Digital Fourier Transformation Research Articles

Mathematical modeling of the rotor dynamics of a turbomachine on gas foil bearings subjected to vibration

BACKGROUND: The use of gas foil bearings is a promising development in the field of turbomachinery due to their economy, autonomous operation capability, and durability. However, gas foil bearings have lower load capacities than other types of bearings. However, turbomachines are complicated, dynamic systems that must meet high standards of safety, sustainability, and durability against external mechanical factors like vibration, shock, etc.
 AIM: Development of a mathematical model of rotor dynamics to predict the displacement of the rotor in foil bearings for maintaining separation between the rotor and the housing while being subjected to vibration.
 METHODS: A mathematical model of the dynamics of a stiff rotor on gas foil bearings was built and analyzed, taking into account the flexibility of the bearing bushing supports and the housing of the turbomachine. Stationary and transient modes of operation, including the transient modes combined with random vibration, are simulated. The system of ordinary derivatives equations describing the mathematical model was solved by the Rado IIA method. Random vibration was modeled using digital Fourier transformation. The modeling results were analyzed by discrete Fourier transformation and short-time Fourier transformation.
 RESULTS AND CONCLUSIONS: Rotor movement trajectories were obtained and the results were compared with authors previous experimental data. Upper bound of maximal displacements was obtained. The maximum values of rotor displacement can be used to set the optimal values of blade tip gaps.

Development of ventilation and sound-absorbing materials using specimens generated by the multi-objective optimization method

In hot and humid tropical countries, the houses are designed to be naturally ventilated with vent louvers. However, these louvers play as direct paths for noise entering the house. It is necessary to create geometries that can maximize the noise transmission loss and the ventilation performance of the housing structure. The present study aims to develop ventilation and sound-absorbing material using the multi-objective optimization method. This material has a specific design that enables wind from the exterior of the building to pass through while reducing noise. This study is presented in two parts. This paper, Part 1, explains the multi-objective optimization method and analysis calculation result. In the following paper, Part 2, the acoustic experiment of the ABS specimens manufactured by the 3D printer and results will be reported. An optimization problem is formulated by the Digital Fourier transformation, which searches the patterns of existing and blank elements. The sum of the magnitudes of the flow velocities in all the elements and those in the bottom elements are obtained from fluid potential flow analysis and used as by-objective functions. Multi-objective optimization is performed using "Platypus," an external library of Python. As a result, models that maximized the sum of the magnitude of each flow velocities are obtained.

Reducing noise by repetition: introduction to signal averaging

This paper describes theory and experiments, taken from biophysics and physiological measurements, to illustrate the technique of signal averaging. In the process, students are introduced to the basic concepts of signal processing, such as digital filtering, Fourier transformation, baseline correction, pink and Gaussian noise, and the cross- and autocorrelation functions. From these computations, the students estimate physically interesting parameters such as the pulse rate and blood flow velocity. They also learn about some of the pitfalls encountered in quantifying the signal and noise components for a meaningful computation of the signal-to-noise ratio.

Data aided symbol timing estimation in space–time coding systems with continuous phase modulation

AbstractSpace–time coding has been proposed recently in the MIMO wireless communication systems for improving the capacity and data rate without bandwidth expansion. Symbol timing synchronisation is an important issue in such systems. In this paper, a novel data aided symbol timing estimation algorithm was proposed for burst‐mode transmission systems of space–time trellis coding combined with continuous phase modulation (CPM) for Rayleigh fading channels. A training sequence is embedded before transmission of each packet. The receiver calculates the Digital Fourier Transformation (DFT) of the phase of the differential signals. The symbol timing offset can be estimated from the phase of the tone component of the DFT outputs. MATLAB simulation results show that the variance of the timing estimation error is very small. This algorithm can estimate the initial timing offset rapidly and accurately. Space–time coding has been proposed recently in the MIMO wireless communication systems for improving the capacity and data rate without bandwidth expansion. Symbol timing synchronisation is an important issue in such systems. In this paper, a novel data aided symbol timing estimation algorithm was proposed for burst‐mode transmission systems of space–time trellis coding combined with continuous phase modulation (CPM) for Rayleigh fading channels. A training sequence is embedded before transmission of each packet. The receiver calculates the Digital Fourier Transformation (DFT) of the phase of the differential signals. The symbol timing offset can be estimated from the phase of the tone component of the DFT outputs. MATLAB simulation results show that the variance of the timing estimation error is very small. This algorithm can estimate the initial timing offset rapidly and accurately. Copyright © 2009 John Wiley & Sons, Ltd.

Fourier transform ion cyclotron resonance spectroscopy

An ion cyclotron resonance (ICR) absorption spectrum has been obtained by exciting an ICR spectral segment with a fixed-frequency electric field pulse, followed by broad-band detection, digitization of the (time-domain) transient response, and digital Fourier transformation to produce the (frequency-domain) absorption spectrum. For a given signal-to-noise ratio and resolution, the FT-ICR method generates a spectrum in a time which is two orders of magnitude shorter than that required in conventional slow-sweep ICR detection. In the present example, a signal-to-noise ratio of 8 :1 and a mass resolution of about 0.005 amu for CH 4 + (from CH 4 at a pressure of 8 X 10 -7 torr) have been achieved, using a single data acquisition period of 25.6 msec.

High fidelity correction of pressure signals from fluid-filled systems by harmonic analysis.

Fluid-filled systems are generally used for invasive pressure measurements in cardiology, anesthesiology and intensive care medicine. Wave reflection and attenuation cause considerable signal distortion. The transducer signal is amplified (no filtering) and sampled (rate 1 kHz) using an autocorrelation based algorithm to detect instantaneous cycle length. A digital Fourier transformation (DFT) for each heart cycle is performed. Amplitude and phase distortion are corrected using data matrices determined in in vitro experiments or calibration measurements for each fluid-filled system to be used. As a measure for accuracy the maximum of the difference of reference and corrected pressures (DIFF) was selected. 960 analyses were performed to assess the impact of correction, used system, mean pressure, time and A/D sampling rate on the agreement with reference pressure. Clinical examples are presented. Mean pressure was correlated with DIFF (r = 0.83). The correction algorithm achieves a significant (p < 0.001) reduction of DIFF from 20-30 mm Hg to 0-5 mm Hg in the high pressure range and from 1-3 mm Hg to 0-1.5 mm Hg in the low pressure system in in vitro experiments and in clinical pressure recordings. Sampling frequency < 1 kHz reduces accuracy. High fidelity correction of pressure signals from fluid-filled systems by harmonic analysis is feasible.

Estimating vibrational velocity spectra by processing doppler signals in a laser vibrometer

Vibrational velocity spectral analysis is considered for digital processing of Doppler signals in a laser vibrometer. Local approximation is used to estimate the vibrational velocity functions. The dimensions in the digital Fourier transformation are reduced by the use of polynomial local models.

Dynamic characteristics of an arc sensor in GMA welding in droplet transfer mode: Study of improvement of sensitivity and reliability of arc sensors in GMA welding (3rd Report)

Summary This paper describes a method for experimental determination of the dynamic characteristics of an arc sensor in GMA (MIG/MAG) welding in droplet transfer mode. The method basically involves a vibration device being used to excite sinusoidal waveforms of the torch height as well as data processing by means of an FIR digital low-pass filter and dispersive Fourier transformation (DFT). The experimental results show that the sensitivities of the arc sensor are much greater than in DC open arc welding. The response of the welding current to torch height variation is maximised at around 3 Hz. Although the response continues up to a higher level when the frequency exceeds around 5–6 Hz, the SN ratio is poorer than that at 3 Hz. The response of the welding current shows a phase lag relative to the torch height variation. The response of the welding voltage, however, shows a phase advance relative to the torch height variation, and the response increases with an increasing variation frequency of the torch height, but its SM ratio is much poorer than that of the welding current. To clarify the effects of shielding gases on the arc sensor, experiments using four types of shielding gas - pure Ar, Ar + 10% CO2, Ar + 20% CO2, and CO2 — were conducted. The results show that, contrary to those obtained in open arc welding, the responses in short-circuiting arc welding using pure Ar are higher than those using Ar and CO2 mixed gases. Simulations using an arc sensor model proposed by the authors are also run for short-circuiting arc welding and the results analysed. The analytical results based on this model show the theoretical and experimental results to be similar qualitatively but to disagree quantitatively. The theoretical results further show that not only the average short-circuit frequency, but also the rate of change of the short-circuit frequency induced by variation of the arc length strongly affect the sensitivities of the arc sensor.

短絡アーク溶接におけるアークセンサの動特性 ＧＭＡ溶接におけるアークセンサの感度向上と信頼性改善に関する研究 （第３報）

This paper gives a method to experimentally determine the dynamic characteristics of arc sensor in GMA welding in dip transfer mode. The method mainly involves a vibration device to excite sinusoidal wave forms of torch height and data processing by means of FIR digital low-pass filter as well as digital fourier transformation (DFT). Experimental results show that the sensitivities of arc sensor are quite greater than that in DC open arc welding. The response of welding current to the variation in torch height gets to reach the highest level at around 3 Hz in our experiments. Although the response continues to hold higher level when the frequency exceeds about 5-6 Hz, the SN ratio becomes poorer than that at 3 Hz. The response of welding current shows a delayed phase relative to the variation in torch height. Contrary to this, the response of welding voltage has an advanced phase relative to the variation in torch height, and the response becomes higher and higher with the increase of the variation frequency of torch height, but it's SN ratio is quite poorer than that of the response of welding current.To clarify the effects of shielding gases on the arc sensor, experiments were made by using different mixed gases of Ar and CO2. It is found that contrary to these in open arc welding, the responses in short-circuit arc welding using pure Ar are higher than that using mixed gases of Ar and CO2.Simulation analysis was also made based on an arc sensor's model proposed by authors for the short-circuit arc welding. The results displayed that the theoretical and experimental results are quite similar in qualitatively but did not yet achieve agreement quantitatively. The theorectical results also show that not only the average short-circuit frequency, but also the change rate of the short-circuit frequency induced by the variation in arc length have great effect on the sensitivities of the arc sensor.

Experimental Deformation Mechanics of Materials from their Near-Atomic-Resolution Defect Images

ABSTRACTA novel approach to quantitative interpretation of high-resolution electron microscopy images of defects in materials has been developed. The emphasis of this paper is on the methodology, which has been named Computational Fourier Transform Moiré Analysis. The essential principle of this technique is to extract an accurate displacement field about a defect from its near-atomic-resolution picture using digital Fourier transformation procedures. From this data, the displacement gradient can be calculated which yields much information on the experimental deformation mechanics of the material under investigation. As a by-product, we produce the computational Moiré pattern without the need of an external perfect reference lattice image normally associated with the interference phenomena. This method is illustrated using a bounding Frank partial dislocation for a Frank loop of the vacancy type. Results are presented on its strain field, Burgers vector and dislocation core shape and dimensions. Further mention will be made on the types of J-integral calculations that can result from this experimental study.

Accuracy of digital Fourier transformation detection systems for high speed rotating analyser ellipsometers

Computer simulations have been performed in order to assess the accuracy of a fast Fourier transformation detection system for a high speed rotating analyser ellipsometer with a data acquisition time of the order of 10 ms for an entire measurement. The effect of mechanical imperfections of the analyser assembly and of electrically and optically generated periodic and random noise was studied.

Modification of thermal techniques: Derivative, digital filter, Fourier transform

Continued efforts to identify compatible or incompatible blends have demonstrated a need to separate overlapping curves or peaks in a thermal trace. One way to do this is by using the derivatives of these curves. While the function is available on most modern thermal analysis units, its usefulness is often limited by noise in the system. Two techniques which can help to greatly reduce noise are digital filtering and Fourier transformation of the data. Both approaches have been used on identical sets of noisy data. The FT method appears to offer greater potential for producing useful derivatives from noisy composite curves.

Evaluation of a fourier transform method for accurate critical dimension measurements

Controls of critical dimensions are important on production lines of the semiconductor industry. They are generally carried out using non destructive optical devices. In this paper we present the principle and the performances of a new optical measurement technique involving digital Fourier Transformation. This method overcomes the difficulties encountered with the traditional threshold methods. The mathematical model that supports the method takes into account the interference phenomena and allows the ellimination of the effects of the optical properties of the line. The measurements are precise (0.003μm), repeatable (σ<0.02μm), accurate (better than 2%), independant of the materials, independant of operator training, stable in time and very fast (1s).

Impulse studies of double diffraction: A discrete Huygens interpretation

A closed-form analytical impulse solution of diffraction by a rigid wedge is interpreted from the point of view of discrete Huygens wavelets emanating from the crest of the wedge. The strengths of these secondary sources and the impulse field diffracted over a second wedge are calculated. Digital Fourier transformation is then used to determine the spectral loss during double diffraction. The technique is applied to a thick plate, an angled wide barrier, and a strip; successful predictions of laboratory experiments are achieved. In principle, the method may be used for any number of diffractions by straight line segments of an extended barrier or scattering surface.

Analyses of artifacts in the data processing of correlation NMR. Tilted baseline problem and aliasing of the solvent signal

Mathematical analyses of artifacts which are difficult to avoid in a conventional data processing of correlation NMR are given. In the discrete Fourier transformation, which is used in the digital processing, it is tacitly assumed that a sequence of data is periodic. When the baseline is tilted, the first and the last points of the sequence are different in magnitude, and therefore a discontinuity results in the sequence. In the digital Fourier transformation of this type of sequence, the truncation error becomes considerable, resulting in a severe baseline oscillation in the correlation NMR spectrum. In the limit of the zero sweep rate, this type of oscillation is equivalent to the Gibbs phenomenon which is well known in the theory of Fourier series. A mathematical basis for the wing processing, which we have previously proposed, is given. Another advantage of wing processing is that signals which exist outside the frequency range covered by the sweep but give a residual ringing in the rapid scan response can correctly be recognized as such, and the aliased lines do not appear and disturb the NMR spectrum of interest.

Stable multifrequency emission of picosecond pulses from a cw dye laser pumped by phase-locked radiation

A simple method was developed for generating phase-locked picosecond (<10 psec) pulses at several frequencies at the same time in the same resonator of a cw dye laser pumped by phase-locked radiation. A periodic time substructure of a multifrequency pulse was studied (the minimum duration of the autocorrelation function spikes was 0.12 psec). The experimental results were compared with those of a direct digital Fourier transformation of the stimulated emission spectra and with analytic estimates. The characteristics and feasibility of applications of the multifrequency regime were analyzed.

Spectral data of surface viscoelastic modulus acquired via digital fourier transformation

The time domain behavior of dynamic surface tension was experimentally observed for submicellar aqueous solutions (2 × 10 −3 and 4 × 10 −3 mole m −3) of the surfactant dimethyldodecylphosphine oxide. The frequency domain behavior was calculated. by mapping one domain into the other with the Fourier transform operator. Two consecutive numerical processing runs were performed with different discretizations of the same input signal (0.1− and 3.0-sec time intervals between readings, respectively). By choosing an appropriate part of the output array from each run, satisfactorily accurate spectra of surface viscoelastic modulus were obtained. Values of parameters, determined from the reported spectra on the basis of the Lucassen theory, compare favorably with those given in the literature (obtained from equilibrium data).

Fourier transform ion cyclotron resonance spectroscopy

An ion cyclotron resonance (ICR) absorption spectrum has been obtained by exciting an ICR spectral segment with a fixed-frequency electric field pulse, followed by broad-band detection, digitization of the (time-domain) transient response, and digital Fourier transformation to produce the (frequency-domain) absorption spectrum. For a given signal-to-noise ratio and resolution, the FT-ICR method generates a spectrum in a time which is two orders of magnitude shorter than that required in conventional slow-sweep ICR detection. In the present example, a signal-to-noise ratio of 8:1 and a mass resolution of about 0.005 amu for CH 4 + (from CH 4 at a pressure of 8 X 10 −7 torr) have been achieved, using a single data acquisition period of 25.6 msec.

Digital Beamforming in the Frequency Domain

A recent proposal to use digital Fourier transformation in forming acoustic beams is discussed tutorially. Relations to other procedures for beamforming, and for spectral analysis, are given. Need is shown for a lower limit on the data batch size.

High Resolution Far Infrared Interferometry with Application to Solid State Physics

The relative usefulness of a diffraction grating monochromator, a lamellar grating interferometer and a Michelson interferometer will be discussed with reference to a variety of solid state physics problems. The interferometers, used with digital Fourier transformation, achieve a maximum resolution of ∼0.1 cm-1 over the frequency range from 3 to 200 cm-1.