Multiplicative filtering in the linear canonical transform domain

Goel, Naveen Krishan; Singh, Kulbir; Saxena, Rajiv; Singh, Ashutosh Kumar

doi:10.1049/iet-spr.2015.0035

Cited by 17 publications

(6 citation statements)

References 56 publications

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“…The Linear Canonical Transform (LCT) is considered to play an important role in different fields such as optics and signal processing [33]. LCT is a framework inclusive of the Fourier transform, Fractional Fourier transform, Laplace, Gauss‐Weierstrass, Bargmann, and Fresnel transforms, and its extension covering FCT [33–37]. A general framework of the Fourier convolution theorem was reported [27].…”

Section: Discussionmentioning

confidence: 99%

“…Fresnel transforms, and its extension covering FCT [33][34][35][36][37]. A F I G U R E 12 High-pass filters (HPFs).…”

Section: Ft Frameworkmentioning

confidence: 99%

“…Recent research in this field presents several versions of the convolution theorem for LCT and describes the advantages of its implementation in filter design [33][34][35][36][37]. While the Laplace Transform is the generalization of the Fourier Transform for continuous-time systems, the Z transform (ZT) does that for discrete-time systems.…”

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: Discussionmentioning

confidence: 99%

“…Fresnel transforms, and its extension covering FCT [33][34][35][36][37]. A F I G U R E 12 High-pass filters (HPFs).…”

Section: Ft Frameworkmentioning

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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“…In the recent 10 years, [16][17][18][19][20][21] the basic theories of LCT, such as uncertainty principle, the relationship between LCT and ambiguity function and Winger Ville distribution, have been gradually studied. Combined with these basic theories, LCT has been widely used in scientific research and engineering technology, for example, instantaneous frequency estimation, 22 signal detection and estimation, 23 linear regular domain filter design, 24,25 radar system, 26 image processing, 27 speech signal analysis, 28 and optics. [29][30][31] Now, LCT has become the focus of interdisciplinary research.…”

Section: Introductionmentioning

confidence: 99%

Stability estimates for phase retrieval from discrete linear canonical Gabor transformation measurements

Liu

et al. 2022

Math Methods in App Sciences

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Phase retrieval gives the problem of recovering some signal from phaseless measurements. This paper mainly studies the stability estimation of phase recovery from the measurement of discrete linear canonical Gabor transformation (DLCGT). We first show that we can recover the signal x on the connected components of G in global phase sense. Then, we give the stability estimates results from the DLCGT measurements and the autocorrelation relation.

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“…Well‐known signal processing operations, such as the Fourier transform (FT), the fractional FT (FRFT) [9–11], the Fresnel transform and the scaling operations are special cases of the AFT [4, 12]. Due to the extra degrees of freedom, AFT is more flexible and has been shown to be a powerful tool for filter design, time–frequency analysis, phase retrievals, multiplexing in communication, and many other applications [3–5, 13–21].…”

Section: Introductionmentioning

confidence: 99%

Time–frequency analysis method based on affine Fourier transform and Gabor transform

Wei

Wang

2017

IET signal process.

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The affine Fourier transform (AFT) plays an important role in many fields of optics and signal processing. The Gabor transform (GT) is a kind of linear time–frequency representation (TFR). Compared with many bilinear TFRs, the GT does not have the cross‐term problem. In this study, the authors propose a time–frequency analysis method based on the AFT and GT. First, they obtain an affine relation between the AFT and the modified GT (MGT). Since the MGT is closely related to the AFT, they can use it as an assistant tool for signal processing in the AFT domain. Moreover, many useful relations between the AFT and the MGT are derived, such as recovery relation, projection relation and power integration relation. Then, they demonstrate that the AFT also has the affine relation with other TFRs, such as the Gabor–Wigner transform and the general class of quadratic distribution. Last, using the new time–frequency analysis method associated with the AFT and MGT, they present the filter design for multiple component chirp signal separation. Moreover, the simulation results illustrate the effectiveness of the proposed method.

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Multiplicative filtering in the linear canonical transform domain

Cited by 17 publications

References 56 publications

Sampling technique for Fourier convolution theorem based k‐space filtering

Sampling technique for Fourier convolution theorem based k‐space filtering

Stability estimates for phase retrieval from discrete linear canonical Gabor transformation measurements

Time–frequency analysis method based on affine Fourier transform and Gabor transform

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