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

Zhang, Zhichao

doi:10.1016/j.ijleo.2016.03.025

Cited by 19 publications

(6 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We study time-frequency performance of the STLCT in this paper. In fact, the LCT has been introduced to classic timefrequency analysis tool, such as Wigner distribution (WD) and STFT [28][29][30]. For instance, in [29], Zhang and Luo considered the time-frequency tool and its application using the Gaussian windowed STFT and LCT.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-Frequency Properties of the Short-Time Linear Canonical Transform and Its Application

Huang

Sun

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The short-time linear canonical transform (STLCT) is a novel time-frequency analysis tool, which has attracted some attention recently. However, its applications in signal processing are limited because the time-frequency properties of the STLCT are still little known. Most existing studies focus on mathematical properties rather than time-frequency properties in signal processing. To handle this problem, first, we investigate some basic time-frequency properties such as 2-D resolution of the time-frequency plane, the STLCT domain support, computation of the STLCT, etc by generalizing the short-time Fourier transform to the STLCT. Then, based on these derived properties, we find that the Gaussian window is optimal window of the STLCT. Signal separation verified the results.

show abstract

Section: Introductionmentioning

confidence: 99%

“…In fact, the LCT has been introduced to classic timefrequency analysis tool, such as Wigner distribution (WD) and STFT [28][29][30]. For instance, in [29], Zhang and Luo considered the time-frequency tool and its application using the Gaussian windowed STFT and LCT. e performance of frequency location depends on sliding window of the STFT.…”

Section: Introductionmentioning

confidence: 99%

Time-Frequency Properties of the Short-Time Linear Canonical Transform and Its Application

Huang

Sun

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…4 Mathematical Problems in Engineering Equation (14) presents the orthogonal relationship between original window and dual one. Let = 0, according to properties of the Dirac function, we obtain 0 ∑ℎ * ( − ) ( − ) = 1.…”

Section: Theorem 1 the Basis Of The Stlcs Is Of Orthogonality If Andmentioning

confidence: 99%

“…Suppose {ℎ , , } constitutes a basis. According to (14), ( ) exists in {ℎ , , }; that is to say ( ) can be represented in terms of {ℎ , , }:…”

Section: Which Denotes the Relationship Between Original Window Functmentioning

confidence: 99%

“…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%

See 1 more Smart Citation

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

Huang

Zhang

Chai

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

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.

show abstract

A convolution-based fractional transform

Dou

et al. 2016

Opt Quant Electron

View full text Add to dashboard Cite

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

Cited by 19 publications

References 36 publications

Time-Frequency Properties of the Short-Time Linear Canonical Transform and Its Application

Time-Frequency Properties of the Short-Time Linear Canonical Transform and Its Application

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

A convolution-based fractional transform

Contact Info

Product

Resources

About