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.

An Algorithm of the LMS Adaptive Filtering in Linear Canonical Transform Domain

2013 ◽  
Vol 385-386 ◽  
pp. 1407-1410 ◽  
Author(s):  
Yan Hong Zhang ◽  
Heng Zhao ◽  
Hui Hui Li
Keyword(s):  
Theoretical Analysis ◽  
Adaptive Filtering ◽  
Narrow Band ◽  
Lms Algorithm ◽  
Transform Domain ◽  
Linear Canonical Transform ◽  
Nonstationary Signal ◽  
Filtering Algorithm ◽  
Wideband Signals ◽  
Simulation Results

In allusion to the non-stationary wideband signals, a LMS adaptive filtering algorithm based on linear canonical transform is proposed. In this method, the signal is first transformed to linear canonical transform domain. By using linear canonical transform and selecting appropriate transformation parameters, characteristics of the transformed signal appear to be stationary narrow-band in the corresponding linear canonical transform domain, and then, the transformed signal is filtered adaptively with LMS algorithm in this domain. Theoretical analysis and simulation results show that the algorithm is not only to solve the problem of extracting and filtering of nonstationary signal, and can obtain better filtering performance.

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.

scholarly journals A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with0<α<1and Median Correction

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhiwu Liao
Keyword(s):  
Signal Processing ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Original Signal ◽  
Theory Analysis ◽  
Left Handed ◽  
Signal Value ◽  
Simulation Results ◽  
Definition Of ◽  
Fractional Orders

We propose a new definition of fractional derivatives based on truncated left-handed Grünwald-Letnikov formula with0<α<1and median correction. Analyzing the difficulties to choose the fractional orders and unsatisfied processing results in signal processing using fractional-order partial differential equations and related methods; we think that the nonzero values of the truncated fractional order derivatives in the smooth regions are major causes for these situations. In order to resolve the problem, the absolute values of truncated parts of the G-L formula are estimated by the median of signal values of the remainder parts, and then the truncated G-L formula is modified by replacing each of the original signal value to the differences of the signal value and the median. Since the sum of the coefficients of the G-L formula is zero, the median correction can reduce the truncated errors greatly to proximate G-L formula better. We also present some simulation results and experiments to support our theory analysis.

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.

FPGA-Based Pulse Compression for Linear Frequency Modulated Signal

2010 ◽  
Vol 44-47 ◽  
pp. 3345-3349
Author(s):  
Xi Su ◽  
Peng Bai ◽  
Yi Ying Wang ◽  
Yan Ping Feng
Keyword(s):  
Real Time ◽  
Pulse Compression ◽  
New Method ◽  
Linear Frequency ◽  
Simulation Results ◽  
Modulated Signals ◽  
Linear Frequency Modulated Signal

Nowadays, compressing linear frequency modulated signals is usually based on DSP and realized by software. It is not only has no advantages on real-time operations but also has high requirements of hardware in processing a multitude of FFT points. Accordingly, we propose a new method to achieve the pulse compression of linear frequency modulated signals through FPGA and simulation results are also promoted. In contrast with using DSP, the new method based on FPGA has a much better performance on reliability, speed and a lower demand of hardware quantity.

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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