Uncertainty principles for the short-time linear canonical transform of complex signals

Gao, Wen‐Biao; Li, Bing‐Zhao

doi:10.1016/j.dsp.2020.102953

Cited by 26 publications

(15 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So, in [23], Kit proposed the short-time linear canonical transform (STLCT) to handle this problem. Actually, a STLCT was mentioned in uncertainty principles study even earlier [17]. e definition of the STLCT is…”

Section: Short-time Linear Canonical Transformmentioning

confidence: 99%

“…e LCT is more flexible because it has a total of four free parameters and one constraint. Many theoretical issues of the FT and FRFT have been extended to the LCT, which has found many research results in signal processing [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. But the LCT fails in locating frequency-domain contents due to its global kernel function.…”

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: Short-time Linear Canonical Transformmentioning

confidence: 99%

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

“…e LCT's generality enables it to be capable of solving many mathematical, physical, and engineering problems that other conventional transformations fail to solve. For a signal f(t), its LCT associated with the parameter matrix A � (a, b; c, d) is given by [29][30][31][32][33][34][35]…”

Section: Lctmentioning

confidence: 99%

A Computationally Efficient Optimal Wigner Distribution in LCT Domains for Detecting Noisy LFM Signals

Shi

Sun

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Recently, Wigner distribution (WD) associated with linear canonical transforms (LCTs) is quickly becoming a promising technique for detecting linear frequency-modulated (LFM) signals corrupted with noises by establishing output signal-to-noise ratio (SNR) inequality model or optimization model. Particularly, the closed-form instantaneous cross-correlation function type of WD (CICFWD), a unified linear canonical Wigner distribution, has shown to be competitive in detecting noisy LFM signals under an extremely low SNR. However, the CICFWD has up to nine LCT free parameters so that it requires a heavy computational load. To improve the efficiency of real-time processing, this paper focuses on the instantaneous cross-correlation function type of WD (ICFWD), which has only six LCT free parameters but is not a special case of the CICFWD. The main advantage of ICFWD is that it could be expected to reduce the computational complexity while maintaining detection performance. This paper first proposes an optimization model to the ICFWD’s output SNR with respect to deterministic signals embedded in additive zero-mean noises. It then deduces the model’s solution to a single component LFM signal added with white noise, leading to the optimal selection strategy on LCT free parameters. Simulation results demonstrate that the ICFWD improves almost a doubling of computing speed in comparison with the CICFWD while sharing the same level of detection performance. To be specific, the computing time of ICFWD in sampling frequencies 5 Hz, 10 Hz, 15 Hz, and 20 Hz is about 0.048 s, 0.111 s, 0.226 s, and 0.392 s, respectively, while 0.075 s, 0.233 s, 0.478 s, and 0.821 s for the computing time of CICFWD; the ICFWD and CICFWD have nearly the same output SNR higher than that of the WD.

show abstract

“…Some important properties of the STLCT have been discussed such as the analogue of the Poisson summation formula, sampling formulas, Paley-Wiener theorem, and uncertainly principles. [9][10][11][12][13] It presents the time and LCT-frequency information, and is originally a local LCT distribution.…”

Section: Introductionmentioning

confidence: 99%

“…The short‐time linear canonical transform (STLCT) is a method devised to study signals whose spectral content changes in time. Some important properties of the STLCT have been discussed such as the analogue of the Poisson summation formula, sampling formulas, Paley–Wiener theorem, and uncertainly principles 9–13 . It presents the time and LCT‐frequency information, and is originally a local LCT distribution.…”

Section: Introductionmentioning

confidence: 99%

Octonion short‐time linear canonical transform

Gao

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.

show abstract

Uncertainty principles for the short-time linear canonical transform of complex signals

Cited by 26 publications

References 37 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

A Computationally Efficient Optimal Wigner Distribution in LCT Domains for Detecting Noisy LFM Signals

Octonion short‐time linear canonical transform

Contact Info

Product

Resources

About