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Conjugate symmetric extension Fourier computer-generated holography with controllable reconstruction focus
A conjugate symmetric extension Fourier computer-generated holography algorithm with controllable reconstruction focus is proposed. The real function...
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Empirical evidence of the extension of the Fourier convolution theorem to Z-space
The Fourier convolution theorem (FCT) is used to filter images in k-space. The literature provides theoretical proof but not experimental evidence of...
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Fourier Transform of Distributions
The Fourier transform is a major tool in the analysis of signals and systems. We will see that its extension to distributions will make the...
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Environmental impact of foreign direct investment in Turkey: does the quality of institutions matter? Evidence from time series analysis using the Fourier extension
Since the 1980s, Turkey has experienced a significant increase in both foreign direct investment (FDI) and its ecological footprint (EFP). While FDI...
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Fourier Methods
The changes in brightness of an astronomical source as a function of time are key probes into that source’s physics. Periodic and quasi-periodic...
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Fourier Methods
The changes in brightness of an astronomical source as a function of time are key probes into that source’s physics. Periodic and quasi-periodic...
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Fourier Series
Chapter 1 covers the classical theory of Fourier series of...
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Fourier Restriction Implies Maximal and Variational Fourier Restriction in Lorentz Space
In this paper, we show that Fourier restriction theorem implies the maximal and variational Fourier restriction in Lorentz space frame. The key...
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Fourier Series
In this chapter, the version of the Fourier analysis that is applicable to continuous and periodic time-domain signals is presented. The discrete...
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Hausdorff–Young Inequalities for Fourier Transforms over Cayley–Dickson Algebras
In this study, we extend Beckner’s seminal work on the Fourier transform to the domain of Cayley–Dickson algebras, establishing a precise form of the...
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Quaternion Fourier Transform
This chapter first focusses on the theoretical foundations of quaternion Fourier transforms. Basically, in the complex Fourier transform the...
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Real Paley-Wiener Theorems for the Space-Time Fourier Transform
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to...
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Discrete Fourier Transforms
This chapter deals with the discrete Fourier transform (DFT). In Sect. 3.1, we show that numerical realizations of Fourier methods, such as the...
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A sparse approximation for fractional Fourier transform
The paper promotes a new sparse approximation for fractional Fourier transform, which is based on adaptive Fourier decomposition in Hardy-Hilbert...
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An Exposition of Digital Taylor-Fourier Transform
Digital Taylor-Fourier Transform (DTFT) is a Taylor series-based extension to Discrete Fourier Transform. It is becoming popular due to its ability...
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Navier-Stokes-Fourier Models
For simple substances, i.e., substances where no change of composition occurs, the transport equations of the previous chapter reduce to the...
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Fourier coefficients of Hilbert modular forms at cusps
The aim of this article is to study the fields generated by the Fourier coefficients of Hilbert newforms at arbitrary cusps. Precisely, given a...
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Discrete-Time Fourier Transform
In this chapter, Discrete-Time Fourier Transform, the version of the Fourier analysis that is more suitable for theoretical analysis of signals and...