Inequalities for derivatives with the Fourier transform

Osipenko, K. Yu.

doi:10.1016/j.acha.2021.02.001

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…It is observed that the (𝑓 𝐿 ) components contain the most information in the data while the (𝑓 𝐻 ) components contain the noisy part, which is to be removed. An important aspect of the filtration process is the choice of the kernel of the transform (Osipenko, 2021 [33]). The Fourier Transform and its derivatives such as the Laplace Transform (LT), the Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), Z-Transform, Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST), rely on the complex exponential Kernel function, given by (Falsone at l., 2021, [34]):…”

Section: 𝑇 = Transformmentioning

confidence: 99%

A Stochastic Regression and Sentiment Analysis-Based Approach for Forecasting Trends in the Stock Market

L. K. Vishwamitra

2024

jes

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Stochastic regression problems especially applied to time series forecasting problems often encounter the challenge of volatility and unpredictable seasonality in datasets. One such application happens to forecasting the movement of stock markets globally. Stock data across the world exhibits an intrinsic baseline noise, which often can’t be correlated to previous temporal patterns. Rather, such divergences are an effect of multiple non-numeric variables which govern stock movement such as political scenarios, trade wars, imminent economic waxing and waning trends to name a few. However, it is essential to incorporate these factors while training a model so as to design a strongly sentient and anticipatory regression algorithm which is both pervasive and robust, encompassing as many numeric and non-numeric factors as possible. While conventional machine learning and deep learning approaches tend to leverage tested model architectures, they often miss out on the optimization of both training data and training method to yield potentially high forecasting accuracy. The paper combines stochastic regression in terms of momentum based training and data optimization which is shown to exhibit considerable lower forecasting error compared to existing approaches. To encompass a wider feature space, sentiment analysis has been incorporated to correlate stock movements with public opinions. The proposed approach has been tested on a multitude of benchmark datasets, to validate the performance of the approach. The mean absolute percentage error (MAPE) and regression values have been selected as primary metrics for the performance evaluation. The proposed approach attains a mean MAPE value of 3.22%. The analysis of the MAPE and forecasting accuracy w.r.t. existing benchmark approaches proves the improved forecasting performance of the proposed approach over a period of 300 days.

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Section: 𝑇 = Transformmentioning

confidence: 99%

A Stochastic Regression and Sentiment Analysis-Based Approach for Forecasting Trends in the Stock Market

L. K. Vishwamitra

2024

jes

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“…It should be noted that by including high-frequency elements, the edge of the original image is improved. An image's high-frequency factor is extracted by looking for the edge of segmentation [8].…”

Section: Applications Of Fourier Transformmentioning

confidence: 99%

A survey of convolution

Zou

2023

Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022)

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Convolution is a mathematical method of integral transformation and an important operation in analytical mathematics. The concept of convolution can also be extended to sequence, measure and generalized functions. Convolution has many applications in mathematics and engineering. For example, it can be widely used as a linear operation in image filtering, digital signal processing, electronic engineering and other application scenarios such as fluid mechanics, statistics, physics, astronomy, thermodynamics, optics. It plays a very key role in such important disciplines as it is a very common tool to help people solve problems. This paper gives a more detailed description of continuous convolution, discrete convolution and two-dimensional convolution through formula method and definition method, and points out their common application fields, and then discusses discrete convolution and continuous convolution through common scenes in life which is the simple explanation. The deep application of convolution in the signal field and Fourier transform field is sorted out. Finally, combining with the background of the era of big data, the multi-faceted applications of the future convolutional network neural field are discussed.

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“…Inequalities for the Fourier transform (FT) are widely used in mathematics, physics and engineering [1][2][3][4][5][6]. The classical N-dimensional Heisenberg's inequality of the FT is given by the following formula [7]:…”

Section: Introductionmentioning

confidence: 99%

Inequalities for the Windowed Linear Canonical Transform of Complex Functions

Gao

2023

Axioms

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In this paper, we generalize the N-dimensional Heisenberg’s inequalities for the windowed linear canonical transform (WLCT) of a complex function. Firstly, the definition for N-dimensional WLCT of a complex function is given. In addition, the N-dimensional Heisenberg’s inequality for the linear canonical transform (LCT) is derived. It shows that the lower bound is related to the covariance and can be achieved by a complex chirp function with a Gaussian function. Finally, the N-dimensional Heisenberg’s inequality for the WLCT is exploited. In special cases, its corollary can be obtained.

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Inequalities for derivatives with the Fourier transform

Cited by 5 publications

References 11 publications

A Stochastic Regression and Sentiment Analysis-Based Approach for Forecasting Trends in the Stock Market

A Stochastic Regression and Sentiment Analysis-Based Approach for Forecasting Trends in the Stock Market

A survey of convolution

Inequalities for the Windowed Linear Canonical Transform of Complex Functions

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