scholarly journals Image Watermarking in the Linear Canonical Transform Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bing-Zhao Li ◽  
Yu-Pu Shi
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Image Watermarking ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Watermark Embedding ◽  
Simulation Results ◽  
The Fourier Transform ◽  
Signal Processing Methods

The linear canonical transform, which can be looked at the generalization of the fractional Fourier transform and the Fourier transform, has received much interest and proved to be one of the most powerful tools in fractional signal processing community. A novel watermarking method associated with the linear canonical transform is proposed in this paper. Firstly, the watermark embedding and detecting techniques are proposed and discussed based on the discrete linear canonical transform. Then the Lena image has been used to test this watermarking technique. The simulation results demonstrate that the proposed schemes are robust to several signal processing methods, including addition of Gaussian noise and resizing. Furthermore, the sensitivity of the single and double parameters of the linear canonical transform is also discussed, and the results show that the watermark cannot be detected when the parameters of the linear canonical transform used in the detection are not all the same as the parameters used in the embedding progress.

Wavelet packets associated with linear canonical transform on spectrum

2021 ◽  
pp. 2150030
Author(s):  
M. Younus Bhat ◽  
Aamir H. Dar
Keyword(s):  
Fourier Transform ◽  
Multiresolution Analysis ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Integral Transforms ◽  
Wavelet Packets ◽  
Linear Canonical Transform ◽  
Fresnel Transform ◽  
The Fourier Transform ◽  
Vector Valued

The linear canonical transform (LCT) provides a unified treatment of the generalized Fourier transforms in the sense that it is an embodiment of several well-known integral transforms including the Fourier transform, fractional Fourier transform, Fresnel transform. Using this fascinating property of LCT, we, in this paper, constructed associated wavelet packets. First, we construct wavelet packets corresponding to nonuniform Multiresolution analysis (MRA) associated with LCT and then those corresponding to vector-valued nonuniform MRA associated with LCT. We investigate their various properties by means of LCT.

scholarly journals Wigner-Ville Distribution Associated with the Linear Canonical Transform

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Rui-Feng Bai ◽  
Bing-Zhao Li ◽  
Qi-Yuan Cheng
Keyword(s):  
Signal Processing ◽  
Signal Detection ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Nonstationary Signal ◽  
Linear Frequency ◽  
Simulation Results ◽  
Definition Of ◽  
Linear Frequency Modulated Signal

The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates the Wigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of Wigner-Ville distribution associated with the linear canonical transform is given. Then, the main properties of the newly defined Wigner-Ville transform are investigated in detail. Finally, the applications of the newly defined Wigner-Ville transform in the linear-frequency-modulated signal detection are proposed, and the simulation results are also given to verify the derived theory.

The properties of generalized offset linear canonical Hilbert transform and its applications

2017 ◽  
Vol 15 (04) ◽  
pp. 1750031 ◽  
Author(s):  
Shuiqing Xu ◽  
Li Feng ◽  
Yi Chai ◽  
Youqiang Hu ◽  
Lei Huang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Hilbert Transform ◽  
Analytic Signal ◽  
Linear Canonical Transform ◽  
Single Sideband ◽  
Generalized Hilbert Transform ◽  
Offset Linear Canonical Transform ◽  
The Fourier Transform ◽  
The Hilbert Transform

The Hilbert transform is tightly associated with the Fourier transform. As the offset linear canonical transform (OLCT) has been shown to be useful and powerful in signal processing and optics, the concept of generalized Hilbert transform associated with the OLCT has been proposed in the literature. However, some basic results for the generalized Hilbert transform still remain unknown. Therefore, in this paper, theories and properties of the generalized Hilbert transform have been considered. First, we introduce some basic properties of the generalized Hilbert transform. Then, an important theorem for the generalized analytic signal is presented. Subsequently, the generalized Bedrosian theorem for the generalized Hilbert transform is formulated. In addition, a generalized secure single-sideband (SSB) modulation system is also presented. Finally, the simulations are carried out to verify the validity and correctness of the proposed results.

scholarly journals Identification of Sonar Detection Signal Based on Fractional Fourier Transform

2018 ◽  
Vol 25 (s2) ◽  
pp. 125-131
Author(s):  
Wang Biao ◽  
Tang Jiansheng ◽  
Yu Fujian ◽  
Zhu Zhiyu
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Adaptive Threshold ◽  
Good Time ◽  
Transform Domain ◽  
Time Frequency ◽  
Watermark Embedding ◽  
Before And After ◽  
Different Characteristics ◽  
Fourier Transform Domain

Abstract Aiming at the source of underwater acoustic emission, in order to identify the enemy emission sonar source accurately. Using the digital watermarking technology and combining with the good time-frequency characteristics of fractional Fourier transform (FRFT), this paper proposes a sonar watermarking method based on fractional Fourier transform. The digital watermark embedding in the fractional Fourier transform domain and combined with the coefficient properties of the sonar signal in the fractional Fourier transform to select the appropriate watermark position. Using the different characteristics of the signals before and after embedding, an adaptive threshold was set for the watermark detection to realize the discrimination of sonar signals. The simulation results show the feasibility and has better resolution and large watermark capacity of this method, while the robustness of the watermark is better, and the detection precision is further improved.

Performance Analysis of 4-WFRFT Based Carrier Modulations under Burst Interference

2010 ◽  
Vol 171-172 ◽  
pp. 500-503 ◽  
Author(s):  
Tao Li ◽  
Xuan Li Wu ◽  
Lin Mei ◽  
Xue Jun Sha
Keyword(s):  
Fourier Transform ◽  
System Performance ◽  
Fractional Fourier Transform ◽  
Transform Domain ◽  
Error Floor ◽  
Single Carrier ◽  
Interference Signals ◽  
Simulation Results ◽  
Systems Simulation ◽  
Fourier Transform Domain

This paper proposed a 4-weighted fractional Fourier transform (4-WFRFT) based carrier modulation technique. The system performance applying such modulation is analyzed under burst interference, and then compared with single carrier (SC) modulation and multi carrier (MC) modulation based systems. Simulation results show that 4-WFRFT system achieves a better performance than those of SC and MC systems since the 4-WFRFT has the capability to disperse the energy of interference signals in fractional Fourier transform domain. When the SIR of burst interference is -2dB, there is no error floor occurs in 4-WFRFT system, while the error floor appears in both SC and MC systems.

scholarly journals A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

2013 ◽  
Vol 23 (3) ◽  
pp. 685-695 ◽  
Author(s):  
Navdeep Goel ◽  
Kulbir Singh
Keyword(s):  
Fourier Transform ◽  
Quantum Mechanics ◽  
Fractional Fourier Transform ◽  
Integral Transform ◽  
Linear Canonical Transform ◽  
Product Theorem ◽  
Special Cases ◽  
Fresnel Transform ◽  
The Fourier Transform ◽  
Representation Transformation

Abstract The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution and product theorem in the LCT domain derived by a representation transformation in quantum mechanics, which seems a convenient and concise method. It is compared with the existing convolution theorem for the LCT and is found to be a better and befitting proposition. Further, an application of filtering is presented by using the derived results.

scholarly journals Compressive Sensing in Signal Processing: Algorithms and Transform Domain Formulations

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Irena Orović ◽  
Vladan Papić ◽  
Cornel Ioana ◽  
Xiumei Li ◽  
Srdjan Stanković
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Compressive Sensing ◽  
Signal Reconstruction ◽  
Signal Acquisition ◽  
Transform Domain ◽  
Hermite Transform ◽  
Time Frequency ◽  
Reconstruction Methods ◽  
Fourier Transform Domain

Compressive sensing has emerged as an area that opens new perspectives in signal acquisition and processing. It appears as an alternative to the traditional sampling theory, endeavoring to reduce the required number of samples for successful signal reconstruction. In practice, compressive sensing aims to provide saving in sensing resources, transmission, and storage capacities and to facilitate signal processing in the circumstances when certain data are unavailable. To that end, compressive sensing relies on the mathematical algorithms solving the problem of data reconstruction from a greatly reduced number of measurements by exploring the properties of sparsity and incoherence. Therefore, this concept includes the optimization procedures aiming to provide the sparsest solution in a suitable representation domain. This work, therefore, offers a survey of the compressive sensing idea and prerequisites, together with the commonly used reconstruction methods. Moreover, the compressive sensing problem formulation is considered in signal processing applications assuming some of the commonly used transformation domains, namely, the Fourier transform domain, the polynomial Fourier transform domain, Hermite transform domain, and combined time-frequency domain.

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