In this paper, the design of frequency-locked loop (FLL) is proposed based on computationally efficient discrete Fourier transform (DFT) structures. In recent years, the DFT structures are evolved as ...sliding DFT (SDFT), modulated SDFT, hopping DFT (HDFT), modulated HDFT, and sliding-windowed infinite Fourier transform. Considering their tuned filter characteristics, an attempt has been made to obtain a solution for the instantaneous frequency estimation problem of the input signal under varying center frequency condition. In each DFT structure, the <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>th bin in-phase and quadrature components are separated for instantaneous signal extraction. The feedback loop is designed around these DFT structures, and it was observed that the frequency responses exhibit flat magnitude and phase interestingly when compared with the open-loop structures. Hence, an adaptive sampling frequency adjustment scheme is proposed for these structures as FLL to estimate the instantaneous frequency of the input signal for the wide variation in center frequency. These FLLs with different DFT structures are tested for dynamic performance and wide operating range. The proposed FLLs are implemented in field-programmable gate array (FPGA), and the experimental investigations have been carried out for frequency estimation. Further experimental investigations on these FLLs as a system on chip were carried out with area and power analysis.
The literature on the subject of synchrophasor estimation (SE) algorithms has discussed the use of interpolated discrete Fourier transform (IpDFT) as an approach capable to find an optimal tradeoff ...between SE accuracy, response time, and computational complexity. Within this category of algorithms, this paper proposes three contributions: the formulation of an enhanced-IpDFT (e-IpDFT) algorithm that iteratively compensates the effects of the spectral interference produced by the negative image of the main spectrum tone; the assessment of the influence of the e-IpDFT parameters on the SE accuracy; and the discussion of the deployment of IpDFT-based SE algorithms into field programmable gate arrays, with particular reference to the compensation of the error introduced by the free-running clock of A/D converters with respect to the global positioning system (GPS) time reference. The paper finally presents the experimental validation of the proposed approach where the e-IpDFT performances are compared with those of a classical IpDFT approach and to the accuracy requirements of both P and M-class phasor measurement units defined in the IEEE Std. C37.118-2011.
In this work, we propose a new substitution scheme for color images watermarking based on the Fourier transform. This scheme will be declined into two variants in which the image will be divided into ...three components R, G and B, and then to each component a transform is applied. The parity of the resulting coefficients will then be combined to hide the watermark in the medium frequency band. In our experiments several variants of the Fourier transform are used (Discrete Fourier Transform, a Fractional Fourier Transform as well as a Quaternion Discrete Fourier Transform). For each transform, both variants of our watermarking scheme are applied. The obtained results show that our approach offers good imperceptibility and generates watermarking images robust against various attacks with a high-quality watermark.
•In the spatial domain a combination between the data value samples provides reasonable SNR results (more than 66dB).•These approaches are simple and inexpensive in computation time can be used for ...real-time watermarking required in low-power environments.•The use of transforms makes the message more robust to compression, since it uses the same space used for coding.•The results obtained remain satisfactory compared to some recent work with a SNR greater than 33dB on average.•The decomposition into sub-bands provides acceptable and satisfactory levels of SNR compared to some recent work with a SNR greater than 40dB.
In this paper; we propose two new substitution schemes for digital audio watermarking based on the Fourier transform. The integration of the watermark will be performed by combining the parity of the successive coefficients values; each variant will represent a different combination. In our experiments several variants of the Fourier transform are used (Discrete Fourier Transform, a Fractional Fourier Transform as well as a Quaternion Discrete Fourier Transform). For each transform, both variants of our watermarking scheme are applied and the results obtained show that our approach offers good imperceptibility and generates watermarked audio sample robust against various attacks with a high-quality watermark. However, using small audio file for our experiments considerably reduces the capacity of our approach in the frequency domain.
We present a single synchrophasor estimation (SE) algorithm that is simultaneously compliant with both P and M phasor measurement unit (PMU) performance classes. The method, called ...iterative-interpolated discrete Fourier transform (i-IpDFT), iteratively estimates and compensates the effects of the spectral interference produced by both a generic interfering tone, harmonic or interharmonic, and the negative image of the fundamental tone. We define the three-point i-IpDFT technique for cosine and Hanning window functions and we propose a procedure to select the i-IpDFT parameters. We assess the performance of the i-IpDFT with respect to all the operating conditions defined in the IEEE Std. C37.118 for P- and M-class PMUs. We demonstrate that the proposed SE method is simultaneously compliant with all the accuracy requirements of both PMU performance classes.
Batch algorithms for the generation of optimal orthonormal eigenvectors of a square unitary matrix F are presented. Since the unitarity of a matrix implies the orthogonality of its eigenspaces ...pertaining to its distinct eigenvalues, the problem is decoupled in the sense that optimal eigenvectors are individually generated for the eigenspaces. In one algorithm, the singular value decomposition (SVD) technique is applied to a rectangular matrix whose columns are nonorthogonal eigenvectors of matrix F pertaining to a distinct eigenvalue. In another algorithm, the SVD technique is applied to a square matrix obtained by pre multiplying this rectangular matrix by its complex conjugate transpose. For the sake of generality, this rectangular matrix is allowed to be rank-deficient and the notion of matrix pseudoinverse is resorted to in order to find optimal orthonormal eigenvectors. The general results are applied to the discrete Fourier transform of type IV (DFT-IV) kernel matrix G where the objective is the generation of Hermite-Gaussian-like (HGL) orthonormal eigenvectors as an essential step towards the development of the fractional discrete Fourier transform of type IV (FDFTIV). Since the contributed algorithms necessitate knowledge of the orthogonal projection matrices on the eigenspaces of the unitary matrix G, explicit expressions are derived for those projection matrices. The extensive simulation results show the relative merits of the various algorithms especially for large values of the order N of the matrix.
This paper strives to reduce pilot contamination, a bottleneck for massive multiple-input multiple-output (MIMO) systems, by exploiting channel sparsity. Considering that typical wideband massive ...MIMO channel is correlated in both space and frequency domains, we employ Karhunen-Loéve Transform (KLT) and Discrete Fourier Transform (DFT) to capture the hidden sparsity of the channel. KLT basis is optimal in extracting the uncorrelated information from channel, but requires channel statistical information. As a suboptimal alternative, DFT basis can be determined without channel statistics, which is more viable for practical use. By representing the channel with DFT basis, we find that the subspaces of the desired and interference channels are approximately orthogonal, even when the number of antennas is not so large. Inspired by this observation, we propose a pilot decontamination method, where a pilot assignment policy is designed to help identify the subspace of the desired channel, and a desired channel subspace aware least square channel estimator is derived to remove the pilot contamination. The proposed method does not need channel statistics and pilot co-ordination. By exploiting channel stationary, the method does not introduce extra training overhead. Simulation results demonstrate substantial sum rate gain of the proposed method over existing methods.
The energy produced by renewable energy systems must fulfill quality requirements as defined in the respective standards and directives. Improvement of the quality could be achieved through a more ...accurate estimation of the frequency of the grid's signal that is used to control an inverter. This paper presents an overview of a method for spectrum interpolation and frequency estimation, and a generalized method for very accurate frequency grid estimation using the fast Fourier transform procedure coupled with maximum decay sidelobe windows. An important feature of this algorithm is the elimination of the impact associated with the conjugate's component on the estimation's outcome (i.e, the possibility of designating the frequency even if the signal's measurement time is on the order of 2.5 periods), and the implementation of the algorithm is straightforward. The results of the simulation show that the algorithm could be successfully used for a fast and accurate estimation of the grid signal frequency. The systematic frequency estimation error is approximately 5·10 -11 Hz for a 5-ms measurement window. The algorithm could be used not only for a single sinusoidal signal, but also for a multifrequency signal. This is assuming that the appropriate spectrum leakage reduction (by a time window) will be performed.
In this paper, we established some new operations and formulas of set theory for complex fuzzy sets (CFSs). We introduced the basic results of CFSs with their examples using union, intersection, ...complement, dot product, complex fuzzy probalistic sum, complex fuzzy bold sum, complex fuzzy bold sum over associative law of union, etc. Moreover, we introduced an algorithm to identify a reference signal out of large number of signal having bigger
N
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received by a digital receiver. Thus, a new model is introduced for measuring the values of the signals in a faster way using CFSs.
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