Sampling theorem for the short-time linear canonical transform and its applications

Zhang, Zhichao

doi:10.1016/j.sigpro.2015.01.020

Cited by 33 publications

(14 citation statements)

References 22 publications

(40 reference statements)

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“…This shows that the desired signal r de (t) can be derived from Fig. 2 and (31), which is in accordance with that introduced in [25,26], as implied by (32). Therefore, it is easier to implement in the designing of multiplicative filters through the product in the LCT domain than some suggested in [22][23][24], as discussed in [26].…”

Section: Designing Of Multiplicative Filters Through the Product In Tsupporting

confidence: 82%

“…Particularly, the LCT is very useful and effective in non-stationary signal processing since it can be regarded as the decomposition of a signal based on a non-orthogonal basis [18][19][20][21]. Meanwhile, some fundamental theories and concepts associated with the LCT have been established, for example the convolution and product theorems [22][23][24][25][26][27][28], the uniform and nonuniform sampling theorems [29][30][31][32][33][34], and the uncertainty principles [35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

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New convolution structure for the linear canonical transform and its application in filter design

Zhang

2016

Optik

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Section: Designing Of Multiplicative Filters Through the Product In Tsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

New convolution structure for the linear canonical transform and its application in filter design

Zhang

2016

Optik

Self Cite

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“…As shown in (39) and (42), FRFTs on the infinite and finite D-NN signal models are determined by the choice of orthogonal polynomials which may not be obvious and may depend on the application. There are many different types of orthogonal polynomials which have their own special feature and application.…”

Section: Frfts On the Infinite And Finite D-nn Signal Modelsmentioning

confidence: 99%

Algebraic representation for fractional Fourier transform on one‐dimensional discrete signal models

Zhang

2018

IET signal process.

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Algebraic signal processing provides a general framework for studying theoretical problems (sampling, transform domain analysis etc.) in the classical signal processing. In this study, the authors extend algebraic representation for the conventional Fourier transform (FT) to the fractional FT (FRFT) domain, from which the algebraic structures for the FRFT on infinite and finite one-dimensional signal models are obtained. They show that FRFTs on the infinite and finite discrete-time (DT) signal models, respectively, are none other than the DTFRFT and the closed-form discrete FRFT. They also derive FRFTs on the infinite and finite discrete-nearest neighbour signal models, and finally they discuss their applications in optical and timefrequency signal processing.

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“…Our object is to obtain an appropriate equivalent form of orthogonal condition of the STLCS which can be used in dual window calculation. In [22], Zhang proposed a biorthogonal condition for the STLCS, which can be viewed as a theoretical foundation for frame theorem approach and orthogonal analysis method in seeking dual window. However, the process is too complex such as frame boundary estimation and matrix calculation.…”

Section: Orthogonal Condition Of the Stlcsmentioning

confidence: 99%

“…In [21], Kou et al proved the Paley-Wiener theorems for the STLCT in mathematical applications. In [22], Zhang addressed a sampling theorem for the STLCT by means of a generalized Zak transform associated with the LCT. In [23], Guanlei discussed the uncertainty relation in two STLCT domains.…”

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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Sampling theorem for the short-time linear canonical transform and its applications

Cited by 33 publications

References 22 publications

New convolution structure for the linear canonical transform and its application in filter design

New convolution structure for the linear canonical transform and its application in filter design

Algebraic representation for fractional Fourier transform on one‐dimensional discrete signal models

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

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