Use Of Discrete Fourier Transform Research Articles

Online estimation of thévenin equivalent using discrete fourier transform

This paper presents a method for the determination of the Thévenin equivalent (TE) parameters of a power system using local phasor measurement unit (PMU) measurements. The proposed method is based on an innovative use of Discrete Fourier Transform (DFT), where the DFT coefficients are calculated for the measured voltage and current phasors, which are used to determine the TE parameters. The method presented exploits the characteristics of DFT to develop a new simple and efficient method for TE determination. The calculated DFT is also utilized to detect the presence of measurement errors and to get the best estimate of TE parameters in such conditions and also enable identification of the erroneous measurement. The proposed method is illustrated using a simple system and tested with the data of standard test systems, which all verified the accuracy of the proposed method.

Mode Recovery by S$^2$ Imaging Without a Fourier Transform

In its standard implementation, spatially and spectrally resolved (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) imaging consists in recording near field intensity patterns as a function of the wavelength, followed by a Discrete Fourier Transform (DFT) to assess differential group delays, as well as optical power distribution between modes for the given injection as long as the higher-order mode powers are low. Here we present a variant of S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -imaging which does not make use of DFT. The method is more robust to wavelength jitter of the laser source. Furthermore, in special cases, the method allows retrieving relative modal powers without constraints on HOM power.

Reducing the Impact of the Frequency Change on the Formation of Orthogonal Components of the Relay Protection Input Signals

Digital filters made with the use of discrete Fourier Transform are applied in most microprocessor protections produced both in the home country and abroad. When the input signal frequency deviates from the value to which these filters are configured, a signal is generated at their output with oscillation amplitude that is proportional to the deviation of the signal frequency from the specified one. The article proposes an algorithm for compensating the oscillations of orthogonal components of the output signals of digital filters implemented on the basis of a discrete Fourier transform, when the input signal frequency deviates from the nominal one. A mathematical model of the proposed digital filter with an algorithm for compensating the oscillations of its orthogonal components, as well as a signal model for reproducing input effects, is implemented in the MatLab-Simulink dynamic modeling environment. The digital filter model is provided with two channels, viz. a current channel and a voltage channel, which makes it possible to simulate their operation in relation to protections that use one or two input values, for example, for current and remote protection. Verification of the functioning of the digital filter model with compensation for fluctuations in its output signal was carried out with the use of two types of test effects, viz. a sinusoidal signal with a frequency of 48–51 Hz (idealized effect), and the effects that are close to the real secondary signals of measuring current transformers and voltage transformers in case of short circuits accompanied by a decrease in frequency. The conducted computational experiments with deviation of frequency from the nominal one, revealed the presence of undamped oscillations at the output of standard digital Fourier filters and their almost complete absence in the proposed digital filters. This makes us possible to recommend digital filters based on a discrete Fourier transform supplemented by an algorithm for compensation of fluctuations in the amplitudes of the output signals for the use in microprocessor protection.

Carrier Frequency Offset Effects on OFDM System over Rayleigh Fading Channel

Orthogonal Frequency Division Multiplexing (OFDM) system showed the use of Discrete Fourier Transform (DFT) and Inverse Discrete Fourier Transform (IDFT) to perform the baseband modulation and demodulation. So that, it can increase and improve the efficiency of the modulation and demodulation. Currently, the OFDM is being utilized in the field of broadband wireless communication, which transmit signals orthogonally, that increases speed of information transmission. It also has high proficiency with high bandwidth and provide large data rates and robust against the multipath delay spread. On the other hand, there are some issues faced OFDM system which are high Peak Average Power Ratio (PAPR), and sensitive to Phase Noise (PN) and Carrier Frequency Offset (CFO). This paper presents Orthogonal Frequency Division Multiplexing (OFDM) performance evaluation in the presence of CFO with two different environment scenarios were used: an AWGN channel and a Rayleigh fading channel. The simulation was performed to evaluate the effects of CFO based on Bit Error Rate (BER) vs. Energy Bit per Noise Ratio (Eb/No). The results showed that for BER degradation caused by CFO effects have presented in our simulation for both AWGN and Rayleigh fading channel.

Guaranteed-Stable Sliding DFT Algorithm With Minimal Computational Requirements

The discrete Fourier transform (DFT) is the most widely used technique for determining the frequency spectra of digital signals. However, in the sliding transform scenario where the transform window is shifted one sample at a time and the transform process is repeated, the use of DFT becomes difficult due to its heavy computational burden. This paper proposes an optimal sliding DFT (oSDFT) algorithm that achieves both the lowest computational requirement and the highest computational accuracy among existing sliding DFT algorithms. The proposed oSDFT algorithm directly computes the DFT bins of the shifted window by simply adding (or subtracting) the bins of a previous window and an updating vector. We show that the updating vector can be efficiently computed with a low complexity in the sliding transform scenario. Our simulations demonstrate that the proposed algorithm outperforms the existing sliding DFT algorithms in terms of computational accuracy and processing time.

On the feasibility to integrate low-cost MEMS accelerometers and GNSS receivers

The aim of this research was to investigate the feasibility of merging the benefits offered by low-cost GNSS and MEMS accelerometers technology, in order to promote the diffusion of low-cost monitoring solutions.A merging approach was set up at the level of the combination of kinematic results (velocities and displacements) coming from the two kinds of sensors, whose observations were separately processed, following to the so called loose integration, which sounds much more simple and flexible thinking about the possibility of an easy change of the combined sensors.At first, the issues related to the difference in reference systems, time systems and measurement rate and epochs for the two sensors were faced with. An approach was designed and tested to transform into unique reference and time systems the outcomes from GPS and MEMS and to interpolate the usually (much) more dense MEMS observation to common (GPS) epochs. The proposed approach was limited to time-independent (constant) orientation of the MEMS reference system with respect to the GPS one.Then, a data fusion approach based on the use of Discrete Fourier Transform and cubic splines interpolation was proposed both for velocities and displacements: MEMS and GPS derived solutions are firstly separated by a rectangular filter in spectral domain, and secondly back-transformed and combined through a cubic spline interpolation.Accuracies around 5mm for slow and fast displacements and better than 2mm/s for velocities were assessed. The obtained solution paves the way to a powerful and appealing use of low-cost single frequency GNSS receivers and MEMS accelerometers for structural and ground monitoring applications.Some additional remarks and prospects for future investigations complete the paper.

Spectrally Precoded DFT-Based OFDM and OFDMA With Oversampling

Spectrally precoded orthogonal frequency-division multiplexing (SP-OFDM) and SP-OFDM multiple access (SP-OFDMA) are bandwidth-efficient rectangularly pulsed multicarrier signaling formats that can provide power spectral sidelobes decaying asymptotically as f -2L-2 , with L being a preassigned positive-integer design parameter, which results in a compact spectrum. The existing spectral precoders for SP-OFDM and SP-OFDMA are designed based on the rectangularly pulsed analog multicarrier waveform representation that has an unlimited power spectrum; thus, the corresponding waveforms cannot be exactly synthesized in a discrete Fourier transform (DFT) structure. Consequently, these spectral precoders are subject to modification in DFT-based OFDMA and OFDM systems in which signaling waveforms are digitally synthesized with the use of DFT and provide discrete approximation embodiments to analog multicarrier waveform counterparts. In this paper, a general constraint on spectral precoding and the corresponding spectral precoders are developed for DFT-based OFDMA and OFDM with oversampling to ensure the desirable spectral property that the resultant spectrally precoded DFT-based waveforms provide powerspectral-sidelobe envelope bounds decaying asymptotically as f -2L-2 . It is analytically shown that the precoders suitable to DFT-based waveforms can be simply obtained by properly transforming the previously designed precoders suitable to corresponding analog multicarrier waveforms with an appropriate diagonal phase-rotation matrix, while yielding similar spectral performance and peak-to-average power ratio (PAPR) characteristics.

David Lewin and maximally even sets

David Lewin originated an impressive number of new ideas in musical formalized analysis. This paper formally proves and expands one of the numerous innovative ideas published by Ian Quinn in his dissertation, to the import that Lewin might have invented the much later notion of Maximally Even Sets with but a small extension of his very first published idea, where he made use of Discrete Fourier Transform (DFT) to investigate the intervallic differences between two pc-sets. Many aspects of Maximally Even Sets (ME sets) and, more generally, of generated scales, appear obvious from this original starting point, which deserves, in our opinion, to become standard. In order to vindicate this opinion, we develop a complete classification of ME sets starting from this new definition. As a pleasant by-product we mention a neat proof of the hexachord theorem, which might have been the motivation for Lewin's use of DFT in pc-sets in the first place. The nice inclusion property between a ME set and its complement (up to translation) is also developed, as occurs in actual music.

Comparison of Fourier and Bayesian Analysis of NMR Signals. II. Examination of Truncated Free Induction Decay NMR Data

In a recent report [J, J. Kotyk et al., J. Magn. Reson, 98, 483 (1992)], estimates of NMR frequency and amplitude parameters obtained from Bayesian probability theory were shown to be more precise and more accurate than those obtained from the discrete Fourier transform (DFT). This previous study examined the effects of varying signal-to-noise ratio and did not address the performance of either probability theory or the DFT as a function of acquisition time, i.e., truncation. Herein, a quantitative comparison between probability theory and the DFT is presented and discussed in terms of the accuracy and precision they provide in estimating the frequency and amplitude from truncated free induction decay data. For simplicity, data containing only a single frequency are examined. For frequency estimation, Bayesian probability theory gives either more precise and accurate estimates or exactly the same estimates as the DFT. This latter result only occurs when the theory indicates that the Bayesian procedure is functionally identical to the DFT. For amplitude estimation, the results presented herein are consistent with those cited in previous work. Even for the best DFT procedure, probability theory outperforms the DFT by a factor of two or more depending on the signal-to-noise ratio and the prior information supplied in the analysis. The amplitude estimates from probability theory are more precise and/or more accurate than the DFT results for all levels of truncation. Additionally, the only time the DFT amplitude estimates are more precise (less uncertain) are when they are inaccurate (give an incorrect answer). Thus, the use of probability theory offers significant improvement over the use of DFT in highly truncated NMR free induction decay data.

On coding and filtering stationary signals by discrete Fourier transforms (Corresp.)

This correspondence concerns real-time Fourier processing of stationary data and examines the widespread belief that coefficients of the discrete Fourier transform (DFT) are "almost" uncorrelated. We first show that any uniformly bounded <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \times N</tex> Toeplitz covariance matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_N</tex> is asymptotically equivalent to a nonstandard circulant matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_N</tex> derived from the DFT of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_N</tex> . We then derive bounds on a normed distance between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_N</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_N</tex> for finite <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> , and show that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mid T_N - C_N \mid ^ 2 = O(1/N)</tex> for finite-order Markov processes. Finally we demonstrate that the performance degradation resulting from the use of DFT (as opposed to Karhunen-Loève expansion) in coding and filtering is proportional to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mid T_N - C_N \mid</tex> and therefore vanishes as the inverse square root of the block size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \rightarrow \infty</tex> .