Theory and applications of short-time linear canonical transform

2021 ◽  
pp. 103239
Author(s):  
Deyun Wei ◽  
Huimin Hu
Keyword(s):  
Linear Canonical Transform ◽  
Short Time ◽  
Time Linear

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

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lei Huang ◽  
Ke Zhang ◽  
Yi Chai ◽  
Shuiqing Xu
Keyword(s):  
Linear Canonical Transform ◽  
Elementary Functions ◽  
Orthogonal Condition ◽  
Time Domain Signal ◽  
The Time Domain ◽  
Short Time ◽  
Linear Canonical Series ◽  
Dual Window ◽  
Time Linear ◽  
Selection Of

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.

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

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Lei Huang ◽  
Qingying Sun ◽  
Qian Xi ◽  
Yuhu Liu ◽  
Mengsheng An ◽  
...  
Keyword(s):  
Linear Canonical Transform ◽  
Time Frequency ◽  
Short Time ◽  
Frequency Properties ◽  
Time Linear

Short-Time Linear Quadratic Form Technique for Estimating Fast-Varying Parameters in Feedback Loops

2015 ◽  
Vol 17 (6) ◽  
pp. 2289-2302 ◽  
Author(s):  
Mohammad Reza Homaeinezhad ◽  
Iman Tahbaz-zadeh Moghaddam ◽  
Zahra Khakpour ◽  
Hosein Naseri
Keyword(s):  
Quadratic Form ◽  
Feedback Loops ◽  
Linear Quadratic ◽  
Varying Parameters ◽  
Short Time ◽  
Time Linear

scholarly journals The Wigner-Ville Distribution Based on the Linear Canonical Transform and Its Applications for QFM Signal Parameters Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yu-E Song ◽  
Xiao-Yan Zhang ◽  
Chun-Heng Shang ◽  
Hong-Xia Bu ◽  
Xiao-Yan Wang
Keyword(s):  
Signal To Noise Ratio ◽  
Parameters Estimation ◽  
Accurate Estimation ◽  
Linear Canonical Transform ◽  
Estimation Of Parameters ◽  
Position Information ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Definition Of ◽  
Short Time

The Wigner-Ville distribution (WVD) based on the linear canonical transform (LCT) (WDL) not only has the advantages of the LCT but also has the good properties of WVD. In this paper, some new and important properties of the WDL are derived, and the relationships between WDL and some other time-frequency distributions are discussed, such as the ambiguity function based on LCT (LCTAF), the short-time Fourier transform (STFT), and the wavelet transform (WT). The WDLs of some signals are also deduced. A novel definition of the WVD based on the LCT and generalized instantaneous autocorrelation function (GWDL) is proposed and its applications in the estimation of parameters for QFM signals are also discussed. The GWDL of the QFM signal generates an impulse and the third-order phase coefficient of QFM signal can be estimated in accordance with the position information of such impulse. The proposed algorithm is fast because it only requires 1-dimensional maximization. Also the new algorithm only has fourth-order nonlinearity thus it has accurate estimation and low signal-to-noise ratio (SNR) threshold. The simulation results are provided to support the theoretical results.

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