Underwater Tone Detection with Robust Coherently-Averaged Power Processor

To assess the insulation condition of capacitive apparatus, on-line monitoring of dielectric loss angle is an effective measure. Harmonic analysis algorithm is used to calculate dielectric loss angle traditionally, this method can effectively suppress the DC (Direct Current) offset and harmonic interference. However, when the power system frequency fluctuates, the synchronous sampling condition is difficult to meet, so, traditional harmonic analysis method can produce leakage of spectrum and picket-fence effect, which greatly affects the accuracy of dielectric loss angle measurement. In order to reduce this adverse effect, this paper proposes a method called hamming windowed interpolated DFT (Discrete Fourier Transform) algorithm based on modified ideal sampling frequency. Time series analysis based on modified ideal sampling frequency can be used to modify the time series in non-synchronous sampling condition to meet synchronous sampling condition. Hamming windowed interpolated DFT algorithm can inhibit leakage of spectrum and picket-fence effect. Firstly this paper analyzes the principle of traditional DFT algorithm and the reason that causes leakage of spectrum and picket-fence effect in non-synchronous sampling condition. Secondly, the principle of hamming windowed interpolated DFT algorithm based on modified ideal sampling frequency is elaborated. Finally this paper presents the simulation result which shows that the improved approach has higher accuracy.

The purpose of the study is to develop a new method for monitoring the technical condition and functional diagnostics of machines and mechanisms for various purposes based on the spectral analysis of the vibroacoustic signal generated by them. The developed new method for monitoring the technical condition and functional diagnostics of machines and mechanisms for various purposes is based on a generalization of classical discrete Fourier transform (DFT) in the form of parametric DFT (DFT-P). The paper reveals and formulates the problems that arise when using the classical DFT to identify the parameters of hidden periodicities in a vibroacoustic signal generated by machines and mechanisms for various purposes. These are the aliasing effect, the scalloping effect, the picket fence effect. The advantages of DFT-P over DFT in solving the fundamental problems of dynamics and vibroacoustics, solving the problems of noise and vibration are studied in detail. Theoretical foundations for measuring the parameters of a discrete harmonic signal based on parametric discrete Fourier transform have been developed. The reasons for the occurrence of non-invariance of the energy spectrum of a discrete harmonic signal given on a finite interval are investigated by the method of parametric discrete Fourier transform. A technique for determining (estimating) the errors in measuring the amplitude of a harmonic signal by the method of parametric discrete Fourier transform is proposed. An experimental verification of the theoretical results obtained in the work on revealing the parameters of hidden periodicities by parametric DFT method in the functional diagnostics of machines and mechanisms using a vibroacoustic signal was carried out by numerical simulation.

The discrete Fourier transform (DFT) is still a widely used tool for analyzing and measuring both stationary and transient signals in power systems. However, the misapplications of DFT can lead to incorrect results caused by some problems, such as aliasing effect, spectral leakage, and picket-fence effect. This paper establishes a relationship between DFT-based spilled energy and harmonics/noninteger harmonics using the numerical induction method. Based on this study, a strategy of group-harmonics energy diffusion algorithm has been developed for both stationary and nonstationary harmonic/interharmonic evaluation in power systems. Especially, the frequency deviation range is used for frequency estimation, and the restored amplitude is used for retrieving dispersed amplitude. Accordingly, the harmonic/interharmonic frequency and its respective amplitude component can be accurately estimated using a simple mathematic computation. The numerical examples are presented to verify the performance of the proposed algorithm in terms of speed, accuracy, and efficiency.

The Discrete Fourier Transform (DFT) is still a widely-used tool for analyzing and measuring both stationary and transient signals in power systems. However, the misapplications of DFT can lead to incorrect results caused by some problems such as aliasing effect, spectral leakage and picket-fence effect. A strategy of Piecewise-overlapped Group-harmonic Energy Restoring (PGER) algorithm is developed for both stationary and non-stationary harmonic evaluation in power systems. The proposed algorithm can restore dispersing spectral leakage energy caused by the DFT, and thus retrieve the respective real harmonic value. Based on the piecewise-overlapped method, especially every time-varying harmonic can be extracted fast and accurately. The numerical examples are presented to verify the proposed algorithm in term of robust, fast and high-precision performance.

The performance of DFT (Discrete Fourier Transform) algorithm about frequency estimation is obviously declined, because the DFT spectrums have the problem of energy leakage and picket fence effect. Aiming at this problem, an adaptive algorithm based on FFT for frequency estimation is presented. In this paper we analysis the performance of Rife algorithm and point out that the perfor mance is poor when the true frequency is much close to quantized frequency of DFT. The performance of segmented-FFT (Fast Fourier Transform) phase difference method is also analyzed, and we point out that the performance is poor when the phase difference of the maximum spectral line is big. This adaptive algorithm is a combination of these two algorithms. The adaptive algorithm not only retains the advantages of the two algorithms, but also effectively makes up for the shortcomings of the two algorithms. The simulation results show that the anti-noise performance and stability of algorithm have significantly improved.

The processing efficiency of the widely used time-space (t-x) domain vertical seismic profiling (VSP) wavefield separation methods (such as median and singular value decomposition filtering) via one-dimensional discrete Fourier transform (DFT) depends on the wavefield separation method (or algorithm with processing parameter) and the total number of samples in the input VSP data. Once the wavefield separation method is determined, its processing efficiency is set and cannot be optimized. Although the popular frequency-wavenumber (f-k) domain VSP wavefield separation method via two-dimensional DFT has higher processing efficiency than the t-x domain VSP wavefield separation methods, its processing precision is susceptible to the spatial alias and Gibbs effects. For efficiency and precision improvements, we introduced the discrete cosine transform (DCT) operation into VSP wavefield separation for the first time, and proposed a high-efficiency and precision frequency-space (f-x) domain VSP wavefield separation method via DFT and DCT, in which the wavefield separation efficiency and precision can be optimized using the effective bandwidth cutoff frequency of the input VSP data. Based on the relationship between DFT and DCT, we combined their operations in the proposed method into one step (referred to as DCT–DFT) for further efficiency enhancement, thereby designing a high-efficiency and precision f-x domain VSP wavefield separation method via DCT–DFT. Theory analysis and synthetic and field VSP data examples show that the proposed method is highly efficient and precise, and can be widely used for three-dimensional (3D)-VSP data wavefield separation, especially for large distributed acoustic sensing (DAS)-VSP data.

The Discrete Fourier Transform (DFT), which can be calculated efficiently by the Fast Fourier Transform (FFT), is one of the most commonly used tools for frequency estimation of a multi-frequency exponential signal. However, the performance of the FFT is inherently affected by spectral leakage when non-coherent sampling occurs. The Chirp-Z Transform (CZT), which can refine the spectrum to the narrowband range of the source signal accurately, can be generalized to a special form of DFT. This paper proposes a CZT based algorithm which can estimate frequencies of the multi-frequency exponential signal accurately. In our method, the CZT bin, as a nonlinear equation, is firstly used to describe the correspondence among the frequencies, amplitudes, phases and the observed spectrum. Then, the above nonlinear equation is rewritten as a linear equation with unknown frequencies. We further extend the proposed method to the Discrete-time Fourier Transform (DTFT), zero-padding FFT and DFT, which are the special cases of the CZT. We also give the derivation procedure of theoretical variance of our method. In our method, the spectrum leakage is fully considered as useful information to establish the linear equation set. Therefore, it can estimate the frequencies of multi-frequency exponential signal with high accuracy. Simulation results verify the performance of the proposed method.

In many applications, when the representation of a discrete-time signal or a system in the frequency domain is of interest, the Discrete-Time Fourier Transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the Discrete Fourier Transform (DFT), which is simply composed of samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, samples of its z-transform at equally spaced points on the unit circle. A generalization of the DFT, introduced in this chapter, is the Nonuniform Discrete Fourier Transform (NDFT), which can be used to obtain frequency domain information of a finite-length signal at arbitrarily chosen frequency points. We provide an introduction to the NDFT and discuss its applications in the design of 1-D and 2-D FIR digital filters. We begin by introducing the problem of computing frequency samples of the z-transform of a finite-length sequence. We develop the basics of the NDFT, including its definition, properties and computational aspects. The NDFT is also extended to two dimensions. We propose NDFT-based nonuniform frequency sampling techniques for designing 1-D and 2-D FIR digital filters, and present design examples. The resulting filters are compared with those designed by other existing methods.

This paper presents a method to derive efficient frequency estimators from the Discrete Fourier Transform (DFT) of the signal. These estimators are very similar to the phase-based Discrete Fourier Spectrum (DFS) interpolators but have the advantage to allow any type of analysis window (and especially non-rectangular windows). As a consequence, it leads to better estimations in the case of a complex tone (cisoid) perturbed by other cisoids. Overall, our best estimator leads to results similar to those of phase vocoder and reassignment estimators but at a lower complexity, since it is based on a single Fast Fourier Transform (FFT) computation.

This paper presents a shared architecture design for computations of Discrete Fourier Transform (DFT), Inverse DFT (IDFT), and Inverse Modified Cosine Transform (IMDCT) algorithms. The proposed method has following advantages, such as 1) Low hardware costs compared with conventional recursive DFT (RDFT) and recursive IDFT (RIDFT) algorithms. For hardware implementation, 2 real multipliers and 8 real adders are required in the proposed architecture. Compared with previous approaches, it can greatly reduce 80% of number of multipliers and 53% of number of adders. 2) The proposed RDFT-based IMDCT architecture has four times data throughput more than the other existing recursive algorithm 3) Computational cycles of the proposed RDFT-based IMDCT algorithm can be greatly reduced by 50% more than our previous recursive IMDCT algorithms. Hence, the proposed RDFT / RIDFT / RDFT-based IMDCT design is more suitable for portable devices in Digital Radio Mondiale (DRM) system.

An approach for power system harmonic phasor analysis under asynchronous sampling is proposed in this paper. It is based on smoothing sampled data by windowing the signal with the four-term fifth derivative Nuttall (FFDN) window, and then calculating harmonic phasors in the frequency domain with an improved fast Fourier transform (IFFT) algorithm. The applicable rectification formulas of the IFFT are obtained by using the polynomial curve fitting, dramatically reducing the computation load. The FFDN window can effectively inhibit the spectral leakage and the picket fence effect can be modified by the IFFT algorithm under asynchronous sampling, and the overall algorithm can easily be implemented in embedded systems. The effectiveness of the proposed method was analyzed by means of simulations and practical experiments for multifrequency signals with the fluctuation of the fundamental frequency and with the presence of white noise and interharmonics.

An analytical polynomial expression, for accurate and computationally efficient frequency estimation of a single real sinusoid under Additive White Gaussian Noise (AWGN), is derived and proposed in this paper. The method, which can be easily adapted for real time frequency estimation, is based on transforming the frequency estimation problem as the solution of a fourth order (quartic) expressed as powers of a trigonometric function containing the unknown frequency. The coefficients of the quartic polynomial can be found using the complex magnitudes of three Discrete Fourier Transform (DFT) bins, centered at the maximum magnitude value of the DFT coefficients. Simulated results illustrate that, the performance of the proposed estimator has a mean squared-error (MSE) performance which is very close to the Cramer Rao Lower Bound (CRLB) for high signal-to-noise ratio (SNR) region, as well as close to previously published estimators in the low SNR region.

In this paper, a new synthetic frequency estimator of sinusoid signal based on discrete Fourier transform (DFT) amplitudes is proposed. Compared with the existing methods, the proposed method has the advantages of low computational complexity and high precision. The method has two main stages. Firstly, N-point sampled data in the time domain DFT is performed and the coarse estimation is completed by searching the location of the spectrum line with maximum amplitude. Secondly, the synthetic fine estimation is performed by utilizing both the two samples values of Discrete-Time Fourier Transform (DTFT) of the original signal and the maximum amplitude spectrum line and its right or left neighbor. To verify the proposed method, simulation is conducted. The result shows that the root mean square error (RMSE) of frequency estimation of proposed synthetic method is close to the Cramer-Rao Lower Bound, and it outperforms the Candan method. This method is also comparable to Fang method and RCTSL method with zero-padding when conducted under medium and high SNR condition. Moreover, without zeropadding, the proposed method has much lower computational complexity than other known estimators with zero-padding.

This paper presents a new methodology for phasor estimation in the presence of exponentially DC decay (DC offset) and odd harmonics in the signal. The estimations are performed on a half cycle plus four samples of the fundamental component of the system. The method uses digital signal processing techniques such as windowing, DFT (Discrete Fourier Transform) modulation and look up tables (LUT). The performance of the proposed method is compared with others methods presented in the literature. The results from simulation showed that the proposed method has a better performance that the others. In addition to the floating-point implementation, the proposed method was implemented in a reconfigurable hardware platform, FPGA (Field Programmable Gate Array) using fixed-point arithmetic.

The signal processing technique is one of the principal tools for diagnosing power quality (PQ) issues in electrical power systems. The Discrete Fourier Transform (DFT) is a frequency analysis technique used to process power system signals and identify PQ problems. However, the DFT algorithm may lead to spectral leakage and picket-fence effect problems for asynchronously sampled signals that contain harmonic, inter-harmonic, and flicker components. To resolve this shortcoming, a hybrid method for frequency estimation based on a second-level DFT approach and a frequency-domain interpolation algorithm to obtain the accurate fundamental frequency of a power system is proposed in this paper. This method uses a second-level DFT to compute the cosine and sine parts for the fundamental frequency components of the acquired signals. Then, a frequency-domain interpolation approach is adopted to determine the amplitude ratio for the cosine and sine parts of the system’s fundamental frequency. A set of mixed signals with harmonic, inter-harmonic, and flicker components with the fundamental frequency deviation is used. The evaluation results demonstrate the superiority of the new method over other approaches for assessing asynchronously sampled signals contaminated with noise, harmonic, inter-harmonic, and flicker components.