AM/FM Rate Estimation for Time-Varying Sinusoidal Modeling

Fast Pricing and Calculation of Sensitivities of OTM European Options Under Levy Processes

In the article "Effect of element directivity on adaptive beamforming applied to high-frame-rate ultrasound" [ibid., vol. 62, no. 3, pp. 511-523, 2015], the contrast C was correctly defined. The authors note that therefore, 20 log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> 4 = 12.04 dB should be added to all the contrast values in the paper to obtain the correct contrast values.

Vehicles commonly suffer from the narrow-band noises and vibrations, usually a superposition of multiple sinusoidal signals, due to the excitations of engines, electrical motors, gear boxes, and other rotating mechanical parts. These excitations are transmitted to a reference point of some structure with certain transmission paths. The vibration signal measured at the reference point can be used for power system monitoring, fault diagnosis, modal analysis, noise analysis, etc. For convenience, researchers in a laboratory usually use shakers to generate expected narrow-band vibration signals acting on the vehicle structure reference points to simulate the vibration signals. However, there is a prominent difficulty in ensuring the amplitude and phase accuracy of each sub-frequency component simultaneously. In order to improve the accuracy of generating the expected vibration signal, this paper presents a multi-source vibration simulation control technology based on the tracking filter method. The main idea is to use the tracking filter to estimate the amplitude and phase of the target sub-frequency component accurately. Further, on the target sub-frequency, the drive signal of shakers is then corrected based on the amplitude and phase errors to achieve a more accurate target vibration signal. The amplitude and phase of each sub-frequency component in the excitation signal can be controlled independently. Compared with other Fast Fourier Transform (FFT)-based frequency domain analysis algorithms and numerical methods by solving the equations, the tracking filter method has a higher frequency resolution and higher accuracy. It can be easily realized in real time applications due to its simplicity. Finally, verification experiments are completed. The experimental results show that the multi-source vibration simulation control technology presented in this paper can achieve high-precision amplitude and phase on each sub-frequency component of the target vibration signals, which contain up to eight sub-frequency components.

Nowadays, the Fast Fourier transform (FFT) has been widely adopted for harmonic analysis in power system. However, a direct application of FFT-based algorithms may bring about inaccurate results because of spectral leakage and picket-fence effects. In this paper, a high accuracy method based on the all-phase and interpolated FFT is presented for harmonic analysis. Firstly, the input signal is preprocessed to mitigate spectral leakage through all-phase. Secondly, the interpolation algorithm is adopted to eliminate the picket-fence effects. As a result, the analysis accuracy of the harmonic parameters has been greatly improved and the phase estimation is not biased. The formulas of amplitude, frequency and phase are also obtained based on all-phase and interpolated FFT. The simulation results reflect that this method can better meet the requirements of harmonic detection in power system.

Electrocochleography (ECochG) is increasingly used to monitor the inner ear function of cochlear implant (CI) patients during surgery. Current ECochG-based trauma detection shows low sensitivity and specificity and depends on visual analysis by experts. Trauma detection could be improved by including electric impedance data recorded simultaneously with the ECochG. However, combined recordings are rarely used because the impedance measurements produce artifacts in the ECochG. In this study, we propose a framework for automated real-time analysis of intraoperative ECochG signals using Autonomous Linear State-Space Models (ALSSMs). We developed ALSSM based algorithms for noise reduction, artifact removal, and feature extraction in ECochG. Feature extraction includes local amplitude and phase estimations and a confidence metric over the presence of a physiological response in a recording. We tested the algorithms in a controlled sensitivity analysis using simulations and validated them with real patient data recorded during surgeries. The results from simulation data show that the ALSSM method provides improved accuracy in the amplitude estimation together with a more robust confidence metric of ECochG signals compared to the state-of-the-art methods based on the fast Fourier transform (FFT). Tests with patient data showed promising clinical applicability and consistency with the findings from the simulations. We showed that ALSSMs are a valid tool for real-time analysis of ECochG recordings. Removal of artifacts using ALSSMs enables simultaneous recording of ECochG and impedance data. The proposed feature extraction method provides the means to automate the assessment of ECochG. Further validation of the algorithms in clinical data is needed.

Many natural signals exhibit quasi-periodic behaviors and are conveniently modeled as combinations of several harmonic sinusoids whose relative frequencies, magnitudes, and phases vary with time. The waveform shapes of those signals reflect important physical phenomena underlying their generation, requiring those parameters to be accurately estimated and modeled. In the literature, accurate phase estimation and modeling have received significantly less attention than frequency or magnitude estimation. This paper first addresses accurate DFT-based phase estimation of individual sinusoids across six scenarios involving two DFT-based filter banks and three different windows. It has been shown that bias in phase estimation is less than 0.001 radians when the SNR is equal to or larger than 2.5 dB. Using the Cramér–Rao lower bound as a reference, it has been demonstrated that one particular window offers performance of practical interest by better approximating the CRLB under favorable signal conditions and minimizing performance deviation under adverse conditions. This paper describes the development of a shift-invariant phase-related feature that characterizes the harmonic phase structure. This feature motivates a new signal processing paradigm that greatly simplifies the parametric modeling, transformation, and synthesis of harmonic signals. It also aids in understanding and reverse engineering the phasegram. The theory and results are discussed from a reproducible perspective, with dedicated experiments supported by code, allowing for the replication of figures and results presented in this paper and facilitating further research.

We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider.

Discrete Fourier Transform (DFT) allows you to determine the discrete spectrum of a signal. Due to the presence of its high-speed implementation, called Fast Fourier Transform (FFT), this transform is widely used in digital signal processing (DSP). Most DSP tasks that deal with analogy signal and spectrum adapt the DFT to find the signal spectrum between harmonics. One of the most commonly used ways of such adaptation – the use of window functions. The analysis of standard window functions (Kaiser, etc.) showed that their direct application to solving the problem of estimating the parameters (frequency, amplitude, and phase) of nonharmonic sinusoidal components of signals leads both to the need for additional corrections of the estimation results and to additional errors in determining the phase of the signal. The paper proposes a method that allows building a window function without the indicated drawbacks based on standard window functions. The essence of the method is to transform the standard window function so that its spectrum does not contain imaginary components, and the amplitude of the fundamental harmonic would be equal to 1. The results of modeling the proposed method on the example of the Kaiser window showed that the phase estimate of the nonharmonic components of the spectrum using the obtained window function, in contrast to the estimate using standard window functions, is not displaced.

The authors have carried out a study to investigate and clarify the characteristics of purely oscillating pipe flows over the developing region. The main objective of this study is to establish the method of time-dependent velocity profiles obtained by the ultrasonic velocity profile (UVP) measurement method. First, the relationship between the test fluids and the microparticles, as reflectors of ultrasonic pulses, was investigated. In addition, the relationship between the sound speeds of the test fluids and the wall materials was studied. Second, the UVP was used to obtain the instantaneous velocity profiles in oscillating pipe flows, and the developing characteristics of the flows were analyzed. Finally, the “entrance length” (by analogy with a unidirectional pipe flow) required for oscillating pipe flows was analyzed by examining the amplitude of the harmonic spectral components of the oscillating frequency. A fast Fourier transform (FFT) is proposed as the applicable method to estimate the “entrance length”. From the Fourier transform of the velocity on the centerline, nonlinear oscillation of fluid occurs in the “entrance length” of the oscillating flows, and the viscous dissipation of the higher-order velocity harmoncis determines the entrance region. The “entrance length” can be obtained from the dissipation length of the third-order harmonic. These results prove that the UVP method is highly applicable to carry out the flow measurement in the “entrance length” of oscillating pipe flow.

In recent years, motor current signature analysis has been used for fault diagnosis of permanent magnet synchronous machines. However, the fault feature is not obvious and is easily hidden in the main component, since the amplitudes of fault harmonic components are quiet small compared with the fundamental component. A new method to diagnose the mechanical unbalance fault effectively in permanent magnet synchronous machine drives is proposed in this article, where Park's vector is used to eliminate the fundamental component from the fast Fourier transform (FFT) results of motor current signature analysis; the fault feature is then analyzed by discrete wavelet transform. The effectiveness of the proposed method is validated by simulation and experimental results. It is shown that the proposed diagnosis method may work well under different control strategies.

A measurement theory of variation in group velocity using an interference of acoustic waves is proposed, and an experimental result of a piezoelectric substrate is discussed, when a variation in temperature causes the variation in group velocity. This method utilizes a periodic frequency characteristic of an acoustic intensity when two acoustic waves interfere in the substrate. The periodicity is analyzed by fast Fourier transform (FFT), and the amplitude and phase of the Fourier components which have dimensions of time are calculated. Since the phase shifts by the variation in group velocity, the measurement of the former leads to the precise measurement of the latter. The interference of acoustic waves is caused inside an interdigital transducer (IDT) which is used as a reflector for the wave, and the interference intensity is measured using an acoustooptic (AO) interaction.

This paper aims to study the deep electrical conductivity of the Murmansk block (Fennoscandian Shield) using the controlled source audio-frequency magnetotelluric (CSAMT) and audiomagnetotelluric (AMT) methods. One of the most important tasks in deep sounding studies implying the joint application of the AMT and CSAMT methods is to take into account the influence of surface conductors on the measurement results (static shift). To solve this problem, we develop a methodology for processing and interpreting the measurement data of the CSAMT and AMT system using the results of the deep sounding experiment conducted in the frequency range from 1 to 500 Hz performed in 2018 (Murman-2018) as an example. Measurements with the controlled source in the form of two mutually orthogonal horizontal electric dipoles are taken at distances of 12 to 105 km. The generator-measuring complex consisted of the VMTU-10 measuring station (manufactured by OOO VEGA, St. Petersburg) and the Energy-4 generator (developed at the Kola Science Center, Russian Academy of Sciences, Apatity). Using the synchronous time series of the field components at the observation points and the current in the supply dipole, the power spectra of the autocorrelation and cross-correlation functions of the recorded values are calculated based on the fast Fourier transform (FFT). The obtained spectral characteristics are used (i) to determine the amplitudes of the source field’s components and the phase shifts between them, and (ii) to evaluate the components of the AMT field’s impedance tensor. The values of the apparent resistivity are calculated using the amplitudes of the horizontal components of the electromagnetic field and the impedance ratios. The obtained measurement results are corrected for the static shift. For this, the correction coefficients are calculated from the ratio between the apparent resistivity values for the horizontal component of the magnetic field and the apparent resistivity values inferred from the impedance and electrical field values. The data for the cases of axial and equatorial arrays, together with the data of the AMT and remote sounding, made it possible to establish a high degree of lateral homogeneity of the deep electrical section and to expand the frequency range of the obtained curves of the apparent resistivity and impedance phase. A one-dimensional interpretation is made to obtain estimates of the distribution of the deep resistivity.

A comparative study and assessment of doppler ultrasound spectral estimation techniques part II: Methods and results

In this article, we develop a novel algorithm for Doppler acquisition in fast Fourier transform (FFT)-based Global Navigation Satellite System (GNSS) receivers. The Doppler estimation is carried out in FFT domain by finding the frequency shift which maximizes the energy of the correlation vector. Subsequently, energy detection is used for preliminary decision about the presence of the target code. Then, the final decision and code phase estimation are done in the time domain after taking the inverse fast Fourier transform (IFFT). It is shown that the proposed algorithm has the potential for reducing the average number of required IFFTs in the acquisition process. For improving the sensitivity of the proposed approach, time-domain block averaging and FFT-domain non-coherent integration are investigated as alternative methods. They exhibit rather similar performance improvement, but the non-coherent integration approach is found to be computationally more effective.

A model is presented to calculate the dynamic hysteresis behaviour of the magnetostriction in electrical steel under 1-D sinusoidal magnetisation. The input of the model is one period of the 1-D induction wave. On this induction wave, a fast Fourier transform (FFT) is performed, of which the frequency components are fed to the input of a neural network (NN).This neural network calculates the frequency components (amplitude and phase) of the magnetostriction, on which an inverse fast Fourier transform (IFFT) is performed, thus obtaining the magnetostriction wave complementary to the input induction wave. The filtering technique was used to model the magnetostriction of a grain oriented electrical steel. The amplitude of the induction in the sample ranged between 0.6T and 1.8T and the frequency ranged between quasi-static and 200Hz.