Efficient and reliable VLSI algorithms and architectures for the discrete Fourier transform

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.

In today’s era, it is important to analyze and utilize various signals in industrial or laboratory applications. Measured signals provide critical information about the controlled system, which can be contained precisely within a narrow frequency range. Many methods and algorithms exist to process such signals in both the time and frequency domains. In particular, signal processing in the frequency domain is primary in industrial practice because dominant components within a specific narrow frequency band are sought. The discrete Fourier transformation (DFT) algorithm is the tool used in practice to find these frequency components. The DFT algorithm provides the full frequency spectrum with a higher number of calculation steps, and its spectrum frequency resolution is low. Therefore, research has focused on finding a method to achieve high-frequency spectrum resolution. An important factor in selecting the technique was that such an algorithm should be implementable on a microprocessor-based system under harsh industrial conditions. Research results showed that the DFT ZOOM method meets these requirements. The frequency zoom has many advantages but requires some modification. It is implemented in high-performance analyzers, but a thorough and detailed description of the respective algorithm is lacking in technical articles and literature. This article mathematically and theoretically describes the modified frequency zoom algorithm in detail. The steps of the frequency zoom, from creating an analytical signal through frequency shifting and decimation to the frequency analysis of the signal, are realized. The algorithm allows for the analysis of a signal with high-frequency resolution in a limited frequency band. A significant modification of DFT ZOOM is that of using the Hilbert transform to create an analytic signal. This resolves the aliasing issue caused by the overlap between fundamental and sideband spectra. Results from processing deterministic and stochastic signals using the modified DFT ZOOM are presented. The presented experimental results contribute to a more detailed frequency analysis of the signal. As part of this scientific research, the issues of frequency zoom were thoroughly addressed, solving the partial problems of this algorithm, both in theory and in the context of signal theory.

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.

Discrete Fractional Fourier Transform (DFRFT) has received lots of attention in last two decades because of its superior benefits and wide applications in various fields. In this study we present a comparative analysis of the most famous algorithms for the computation of DFRFT. Analysis is done on the parameters like time complexity, accuracy, consistency, basic mathematical properties and generalization of Discrete Fourier Transform (DFT) and approximation of continuous Fractional Fourier Transform (FRFT). Main objective of the research is to portray the major advantages and disadvantages of the previously proposed algorithms so that appropriate algorithm may be selected as per requirements. On the basis of study it has been observed that there exist several definitions and algorithm for computing the DFRFT. These algorithms are based on different techniques, such as eigenvectors, chirp convolution, spectral decomposition, non-Fresnel integral, or orthogonal projection. Each of these algorithms has its own advantages and disadvantages. Despite of these developments, we still feel that there has been dire need of a standard definition and computing method for accurate and efficient computation of DFRFT.

This paper presents an application of the discrete Fourier transform (DFT) to calculate neural activities efficiently in simulating large biologically motivated neural nets. The experimental results demonstrate the DFT technique is more superior in performing calculation of the neural activity which reduces the time complexity to a theoretical order of O(nlog/sub 2/, n), n being the number of neural units at each iteration. Our study also found that although the computational speed is improved drastically, there are tradeoffs involving: (1) the error generated from the transform, (2) initial setting up time, and (3) the memory storage requirement when using the DFT algorithm. More specifically, we outline criteria and conditions under which the DFT method will yield optimal results in large software neural simulations. >

A novel methodology to estimate the state-of-health and remaining-useful-life of a Li-ion battery using discrete Fourier transformation

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.

This paper investigates two primary algorithms for estimating phasor information used in Phasor Measurement Units (PMU). Power systems behavior and responses are more complicated nowadays and subsequently their supervision, control and protection are more critical and challenging. Various supervisory systems should be employed for protective and control purposes. All these supervisory systems rely on PMU technology with data stamps synchronized by Global Positioning System (GPS). A PMU's accuracy and performance in phasor estimation during different power system working conditions to track the actual signal has an impact on the system state estimation and subsequently in the ability in fault and disturbances diagnosis. Many algorithms are proposed recently to be employed for phasor estimation in PMU devices. It is showed that Discrete Fourier based algorithms are the best methods in digital world to implement in PMU devices. Such methods are Discrete Fourier Transform (DFT) and Smart DFT that are compared and investigated in this article. Simplicity and low computational burden of these methods resulted in attracting many literatures to employ them in phasor estimation algorithms. However, their accuracy in off-nominal frequency and performance during different working condition are controversial which are studied in this article. Extensive simulations are performed in MATLAB Simulink to study and compare DFT and SDFT algorithms under different system disturbances.

The discrete Fourier transform (DFT) is a powerful phasor estimation algorithm conventionally used in digital relaying applications. The DFT‐based phasor estimation is usually accompanied by oscillatory error due to the presence of the decaying DC (DDC) components in fault current signals. Accordingly, two modified DFT‐based phasor estimation algorithms are proposed in this paper. The proposed algorithms accurately estimate the exact fundamental phasor by extracting the DDC components using successive outputs of the conventional DFT algorithm. The performance of the proposed algorithms is validated by the mathematically generated and PSCAD‐simulated signals and is compared with previous algorithms. The results demonstrate that the proposed algorithms in this paper are more robust than other ones. Moreover, they are applicable in the DFT algorithm with different data windows.

The concept of Wide-Area Measurement Systems (WAMS) envisages the transmission of current and voltage phasor samples from remote Phasor Measurement Units (PMUs) to control centres, relays or controllers. Compression of the high frequency samples of sinusoidal waveforms into phasors is usually done using Discrete-Fourier Transform(DFT)-like algorithms. The phasor data is normally useful only when the system is in sinusoidal steady state, or nearly so. It is worthwhile to explore means to get reasonably accurate transient information as well, even if it means that some additional compressed information needs to be transmitted from the PMUs. Transient reconstruction has practical utility in the analysis of disturbances (at a remote control centre) and for flagging the initiation and clearing of network disturbances, which may be required for some WAMS analytics. In this paper, it is shown that one-cycle-delayed reconstruction of power system transient waveforms can be done with samples of the dc, fundamental and harmonic phasors reported at a rate of one sample per cycle obtained from the DFT algorithm. For power system transients, a few harmonics are usually adequate to reconstruct the transient waveforms with reasonable accuracy. The paper explains the reconstruction method, presents illustrative examples and discusses possible applications and practical issues.

For the bogie traction motor bearings of rail vehicles under road transportation conditions, its vibration signal full-time domain data acquisition data volume, storage pressure, subsequent data analysis difficulties, and other problems. This study proposes a data compression acquisition and data reconstruction method for bearing vibration signals based on compressed sensing (CS), which can achieve compressed sampling, transmission, and storage of the original signal with fewer observations, and restore the original signal by combining reconstruction algorithms to achieve low error reconstruction. We study the effects of different sparse transform methods on signal sparsity, as well as the signal sparse performance based on different sparse transforms and the signal reconstruction effect of different reconstruction algorithms, and propose a sparse representation method based on the discrete Fourier transform (DFT) and the generalized orthogonal matching pursuit (gOMP) algorithm for CS. Through simulation and experimental comparison, it is concluded that the method can restore and reconstruct the original high-dimensional signal with small reconstruction error, and solve the problems of massive data, inconvenient transmission, and difficult data analysis in engineering.

The determination of phase and RMS value belongs to the most important tasks of signal analysis in the frequency domain. Evaluating these parameters is frequently performed by the DFT (Discrete Fourier Transform) algorithm. In practice, signals are mostly sampled non-coherently. This leads to the well known effect called leakage, which results in spreading frequency spectral component energy to neighboring frequency lines. Therefore, time windows are used for leakage suppression. This paper introduces the problematic of uncertainty analysis of phase and RMS value computed from the DFT spectrum by non-coherent sampling using cosine windows. The analysis is aimed to investigate the influence of quantization noise.

To solve the problem of low accuracy of channel estimation in OFDM systems in the scenario of high-speed multipath channels, it is proposed in the paper that a noise reduction scheme of channel estimation is based on DFT (Discrete Fourier Transform) algorithm. By analyzing the algorithm principles, the mathematical model of the system is built, and the performance of the scheme is analyzed. Simulation results reveal that in high-speed scenario, the scheme has effectively achieved low bit error rate and low mean square error, thus having good application value.

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.

Wireless communication technology is one the most vibrant fields in scientific researches, it breaks the restriction of the physical aspects in wired communication. Thus, everyone can communicate with others all hours in areas where radio could be radiated, it brings greatly expands of communication on the temporal and spatial scales. Channel estimation, as an important technology in wireless communication system, has been required more and more demanding since a huge increase of data volume and faster transmission speed in the communication systems. In this paper, three pilot-assisted channel estimation algorithms are introduced in detail, including Least Squares (LS), Discrete Fourier Transform (DFT) and Minimum Mean Square Error (MMSE) channel estimation algorithms. In addition, three different interpolation algorithms are also investigated and compared.