Generalized convolution and product theorems associated with linear canonical transform

Shi, Jun; Li, Xiaoping; Zhang, Naitong

doi:10.1007/s11760-012-0348-7

Cited by 61 publications

(37 citation statements)

References 15 publications

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“…0 ( )is the LCT of ( ) [13][14][15][16][17][18], satisfying 0 0 − 0 0 . From the LCT domain the canonical convolution with matrix parameter is defined as [2,20] …”

Section: 1linear Canonical Wavelet Transformmentioning

confidence: 99%

Reversible image watermarking technique using LCWT and DGT

Fernandes.J¹,

Sivakannan²,

Prabakaran³

et al. 2017

IJET

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In this contemporary world procuring our confidential data against some unknown person is very significant. Thus to have a high reliability of data security watermarking technique is applied before transmitting the data. This proposed work LCWT and DGT decomposition gives an effective technique to protect hypertensive related information based on reversible watermarking. LCWT has the superiority of multiresolution fundamental analysis of wavelet transform and reflects representation of image domain in LCT. And using DGT decomposition the patient information has to embed inside high frequency subband wavelet and the watermarked information will be extracted by the receiver without any loss, to reconstruct the original image information. The reliability of the proposed method is analyzed by comparing the experimental results of similarity index, normalization and peak signal to noise ratio.

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“…0 ( )is the LCT of ( ) [13][14][15][16][17][18], satisfying 0 0 − 0 0 . From the LCT domain the canonical convolution with matrix parameter is defined as [2,20] …”

Section: 1linear Canonical Wavelet Transformmentioning

confidence: 99%

Reversible image watermarking technique using LCWT and DGT

Fernandes.J¹,

Sivakannan²,

Prabakaran³

et al. 2017

IJET

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show abstract

“…Moreover, convolution and correlation are widely used in signal processing, as well as in optics, in pattern recognition or in the description of image formation with incoherent illumination [16,[24][25][26][27][28][29][30]. The convolution operation in FT domain is defined as…”

Section: The Convolution Theorymentioning

confidence: 99%

“…In addition, convolution theorems for the specific SAFT case FRFT can also be obtained from the above-derived theorems [25][26][27][28]. …”

Section: Corollarymentioning

confidence: 99%

“…Simultaneously, as the generalization of FT, the relevant theory of SAFT has been developed including the convolution theorem, uncertainty principle, sampling theory and so on [16][17][18], which are generalizations of the corresponding properties of the FT, FRFT and LCT [3,9,[19][20][21][22][23][24][25][26][27][28]. Conventional convolution operations for FT are fundamental in the theory of linear timeinvariant (LTI) system [9].…”

Section: Introductionmentioning

confidence: 99%

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A generalized convolution theorem for the special affine Fourier transform and its application to filtering

Zhi

Wei

Zhang

2016

Optik

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“…When we select Gaussian window, the STFT becomes the Gabor transform (GT). In recent years, with the development of nonstationary signal processing technology, the linear canonical transform (LCT) was developed by many scholars [2][3][4][5][6][7][8][9]. It is a generalized form of the FT and the Fractional Fourier transform (FRFT) and has been considered to be a powerful analyzing tool in signal processing and optics [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Computation of the Short‐Time Linear Canonical Transform with Dual Window

Huang

Zhang

Chai

et al. 2017

Mathematical Problems in Engineering

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The short-time linear canonical transform (STLCT), which maps the time domain signal into the joint time and frequency domain, has recently attracted some attention in the area of signal processing. However, its applications are still limited due to the fact that selection of coefficients of the short-time linear canonical series (STLCS) is not unique, because time and frequency elementary functions (together known as basis function) of STLCS do not constitute an orthogonal basis. To solve this problem, this paper investigates a dual window solution. First, the nonorthogonal problem that suffered from original window is fulfilled by orthogonal condition with dual window. Then based on the obtained condition, a dual window computation approach of the GT is extended to the STLCS. In addition, simulations verify the validity of the proposed condition and solutions. Furthermore, some possible applied directions are discussed.

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Generalized convolution and product theorems associated with linear canonical transform

Cited by 61 publications

References 15 publications

Reversible image watermarking technique using LCWT and DGT

Reversible image watermarking technique using LCWT and DGT

A generalized convolution theorem for the special affine Fourier transform and its application to filtering

Computation of the Short‐Time Linear Canonical Transform with Dual Window

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