Improved prewhitening method for linear frequency modulation reverberation using dechirping transformation

This letter presents an autoregressive (AR) prewhitener for linear frequency modulation (LFM) reverberation to enhance the target signal. The proposed method uses a dechirping transformation to inversely compensate the frequency chirp rate of the LFM and give the LFM reverberation a stationary frequency property in each data block. The left or right beam signal adjacent to the current beam is then used as the reference signal, and the frequency response of each data block modeled using the AR coefficients. Finally, these coefficients are used to implement the inverse filter and efficiently prewhiten the LFM reverberation of the current beam.     

Improved discrete fractional Fourier transform

The fractional Fourier transform is a useful mathematical operation that generalizes the well-known continuous Fourier transform. Several discrete fractional Fourier transforms (DFRFT's) have been developed, but their results do not match those of the continuous case. We propose a new DFRFT. This improved DFRFT provides transforms similar to those of the continuous fractional Fourier transform and also retains the rotation properties.     

基于分数阶傅立叶变换的线性调频回波参数估计

本文提出了一种适用于宽带线性调频回波的分数阶傅立叶变换参数估计方法。它通过寻找合适的信号代替发射信号做模版,使得模版信号与接收信号的模糊函数匹配度高,峰值尖锐,失真率低。再利用分数阶傅立叶变换与模糊函数的关系,使用两次分数阶域的峰值搜索代替原有的一次二维搜索降低计算量。仿真实验结果表明,本文提出的方法在精确估计宽带回波的时延和频移的同时降低了计算复杂度。     

基于分数阶傅里叶变换混响抑制的目标回波检测方法

提出了一种声呐发射信号为线性调频信号时,基于分数阶傅里叶变换混响抑制的目标回波信号检测方法。通过计算混响的缓慢时变包络,对混响进行时间域的平稳化处理。对平稳化的混响信号滑动窗截取,对截取信号进行分数阶傅里叶变换,然后在分数阶傅里叶域进行滤波处理,再进行逆分数阶傅里叶变换恢复出时间域信号,最后输出该信号的能量。当滑动窗截取到目标回波信号时,窗内的混响噪声得到抑制,系统输出目标回波的能量,从而实现混响背景下的信号检测。通过计算机仿真和湖试实验结果,表明所提方法可以准确的在混响背景下检测到目标回波信号,并且在混响噪声背景条件下相比于匹配滤波器具有更好的检测性能。     

A method for detecting target echo in reverberation based on fractional Fourier transform

A method for detecting the target echo in reverberation was proposed based on fractional Fourier transform theory when the transmitted signal is linear frequency modulation signal. The slow time-varying envelope of reverberation is computed to process reverberation to be stationary. The stationary reverberation is cut into blocks using a sliding window. A narrow-band filter is applied in FrFT domain for each block and the signal is recovered through inverse FrFT. Output of the system is the energy of the recovered signal. When the target echo is included in one of the blocks, the reverberation noise is reduced, and the output is the energy of the target echo. All the simulation and lake experiment results show that the detection performance of the present method is better than that of the matched filter.     

Improved acoustic signals discrimination using fractional Fourier transform based phase-space representations

In this communication we propose performing two-dimensional correlation operation between phase-space representations based on the fractional Fourier transform, instead of correlating the signals themselves. A numerical examples clearly indicates superior discrimination performance.     

Random fractional Fourier transform

We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.     

用变形全息透镜实现变形分数傅里叶变换

利用一发散点光源和一束倾斜平行光制作出在两个垂直方向上具有不同焦距的变形全息透镜,且用此全息元件实现了变形分数傅里叶变换。变形全息透镜两个方向上的焦距随全息记录条件和再现条件而变化,分析了用这种全息透镜实现变形分数傅里叶变换的条件。实验表明,用该元件能够方便地实现任意级次的变形分数傅里叶变换。     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

Fully phase-encrypted memory using cascaded extended fractional Fourier transform

In this paper, we implement a fully phase-encrypted memory system using cascaded extended fractional Fourier transform (FRT). We encrypt and decrypt a two-dimensional image obtained from an amplitude image. The full phase image to be encrypted is fractional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating through phase conjugation, the conjugate of the encrypted image. A lithium niobate crystal has been used as a phase contrast filter to reconstruct the decrypted phase image, alleviating the need of alignment in the Fourier plane making the system rugged.     

Optimizing holographic data storage using a fractional Fourier transform

We demonstrate a method to optimize the reconstruction of a hologram when the storage device has a limited dynamic range and a minimum grain size. The optimal solution at the recording plane occurs when the object wave has propagated an intermediate distance between the near and far fields. This distance corresponds to an optimal order and magnification of the fractional Fourier transform of the object.     

Color image encryption and decryption using fractional Fourier transform

We propose the encryption of color images using fractional Fourier transform (FRT). The image to be encrypted is first segregated into three color channels: red, green, and blue. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented. The technique is shown to be a powerful one for colored text encryption. We also outline the implementation of the algorithm and examine its sensitiveness to changes in the fractional order during decryption.     

Image encryption and decryption using fractional Fourier transform and radial Hilbert transform

A technique for image encryption using fractional Fourier transform (FRT) and radial Hilbert transform (RHT) is proposed. The spatial frequency spectrum of the image to be encrypted is first segregated into two parts/channels using RHT, and image subtraction technique. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented.     

Asymmetric image encryption using phase-truncated discrete multiple-parameter fractional Fourier transform

An asymmetric image encryption scheme is proposed using a phase-truncated discrete multiple-parameter fractional Fourier transform (DMPFRFT). After applying a pixel-scrambling operation and random-phase mask, an asymmetric ciphertext with stationary white noise can be obtained using phase truncation in the DMPFRFT domain. Using the phase key, an inverse pixel-scrambling operation, and the parameters of the DMPFRFT, the original image can be successfully retrieved. Numerical simulations were conducted to demonstrate the validity and the security of the proposed method, and electro-optical hybrid setups are suggested for encryption and decryption.     

Signal separation using linear canonical and fractional Fourier transforms

Signal separation is an important operation in many areas such as communications, geophysics, and optics including optical signal processing. In this article, the issue of signal separation based on the linear canonical transform (LCT) and the fractional Fourier transform (FRFT) is considered. An iterative algorithm for signal separation in the 2-ray ground reflected model using the FRFT is also presented along with the simulation results.     

Wavelength-controlled variable-order optical fractional Fourier transform

The relationship between optical fractional Fourier transforms (OFRTs) obtained at different wavelengths is derived by use of the ABCD matrix formalism. It is shown that varying the wavelength while retaining the same optical system can be used to control the order of the OFRT. The advantage of this method of varying OFRT order is that no variation in the characteristics of the bulk optics is required. A general experimental verification of the theory is provided by showing the exact equivalence of two OFRT systems of different order when they are replayed using the same input function at different wavelengths.     

Real color fractional Fourier transform holograms

Real color fractional Fourier transform holography is proposed based on fractional Fourier transform holography. The method of fabrication, the principle of reconstruction and the design of system parameters are discussed in detail. The experiments prove real color fractional Fourier transform holograms possess the better function of anti-counterfeit than common fractional Fourier transform holograms.     

Beam analysis by fractional Fourier transform

A method of spatial modal decomposition for optical beams by fractional Fourier transform, and its practical implementation with reduced complexity by use of modal interleavers, are discussed.     

Joint extended fractional Fourier transform correlator

Based on the conventional correlation and fractional correlation, the extended fractional correlation (EFC) is presented. And based on the configuration of the nonconventional joint transform correlator, we propose the joint extended fractional Fourier transform correlator (JEFRTC). The properties of the extended fractional cross correlation peak (EFCCP) in theory are analyzed. A sound conclusion is drawn that the width of EFCCP is narrower than that of fractional correlation peak under some conditions. This JEFRTC can permit lower precision of the systemic parameters when implemented with optical configuration. That will improve correlator’s character discriminability.     

Modified computational integral imaging-based double image encryption using fractional Fourier transform

In this paper, we propose an image encryption technique to simultaneously encrypt double or multiple images into one encrypted image using computational integral imaging (CII) and fractional Fourier transform (FrFT). In the encryption, each of the input plane images are located at different positions along a pickup plane, and simultaneously recorded in the form of an elemental image array (EIA) through a lenslet array. The recorded EIA to be encrypted is multiplied by FrFT with two different fractional orders. In order to mitigate the drawbacks of occlusion noise in computational integral imaging reconstruction (CIIR), the plane images can be reconstructed using a modified CIIR technique. To further improve the solution of the reconstructed plane images, a block matching algorithm is also introduced. Numerical simulation results verify the feasibility and effectiveness of the proposed method.