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.
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.
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.
In this paper, we show that signal sampling operation can be considered as a kind of all-pass filtering in the time domain, when the Nyquist frequency is larger or equal to the maximal frequency in the spectrum of a signal sampled. We demonstrate that this seemingly obvious observation has wideranging implications. They are discussed here in detail. Furthermore, we discuss also signal shaping effects that occur in the case of signal under-sampling. That is, when the Nyquist frequency is smaller than the maximal frequency in the spectrum of a signal sampled. Further, we explain the mechanism of a specific signal distortion that arises under these circumstances. We call it the signal shaping, not the signal aliasing, because of many reasons discussed throughout this paper. Mainly however because of the fact that the operation behind it, called also the signal shaping here, is not a filtering in a usual sense. And, it is shown that this kind of shaping depends upon the sampling phase. Furthermore, formulated in other words, this operation can be viewed as a one which shapes the signal and performs the low-pass filtering of it at the same time. Also, an interesting relation connecting the Fourier transform of a signal filtered with the use of an ideal low-pass filter having the cut frequency lying in the region of under-sampling with the Fourier transforms of its two under-sampled versions is derived. This relation is presented in the time domain, too.
Novel FTIR spectrometer for the monitoring of atmosphere is presented. Its design stands out by a compact form allowing the measures in two IR spectral bands 3-5 and 8-12 μm simultaneously. The spectrometer is composed of two Michelson interferometers with the joint sliding mirror. The paper contains the detailed description of the optics and electronics units, preliminary results of the measurement of biological aerosols and calibration methods.
Cavitation is an essential problem that occurs in all kinds of pumps. This cavitation contributes highly towards the deterioration in the performance of the pump. In industrial applications, it is very vital to detect and decrease the effect of the cavitation in pumps. Using different techniques to analysis and diagnose cavitation leads to increase in the reliability of cavitation detection. The use of various techniques such as vibration and acoustic analyses can provide a more robust detection of cavitation within the pump. In this work therefore, focus is put on detecting and diagnosing the cavitation phenomenon within a centrifugal pump using vibration and acoustic techniques. The results obtained from vibration and acoustic signals in time and frequency domains were analysed in order to achieve better understanding regarding detection of cavitation within a pump. The effect of different operating conditions related to the cavitation was investigated in this work using different statistical features in time domain analysis (TDA). Moreover, Fast Fourier Transform (FFT) technique for frequency domain analysis (FDA) was also applied. Furthermore, the comparison and evaluation system among different techniques to find an adequate technique incorporating for accuracy and to increase the reliability of detection and diagnosing different levels of cavitation within a centrifugal pump were also investigated.
This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous time counterpart for transformation from the time into the frequency domain as well as to those regarding transformation in the inverse direction. In particular, the latter ones remained so far an unresolved problem. It is solved for the first time here. Many detailed explanations accompanying the solution found are presented. Finally, it is also worth noting that our derivations do not exploit any of such sophisticated mathematical tools as the so-called Dirac delta and Dirac comb.
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.
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.
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.
It is well known that the magnitudes of the coefficients of the discrete Fourier transform (DFT) are invariant under certain operations on the input data. In this paper, the effects of rearranging the elements of an input data on its DFT are studied. In the one-dimensional case, the effects of permuting the elements of a finite sequence of length N on its discrete Fourier transform (DFT) coefficients are investigated. The permutations that leave the unordered collection of Fourier coefficients and their magnitudes invariant are completely characterized. Conditions under which two different permutations give the same DFT coefficient magnitudes are given. The characterizations are based on the automorphism group of the additive group ZN of integers modulo N and the group of translations of ZN. As an application of the results presented, a generalization of the theorem characterizing all permutations that commute with the discrete Fourier transform is given. Numerical examples illustrate the obtained results. Possible generalizations and open problems are discussed. In higher dimensions, results on the effects of certain geometric transformations of an input data array on its DFT are given and illustrated with an example.
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