Two-Dimensional Z-space Filtering Using Pulse-Transfer Function

Ciulla, Carlo

doi:10.1007/s00034-022-02113-4

Cited by 6 publications

(5 citation statements)

References 29 publications

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“…The computer program names are detailed in Table I [14]. The comparison of the four filters proposed by this research is made versus: (A) Three Z‐space filters [10] by the name of Bessel2018, Butterworth2018, and Chebyshev2018, respectively; (B) Classic low‐pass filter, classic high‐pass filter, classic image‐space Gaussian filter (Gaussian 2 × 2), and intensity‐curvature functional [15]; (C) Three additional Z‐space filters by the name of ZSpaceBesselFilter2021, ZSpaceButterworthFilter2021, and ZSpaceChebyshevFilter2021, respectively. These last three Z‐space filters also make use of the central k‐space region determined by the Sinc‐shaped convolving function.…”

Section: Resultsmentioning

confidence: 99%

“…Normally, the sampling procedure should calculate pulse‐transfer functions defined in the Argand plane (the complex plane) for Bessel, Butterworth, and Chebyshev transfer functions. The pulse‐transfer functions are featured by the complex variable “z” [10]. This is because the replacement of the variable “s” (Laplace) with the variable “z” is common practice in the literature [11].…”

Section: Methodsmentioning

confidence: 99%

“…However, the pulse‐transfer function is defined in Z‐space and would be then direct Z‐transformed. The Z‐space of the pulse‐transfer function would then be used to filter the departing image by means of the extension of the Fourier convolution theorem to the Z‐space [10].…”

Section: Methodsmentioning

confidence: 99%

“…This was archived by Z-space filtering using the pulse-transfer function. The pulse-transfer function was used to filter the Z-space of MRI images and to obtain low-pass and high-pass filtered MRI [10].…”

Section: Ft Frameworkmentioning

confidence: 99%

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Sampling technique for Fourier convolution theorem based k‐space filtering

et al. 2023

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This research presents a sampling technique for Fourier convolution theorem (FCT) based k-space filtering. One polynomial function and three transfer functions were selected: (1) Gaussian, (2) Bessel, (3) Butterworth, and (4) Chebyshev. The functions were sampled on the image grid, and they are called filtering functions. Each filtering function was multiplied by the Sinc function to obtain the "Sinc-shaped convolving function." The k-space of the Sinc-shaped convolving function is calculated by direct Fourier transform (FT) and it is featured by a central region. This central region of the k-space is rectangular in its shape because it is consequential to the direct FT of the product between the filtering function and the Sinc function. Low-pass and highpass filtering is obtained by inverse FT of the pointwise multiplication between the k-space of the departing image and the k-space of the Sinc-shaped convolving function. A variety of cut-off frequencies, bandwidth, sampling rates, and numbers of poles of the filters were verified as effective to filter the images. Filtering strength can be modified by fine-tuning the size of the central rectangular k-space region of the Sinc-shaped convolving functions. K-space analysis of departing images and filtered images provide additional evidence of effective filtering. Moreover, k-space filtering was compared to Z-space filtering using the extension of the FCT to Zspace. The novelty of this research is the sampling technique used to determine the Sinc-shaped convolving function. The sampling technique uses fine-tuning of bandwidth and sampling rate to determine the strength of the k-space filter.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Ft Frameworkmentioning

confidence: 99%

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Sampling technique for Fourier convolution theorem based k‐space filtering

et al. 2023

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“…Due to the presence of analog electrical elements such as capacitors and inductors, power electronics systems share some common properties with continuous-time systems. However, due to the inherent switching nature of power electronics' topologies, one can also find that power electronics systems also share some properties with discrete-time systems [22]. As such, refs.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Transient Reactive Elements for DC-DC Converter Circuits

et al. 2022

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This paper develops an analytical method for modeling the inductor currents and capacitor voltages (ICCV) of a generic DC-DC converter system. The purpose of the designed methodology is to propose a new generalized modeling technique for DC-DC converter systems that accurately models the transient behavior of those systems. The modeled converter is assumed to operate over some number of circuit stages. Each circuit stage can be separately modeled as a linear time-invariant (LTI) system that is solved through the uni-lateral Laplace transform. Furthermore, the initial conditions (ICs) of these LTI systems are related through different algebraic expressions and discrete-time difference equations that originate from the continuity of the ICCV with respect to time. These discrete-time difference equations are then solved with the uni-lateral Z-transform to determine the ICs of the ICCV at each switching period. The generalized theoretical analysis is applied to the study of the transient behavior of the buck-boost converter across various different circuit parameters. This analysis justified with laboratory experimentation of the buck-boost converter, and the transient behavior of the buck-boost converter is compared for each experimental parameter set. The experimental results and the theoretical analysis provide very similar results across the different converter parameters.

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Two‐dimensional adaptive Whittaker–Shannon Sinc‐based zooming

Ciulla,

Shabani,

Yahaya

2024

Applied Research

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In this work, we introduce a novel image zooming methodology that transitions from a nonadaptive Sin‐based approach to an adaptive Sinc‐based zooming technique. The two techniques base their theoretical foundation on the Whittaker–Shannon interpolation formula and the Nyquist theorem. The evolution into adaptive Sinc‐based zoom is accomplished through the use of two novel concepts: (1) the pixel‐local scaled k‐space and (2) the k‐space filtering sigmoidal function. The pixel‐local scaled k‐space is the standardized and scaled k‐space magnitude of the image to zoom. The k‐space filtering sigmoidal function scales the pixel‐local scaled k‐space values into the numerical interval [0, 1]. Using these two novel concepts, the Whittaker–Shannon interpolation formula is elaborated and used to zoom images. Zooming is determined by the shape of the Sinc functions in the Whittaker–Shannon interpolation formula, which, in turn, depends on the combined effect of the pixel‐local scaled k‐space, the sampling rate, and the k‐space filtering sigmoidal function. The primary outcome of this research demonstrates that the Whittaker–Shannon interpolation formula can achieve successful zooms for values of the sampling rate significantly greater than the bandwidth. Conversely, when the sampling rate is much greater than the bandwidth, the nonadaptive technique fails to perform the zoom correctly. The conclusion is that the k‐space filtering sigmoidal function is identified as the crucial parameter in the adaptive Sinc‐based zoom technique. The implications of this research extend to Sinc‐based image zooming applications.

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Two-Dimensional Z-space Filtering Using Pulse-Transfer Function

Cited by 6 publications

References 29 publications

Sampling technique for Fourier convolution theorem based k‐space filtering

Sampling technique for Fourier convolution theorem based k‐space filtering

Analytical Solution for Transient Reactive Elements for DC-DC Converter Circuits

Two‐dimensional adaptive Whittaker–Shannon Sinc‐based zooming

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