scholarly journals Spectral Analysis of Sampled Signals in the Linear Canonical Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Spectral Analysis ◽  
Spectral Representation ◽  
Digital Signal ◽  
Sampling Theorem ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Research Papers ◽  
One Dimensional ◽  
Uniform Sampling

The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the linear canonical transform domain have been published. In this paper, we investigate the spectrum of sampled signals in the linear canonical transform domain. Firstly, based on the properties of the spectrum of uniformly sampled signals, the uniform sampling theorem of two dimensional signals has been derived. Secondly, the general spectral representation of periodic nonuniformly sampled one and two dimensional signals has been obtained. Thirdly, detailed analysis of periodic nonuniformly sampled chirp signals in the linear canonical transform domain has been performed.

Sampling of bandlimited signals in the offset linear canonical transform domain based on reproducing kernel Hilbert space

2019 ◽  
Vol 18 (02) ◽  
pp. 1950054 ◽  
Author(s):  
Shuiqing Xu ◽  
Zhiwei Chen ◽  
Yi Chai ◽  
Yigang He ◽  
Xiang Li
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Sampling Theorem ◽  
Orthogonal Basis ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Uniform Sampling ◽  
Bandlimited Signals ◽  
Offset Linear Canonical Transform

The offset linear canonical transform (OLCT) has proven to be a novel and effective method in signal processing and optics. Many important properties and results of the OLCT have been well studied and published. In this work, the sampling theorem of the OLCT bandlimited signals based on reproducing kernel Hilbert space has been proposed. First, we show that the bandlimited signals in the OLCT domain form a reproducing kernel Hilbert space. Then, an orthogonal basis for the OLCT bandlimited signals has been obtained based on the reproducing kernel Hilbert space. By using the orthogonal basis, the uniform sampling theory for bandlimited signals associated with the OLCT has been obtained. Furthermore, the nonuniform sampling of the OLCT bandlimited signals also has been attained. Finally, the simulations are provided to prove the usefulness and correctness of the derived results.

scholarly journals A Version of Uncertainty Principle for Quaternion Linear Canonical Transform

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Mawardi Bahri ◽  
Resnawati ◽  
Selvy Musdalifah
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Young Inequality ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Research Papers ◽  
Quaternion Fourier Transform ◽  
Quaternion Linear Canonical Transform ◽  
The Relationship

In recent years, the two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We also discuss the generalization of the Hausdorff-Young inequality in the QLCT domain.

scholarly journals Two New Spiro-Heterocyclic γ-Lactams from A Marine-Derived Aspergillus fumigatus Strain CUGBMF170049

Marine Drugs ◽  
2019 ◽  
Vol 17 (5) ◽  
pp. 289 ◽  
Author(s):  
Xiuli Xu ◽  
Jiahui Han ◽  
Yanan Wang ◽  
Rui Lin ◽  
Haijin Yang ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Circular Dichroism ◽  
Aspergillus Fumigatus ◽  
2D Nmr ◽  
Two Dimensional ◽  
One Dimensional ◽  
Helvolic Acid ◽  
Circular Dichroïsm

Two new spiro-heterocyclic γ-lactam derivatives, cephalimysins M (1) and N (2), were isolated from the fermentation cultures of the marine-derived fungus Aspergillus fumigatus CUGBMF17018. Two known analogues, pseurotin A (3) and FD-838 (4), as well as four previously reported helvolic acid derivatives, 16-O-propionyl-16-O-deacetylhelvolic acid (5), 6-O-propionyl-6-O-deacetylhelvolic acid (6), helvolic acid (7), and 1,2-dihydrohelvolic acid (8) were also identified. One-dimensional (1D), two-dimensional (2D) NMR, HRMS, and circular dichroism spectral analysis characterized the structures of the isolated compounds.

scholarly journals Sampling in the Linear Canonical Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Hilbert Transform ◽  
Sampling Rate ◽  
Sampling Theorem ◽  
Fourier Domain ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Generalized Hilbert Transform ◽  
Simulation Results ◽  
Bandpass Signals

This paper investigates the interpolation formulae and the sampling theorem for bandpass signals in the linear canonical transform (LCT) domain. Firstly, one of the important relationships between the bandpass signals in the Fourier domain and the bandpass signals in the LCT domain is derived. Secondly, two interpolation formulae from uniformly sampled points at half of the sampling rate associated with the bandpass signals and their generalized Hilbert transform or the derivatives in the LCT domain are obtained. Thirdly, the interpolation formulae from nonuniform samples are investigated. The simulation results are also proposed to verify the correctness of the derived results.

DETERMINATION OF VOLCANIC THICKNESS AND UNDERLYING STRUCTURES FROM AEROMAGNETIC MAPS IN THE SILET AREA OF ALGERIA

Geophysics ◽  
1975 ◽  
Vol 40 (1) ◽  
pp. 79-90 ◽  
Author(s):  
C. E. Curtis ◽  
S. Jain
Keyword(s):  
Spectral Analysis ◽  
Dimensional Analysis ◽  
Magnetic Survey ◽  
Average Thickness ◽  
Two Dimensional ◽  
One Dimensional

In the course of the interpretation of an aero‐magnetic survey of Algeria, techniques based on spectral analysis were found to be quite useful in the determination of volcanic thicknesses and the resolution of underlying structural trends in a mineralized region near Silet. One‐dimensional analysis, applied to a series, of traverses crossing the area, indicates the average thickness of volcanics to be about 100 m. Two‐dimensional spectra were used to design appropriate filters for attenuating anomalies from shallow sources thereby enhancing the responses of the underlying regional structures.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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