Algorithms For Discrete Fourier Research Articles

Real-Time Detection Method for Saturation Speed of Air-Core Coil Current Transformer

Traditional methods generally rely on a fixed threshold to determine whether the current transformer is saturated. However, this threshold based judgment method is difficult to adapt to different working conditions and changes in current waveforms. In view of the different characteristics of current transformer and the diversity of working environment, it may not be accurate to judge its saturation state only by relying on a fixed threshold. In order to improve the efficiency of current transformer speed saturation detection and reduce the error, a new type of air core coil current transformer speed saturation real-time detection method is proposed. Based on the working and current characteristics of the fast saturation current transformer, the discrete Fourier algorithm is used to suppress power frequency interference signals, with the fundamental frequencies set to 45 Hz and 55 Hz respectively, in order to separate the signal from power frequency interference and reduce the interference intensity of the power frequency interference signal; Identify all faults and saturation points, and extract effective data segments. The wavelet transform characteristics of the secondary current waveform of current transformer in saturated and unsaturated states are deeply studied. By analyzing the changes of different operating conditions and current waveforms, more discriminant features are extracted by using the characteristics of wavelet transform, so as to realize the real-time and accurate detection of saturation state. The results indicate that after adopting the proposed method, the highest accuracy of data segment extraction reached 97%; The maximum detection error is only 4%. The detection time is only 1.31 s. This indicates that the proposed method improves the detection performance and is practical.

DEVELOPMENT OF A MEASUREMENT SYSTEM AND SOFTWARE PRODUCT TO COLLECT AND ANALYSE ELECTRICITY QUALITY PARAMETERS

In the real operating conditions of electrical networks, there are modes of operation characterised by deviations of their parameters from their nominal values. Of particular importance for the operation of electrical equipment are variations in the amplitude and frequency of the supply voltage. The permissible and limit deviations of these parameters are regulated in accordance with national standards. To calculate the main power quality parameters it is not sufficient to know only the methods of their calculation. Additional algorithms are needed to determine fundamental harmonic voltages and frequencies. Such a method is the discrete Fourier transform. This algorithm is designed for signal analysis. However, this algorithm was not widely used in calculating Fourier coefficients in modern software packages. The reason is that it takes much time and computer resources to determine the Fourier coefficients which reduces the attractiveness of this approach. For this reason, it is advisable to use the fast Fourier transform algorithm. This algorithm uses the periodicity properties of the trigonometric function, which allows reducing the number of multiplication operations. The results of using the fast Fourier transform algorithm are similar to the discrete Fourier algorithm, but the number of operations required for calculation is several times less. At the same time, fast and discrete Fourier transform algorithms can give quite a significant error in determining the frequency estimate. This deviation is related to multiplicity of time between signal measurements and its period. If the period of the analogue signal is a multiple of the sampled signal measurement distance, an additional Quin method must be used to reduce the error in determining the frequency of the main signal. In this regard, the development of algorithms and software complex for automated measurement systems of electrical power quality indicators using digital data acquisition and processing devices in real time is an urgent task.

Deep mining of communication information association based on discrete Fourier transform

In order to better analyze communication information and improve the efficiency of communication information association mining, a discrete Fourier algorithm is proposed to extract association rules from information flow data with different time granularity. With the help of the MapReduce parallel programming model, a deep mining algorithm on the association of communication information is designed. Firstly, the data is linearly normalized, and the algorithm model of data depth mining is proposed according to the discrete Fourier transform. The data source uses the message middleware Kafka, and the intermediate results are stored in the memory database redis through the serialization technology. By using the structural information and comparison algorithm of the database, K pairs with the largest Pearson correlation coefficient are searched, association rules are mined, meaningless items are filtered out, construct an association deep mining model to realize rapid mining of association rules related to tasks. Experimental results and analysis show that the algorithm is efficient and stable in discovering association rules from high-speed information data flow, and supports different time granularity.

An Interpolation Algorithm for Discrete Fourier Transforms of Weighted Damped Sinusoidal Signals

An algorithm for improving the accuracy of the estimation of parameters that characterize a multifrequency damped sinusoidal signal is presented. The core ideas of the algorithm is that the signal is weighted using Hann window before discrete Fourier transform and the frequencies, amplitudes, phases, and damping factors of the signal are obtained by frequency domain interpolation. It is shown that the purpose of improving the accuracy of parameter estimation is achieved using Hann window, which reduces long-range leakage and frequency-domain interpolation that eliminates the effect of the picket fence. The sensitivity analysis of the changing of the signal parameters, noise and spectral resolution, shows that both the effects of strong noise and spectral interference are considered, proving the reliability and high-accuracy parameters estimation in a number of engineering applications. Otherwise, the characteristic of efficiency computational and low memory demands are advantageously adopted for the poor computing resources situations. Extracting the impact signal of the rotor test bed using this method is illustrated. The result shows that the method can be an optional method for the fault features extraction of the mechanical impact.

Introduction to the special issue on Low-power circuit techniques

This special issue of ‘‘Low-power circuit techniques’’ in the Springer Journal of Analog Integrated Circuits and Signal Processing is published with six papers, which are selected from presented papers at the 2012 International Conference on Analog VLSI Circuits (AVIC 2012). This conference is believed to be the only conference that bares the key word ‘‘Analog VLSI’’, and have accepted very wide range of papers concerning analog circuits. Among them, we called for papers related to low-power circuit techniques for this special issue. The Research Committee on Electronic Circuits of the Institute of Electrical Engineers of Japan (IEEJ) was sponsoring and cooperating with Analog Devices Inc., the University of Valencia and the Polytechnic University of Valencia to hold the 2012 International Conference on Analog VLSI Circuits in Valencia, Spain, on October 24–26, 2012. This conference is the successor of former International Analog VLSI Workshop, which had been successfully held for 14 years. The purpose of the conference is to exchange information, ideas and recent research results on analog VLSI circuits and their applications. This workshop has formed a long-standing community for various analog VLSI circuit specialists from both industry and academia worldwide, and promoted active brainstorming among them at the site. The first two papers are related to power supply circuits and DC–DC converter circuits. The first paper by Nomura et al. presents photovoltaic cell design, oscillator, and bootstrap charge pump circuit integrated on an 0.18 lm CMOS chip, to provide power generation and voltage boost functions on stand-alone microsystems. Sato et al. present a theoretical analysis of efficiency in charge pumps for LED drivers and describe a novel procedure to minimize power loss by applying adiabatic process to charge pump circuits. The third paper by Tanimoto et al. presents a fullydifferential OTA operating from 1-V power supply. The OTA consists from CMOS cascode inverters to obtain a high voltage gain while maintaining rail-to-rail input common-mode range at 1-V power supply. They also fabricated a test chip by using 0.15 lm CMOS technology and confirmed the design techniques to be useful. The fourth and the fifth papers are concerning to high speed communication signal processing. Nakagawa et al. present a passive complex filter design approach, which is relevant to low power analog signal processing at very high frequency. The concept is exemplified with two complex filters operating at 100 kHz and 10 MHz but maybe extended beyond tens of GHz. The fifth paper by Yazaki et al. presents a design of a 20-Gbps CMOS optical receiver, which does not require inductor to suppress power supply noise by a unique design of power supply noise canceling circuit. The designed chip was fabricated in 90 nm CMOS technology and demonstrated effectiveness of the design. The last paper by Carbajo et al. presents a new version of the well known Goertzel algorithm for discrete Fourier J. Calpe-Maravilla Analog Devices S.L., Edificio 8F, Planta 3, Campus UPV, 46022 Valencia, Spain e-mail: javier.calpe@analog.com

Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D (15)N- and (13)C-edited NOESY-HSQC spectra of human ubiquitin.

Low Computational Complexity, Low Power, and Low Area Design for the Implementation of Recursive DFT and IDFT Algorithms

A novel recursive algorithm for discrete Fourier transform (DFT) and its inverse transform (IDFT) is proposed in this brief. It was found that the proposed algorithm and its implementation outperformed other existing recursive algorithms. The proposed algorithm was found to 1) reduce multiplication computations by 50.5% using the symmetric identity of coefficients and a resource-sharing technique and register-splitting scheme; 2) decrease read-only memory sizes by 50% compared with conventional algorithms; 3) reduce the number of multipliers implemented by 80% compared with the latest algorithm; and 4) increase data throughput by 100% per transformation. This design is suitable for communication systems and digital radio mondiale (DRM) systems, such as dual-tone multifrequency detection and coded orthogonal frequency-division-multiplexing modulation. The algorithm was designed and fabricated using a 0.18 ?m 1P6M complementary metal-oxide-semiconductor process. The core area is 397 × 388 ?m2, including the DFT and IDFT modules. For modern applications (voice over packet and DRM), this processor only consumes 2.96 mW at 25 MHz. Furthermore, it can calculate the 212/165/106/288/256/176/112-point DFTs and IDFTs.

Design of low-cost and high-throughput linear arrays for DFT computations: algorithms, architectures, and implementations

Recursive algorithms for discrete Fourier transform (DFT) computation are proposed, where the common entries of the decomposed matrices are factored out in order to reduce the number of multipliers during implementation. The derived algorithms are essentially band-matrix-vector multiplications with matrix bandwidth of 3 in the radix-2 case and bandwidth of 7 in the radix-4 case. Low cost architectures are derived using an efficient mapping technique for the corresponding heterogeneous dependence graphs of the decomposed band matrices. Only log/sub 2/ N(3 log/sub 4/ N) adders and log/sub 2/ N-1(log/sub 4/ N-1) multipliers are needed to compute the DFT of size N using the proposed radix-2 (radix-4) linear array architectures, a great saving in hardware cost compared to previous approaches. Due to the simplicity and regularity of the architectures, it is possible to reduce the power consumption of the DFT processors by temporarily disabling the multiplier units at proper time steps. VLSI implementations of an 8-point radix-2 DFT processor and a 64-point radix-4 DFT processor are also given.

Fast generalized DFT and DHT algorithms

This paper presents fast algorithms for complex and real generalized discrete Fourier transform (GDFT). It shows that the length- N GDFT can be computed by a split-radix algorithm of discrete Fourier transform (DFT) whose input and output sequences are rotated by twiddle factors. It also reveals that the odd-time, odd-frequency and odd-squared DFTs are closely related to the discrete cosine transform (DCT). Compared with recently reported split-radix GDFT algorithm, the proposed one provides a simpler computational structure and significant savings on the number of arithmetic operations.

Interpolation Algorithms for Discrete Fourier Transforms of Weighted Signals

A new scheme is presented for the determination of the parameters that characterize a multifrequency signal. The essential innovation is that the signal is weighted before the discrete Fourier transform (DFT) is calculated from which the frequencies and complex amplitudes of the various components of the signal are obtained by interpolation. It is shown that by using the Hanning window for tapering substantial improvements are achieved in the following respects: i) more accurate results are obtained for interpolated frequencies, etc., ii) harmonic interference is much less troublesome even if many tones with comparable strengths are present in the spectrum, iii) nonperiodic signals can be handled without an a priori knowledge of the tone frequencies. The stability of the new method with respect to noise and arithmetic roundoff errors is carefully examined.

The bit-complexity of arithmetic algorithms

Time-complexity and space-complexity of arithmetic algorithms without divisions measured by the number of binary bits processed in computations are estimated for algorithms for discrete Fourier transform (DFT) and polynomial multiplication (PM, or convolution of vectors). It is proved that Ω(N 2) bit-operations are required in an evaluation-interpolation algorithm for PM over the field of real constants while O( N log 2 N) arithmetic operations suffice.