretical result has been made by laboratory measurements. Some results of the detection of various types of gases has been also included in the paper.
Modern production technology requires new ways of surface examination and a special kind of surface profile parameters. Industrial quality inspection needs to be fast, reliable and inexpensive. In this paper it is shown how stochastic surface examination and its proper parameters could be a solution for many industrial problems not necessarily related with smoothing out a manufactured surface. Burnishing is a modern technology widely used in aircraft and automotive industries to the products as well as to process tools. It gives to the machined surface high smoothness, and good fatigue and wear resistance. Every burnished material behaves in a different manner. Process conditions strongly influence the final properties of any specific product. Optimum burnishing conditions should be preserved for any manufactured product. In this paper we deal with samples made of conventional tool steel – Sverker 21 (X153CrMoV12) and powder metallurgy (P/M) tool steel – Vanadis 6. Complete investigations of product properties are impossible to perform (because of constraints related to their cost, time, or lack of suitable equipment). Looking for a global, all-embracing quality indicator it was found that the correlation function and the frequency analysis of burnished surface give useful information for controlling the manufacturing process and evaluating the product quality. We propose three new indicators of burnishing surface quality. Their properties and usefulness are verified with the laboratory measurement of material samples made of the two mentioned kinds of tool steel.