The Hopping Discrete Fourier Transform [sp Tips&amp;amp;Tricks]

Park, Chun-Su; Ko, Sung-Jea

doi:10.1109/msp.2013.2292891

Cited by 48 publications

(22 citation statements)

References 6 publications

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“…Based on the specific SE technique, different DFT bins are required to be computed. In general, if this number is relatively small, the socalled "sliding" DFT algorithms (see for instance [14] and [15]) are preferred due to the relatively low number of operations needed to update a single DFT bin (see [16] for an extensive analysis of the computational advantages and limits of this category of algorithms).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Integration of an IEEE Std. C37.118 compliant PMU into a real-time simulator

Romano

Pignati

Paolone

2015

2015 IEEE Eindhoven PowerTech

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Abstract-The simulation of Phasor Measurement Units (PMUs) into real-time simulators (RTSs) is typically limited by the complexity of the synchrophasor estimation (SE) algorithm. This is especially true when dealing with distribution network PMUs due to the more demanding accuracy requirement and, for the case of class-P PMUs, for the limited latency. In this respect, if the SE algorithm is too simplistic, the performances of the simulated PMU might not match the specific application needs. On the other hand, when higher precision of the synchrophasors estimations is required, an increased computational complexity of the SE algorithm is obtained and, as a consequence, few devices can be simulated into a RTSs at the same time. The work presented in this paper illustrates the design and the deployment of a C37.118 class-P compliant PMU into the Opal-RT RTS. The RTS-deployed PMU has demonstrated to match the requirements of both transmission and distribution networks. The simulated PMU has been experimentally validated and demonstrated to be well suited for its integration into any RTS.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Integration of an IEEE Std. C37.118 compliant PMU into a real-time simulator

Romano

Pignati

Paolone

2015

2015 IEEE Eindhoven PowerTech

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“…In HDFT, the SDFT has been extended to more general case by using arbitrary time hop [10]. Here, we only consider the case , for simplicity of investigation, and the other cases can be easily derived.…”

Section: B Hdftmentioning

confidence: 99%

“…To simplify (3), is defined as the -th bin of the -point updating vector transform (UVT) which can be expressed as [10] (4)…”

Section: B Hdftmentioning

confidence: 99%

“…In practice, the quantization error of the twiddle factor causes the pole to move slightly inside or outside the unit circle, and the instabilities and accumulated errors are inevitably introduced. In the application where the DFT output only needs to be computed every ( ) samples, the Hopping DFT (HDFT) with the time hop is presented to reduce the computational workload [10]. However, since the location of the poles of HDFT is the same as SDFT, HDFT is also not immune to the instabilities and accumulated errors caused by finite precision representation of the twiddle factor in practice.…”

Section: Introductionmentioning

confidence: 99%

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High-Precision, Permanently Stable, Modulated Hopping Discrete Fourier Transform

Wang

Yan

Qin

2015

IEEE Signal Process. Lett.

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A new modulated hopping Discrete Fourier Transform (mHDFT) algorithm which is characterized by its merits of high accuracy and constant stability is presented. The proposed algorithm, which is based on the circular frequency shift property of DFT, directly moves the -th DFT bin to the position of , and computes the DFT by incorporating the successive DFT outputs with arbitrary time hop . Compared to previous works, since the pole of mHDFT precisely settles on the unit circle in the Z-plane, the accumulated errors and potential instabilities, which are caused by the quantization of the twiddle factor, are always eliminated without increasing much computational effort. The numerical simulation results verify the effectiveness and superiority of the proposed algorithm.Index Terms-Hopping discrete Fourier transforms (HDFT), modulated hopping discrete Fourier transforms (mHDFT), sliding discrete Fourier transforms (SDFT).

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“…Let f(x) be the original signal with length L, and assume that the window at time instant p contains N values f(p), f(p+1), …, f(p+N-1), 0 ≤ p, p+N-1 < L, then, the sliding orthogonal transform is defined by [15,16] In the past decades, many works have been reported in the literature for the fast computation of sliding transforms. They can be classified into two categories: 1) the structures of radix-2 and radix-4 fast algorithms such as sliding FFT [17] , Hopping DFT [18], sliding Walsh Hadamard transform [19], sliding Haar transform [20], sliding conjugate symmetric sequency-ordered complex Hadamard transform [21]; 2) the first-and second-order shift properties of sliding transforms including sliding DFT [22,23], sliding DCT [15], sliding DHT [16], sliding discrete fractional Fourier transform [24], sliding Walsh Hadamard transform [25], sliding Haar transform [26], modulated sliding discrete Fourier transform [27], and sliding geometric moment (SGM) [28].…”

mentioning

confidence: 99%

Fast Computation of Sliding Discrete Tchebichef Moments and Its Application in Duplicated Regions Detection

Chen

Coatrieux

et al. 2015

IEEE Trans. Signal Process.

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International audienceComputational load remains a major concern when processing signals by means of sliding transforms. In this paper, we present an efficient algorithm for the fast computation of one-dimensional and two-dimensional sliding discrete Tchebichef moments. To do so, we first establish the relationships that exist between the Tchebichef moments of two neighboring windows taking advantage of Tchebichef polynomials’ properties. We then propose an original way to fast compute the moments of one window by utilizing the moment values of its previous window. We further theoretically establish the complexity of our fast algorithm and illustrate its interest within the framework of digital forensics and more precisely the detection of duplicated regions in an audio signal or an image. Our algorithm is used to extract local features of such a signal tampering. Experimental results show that its complexity is independent of the window size, validating the theory. They also exhibit that our algorithm is suitable to digital forensics and beyond to any applications based on sliding Tchebichef moments

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The Hopping Discrete Fourier Transform [sp Tips&Tricks]

Cited by 48 publications

References 6 publications

Integration of an IEEE Std. C37.118 compliant PMU into a real-time simulator

Integration of an IEEE Std. C37.118 compliant PMU into a real-time simulator

High-Precision, Permanently Stable, Modulated Hopping Discrete Fourier Transform

Fast Computation of Sliding Discrete Tchebichef Moments and Its Application in Duplicated Regions Detection

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