Gibbs phenomenon for fractional Fourier series

Zhu, Hongqing; Ding, Meiyu; Li, Y.

doi:10.1049/iet-spr.2010.0348

Cited by 17 publications

(6 citation statements)

References 34 publications

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“…Windowing is essentially a numerical operation on the segment obtained through framing, which means that the signal is smoothed to reduce the error caused by framing, making the overall situation more continuous and avoiding the Gibbs effect [32,33]. The commonly used window functions include the Rectangular window and the Hamming window.…”

Section: Windowingmentioning

confidence: 99%

The Sustainable Development of Intangible Cultural Heritage with AI: Cantonese Opera Singing Genre Classification Based on CoGCNet Model in China

Chen

Zhao

Wang³

et al. 2022

Sustainability

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Chinese Cantonese opera, a UNESCO Intangible Cultural Heritage (ICH) of Humanity, has faced a series of development problems due to diversified entertainment and emerging cultures. While, the management on Cantonese opera data in a scientific manner is conducive to the sustainable development of ICH. Therefore, in this study, a scientific and standardized audio database dedicated to Cantonese opera is established, and a classification method for Cantonese opera singing genres based on the Cantonese opera Genre Classification Networks (CoGCNet) model is proposed given the similarity of the rhythm characteristics of different Cantonese opera singing genres. The original signal of Cantonese opera singing is pre-processed to obtain the Mel-Frequency Cepstrum as the input of the model. The cascade fusion CNN combines each segment’s shallow and deep features; the double-layer LSTM and CNN hybrid network enhance the contextual relevance between signals. This achieves intelligent classification management of Cantonese opera data, meanwhile effectively solving the problem that existing methods are difficult to classify accurately. Experimental results on the customized Cantonese opera dataset show that the method has high classification accuracy with 95.69% Precision, 95.58% Recall and 95.60% F1 value, and the overall performance is better than that of the commonly used neural network models. In addition, this method also provides a new feasible idea for the sustainable development of the study on the singing characteristics of the Cantonese opera genres.

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Section: Windowingmentioning

confidence: 99%

The Sustainable Development of Intangible Cultural Heritage with AI: Cantonese Opera Singing Genre Classification Based on CoGCNet Model in China

Chen

Zhao

Wang³

et al. 2022

Sustainability

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“…method in [15,16], the tolerance error index [40] is used to indicate the end of the iteration process. This index is the ratio of the matrix-norm of a mi (m th harmonic magnitude of X i ) to that of a 00 .…”

Section: Plos Onementioning

confidence: 99%

“…In order to show that the proposed method can obtain more accurate state variables, of the positive Luo converters, compared to the simplified equivalent small parameter (SESP) method in [ 15 , 16 ], the tolerance error index [ 40 ] is used to indicate the end of the iteration process. This index is the ratio of the matrix-norm of a mi ( m th harmonic magnitude of X i ) to that of a 00 .…”

Section: Comparison and Simulation Of The Conventional Schemes And Thmentioning

confidence: 99%

A modified modeling and dynamical behavior analysis method for fractional-order positive Luo converter

Jia

Liu

2020

PLoS ONE

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Compared to the integer-order modeling, the fractional-order modeling can achieve higher accuracy for designing and analyzing the DC-DC power converters. However, its applications in pulse width modulation (PWM) converters are limited due to the computational complexities. In this paper, a modified fractional-order modeling methodology for DC-DC converters is proposed, and its effectiveness is verified on the fractional-order positive Luo converters. Instead of using fractional-order calculus, the proposed methodology analyzes the harmonic components of the PWM converters by utilizing the non-linear vector differential equations of the periodically time-variant system. The final solution of the state variables is composed of two parts: the steady-state solution and the transient solution. The approximate steady state solution can be obtained by using the equivalent small parameter (ESP) method and the harmonic balance theory, while the main part of the transient solution can be obtained according to the explicit Grü nwald-Letnikov (GL) approximation. In addition, the influence of the fractional orders on the performance of the DC-DC converters, and on the dynamic behaviors of the fractional-orders systems are also discussed in this paper. Compared to the conventional fractional-order numerical models, the proposed model is able to present the time-domain information more precisely, which helps to better reveal and analyze the non-linear behaviors of the DC-DC converters. The effectiveness of the work is demonstrated by the simulation and experimental results of the equivalent circuits built with fractional-order components.

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“…where y k (x) is the interpolation function in (14). In this section, in order to obtain the MMS expansion, we also need to derive the basic exponential representation for e ju'x/b (u ∈ R(Ω)) which involves the analysis filter functions (transfer functions) H k (u) and the synthesis filter functions Y k (u, x).…”

Section: Multidimensional Multichannel Sampling Expansion In the Lct mentioning

confidence: 99%

“…These systems belong to the class of quadratic-phase systems, which are also known as ABCD systems or lossless first-order optical systems [4]. The LCT has found many applications in optics, optimal filtering, signal separation, phase retrieval, time-frequency analysis, radar system analysis and many others [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain

Wei

2014

IET signal process.

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The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. In this study, the authors address the problem of signal reconstruction from the multidimensional multichannel samples in the LCT domain. Firstly, they pose and solve the problem of expressing the kernel of the multidimensional LCT in the elementary functions. Then, they propose the multidimensional multichannel sampling (MMS) for the bandlimited signal in the LCT domain based on a basis expansion of an exponential function. The MMS expansion which is constructed by the ordinary convolution structure can reduce the effect of the spectral leakage and is easy to implement. Thirdly, based on the MMS expansion, they obtain the reconstruction method for the multidimensional derivative sampling and the periodic non-uniform sampling by designing the system filter transfer functions. Finally, the simulation results and the potential applications of the MMS are presented. Especially, the application of the multidimensional derivative sampling in the context of the image scaling about the image super-resolution is discussed.

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Gibbs phenomenon for fractional Fourier series

Cited by 17 publications

References 34 publications

The Sustainable Development of Intangible Cultural Heritage with AI: Cantonese Opera Singing Genre Classification Based on CoGCNet Model in China

The Sustainable Development of Intangible Cultural Heritage with AI: Cantonese Opera Singing Genre Classification Based on CoGCNet Model in China

A modified modeling and dynamical behavior analysis method for fractional-order positive Luo converter

Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain

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