Watermarking methods require robustness against various attacks. Conventional watermarking methods use error-correcting codes or spread spectrum to correct watermarking errors. Errors can also be reduced by embedding the watermark into the frequency domain and by using SIFT feature points. If the type and strength of the attack can be estimated, the errors can be further reduced. There are several types of attacks, such as scaling, rotation, and cropping, and it is necessary to aim for robustness against all of them. Focusing on the scaling tolerance of watermarks, we propose a watermarking method using SIFT feature points and DFT, and introduce a pilot signal. The proposed method estimates the scaling rate using the pilot signal in the form of a grid. When a stego-image is scaled, the grid interval of the pilot signal also changes, and the scaling rate can be estimated from the amount of change. The accuracy of estimating the scaling rate by the proposed method was evaluated in terms of the relative error of the scaling rate. The results show that the proposed method could reduce errors in the watermark by using the estimated scaling rate.

The present study proposes a scheme in which variable-length orthogonal codes generated by combining inverse discrete Fourier transform matrices over a finite field multiplex user data into a multiplexed sequence and its sequence forms one or a plural number of codewords for Reed-Solomon coding. The proposed scheme realizes data multiplexing, error correction coding, and multi-rate transmitting at the same time. This study also shows a design example and its performance analysis of the proposed scheme.

This letter introduces a prime-factor Galois field Fourier transform (PF-GFFT) architecture to frequency domain decoding (FDD) of cyclic codes. Firstly, a fast FDD scheme is designed which converts the original single longer Fourier transform to a multi-dimensional smaller transform. Furthermore, a ladder-shift architecture for PF-GFFT is explored to solve the rearrangement problem of input and output data. In this regard, PF-GFFT is considered as a lower order spectral calculation scheme, which has sufficient preponderance in reducing the computational complexity. Simulation results show that PF-GFFT compares favorably with the current general GFFT, simplified-GFFT (S-GFFT), and circular shifts-GFFT (CS-GFFT) algorithms in time-consuming cost, and is nearly an order of magnitude or smaller than them. The superiority is a benefit to improving the decoding speed and has potential application value in decoding cyclic codes with longer code lengths.

Frame synchronization detection before data transmission is an important module which directly affects the lifetime and coexistence of underwater acoustic communication (UAC) networks, where linear frequency modulation (LFM) is a frame preamble signal commonly used for synchronization. Unlike terrestrial wireless communications, strong bursty noise frequently appears in UAC. Due to the long transmission distance and the low signal-to-noise ratio, strong short-distance bursty noise will greatly reduce the accuracy of conventional fractional fourier transform (FrFT) detection. We propose a multi-segment verification fractional fourier transform (MFrFT) preamble detection algorithm to address this challenge. In the proposed algorithm, 4 times of adjacent FrFT operations are carried out. And the LFM signal identifies by observing the linear correlation between two lines connected in pair among three adjacent peak points, called ‘dual-line-correlation mechanism’. The accurate starting time of the LFM signal can be found according to the peak frequency of the adjacent FrFT. More importantly, MFrFT do not result in an increase in computational complexity. Compared with the conventional FrFT detection method, experimental results show that the proposed algorithm can effectively distinguish between signal starting points and bursty noise with much lower error detection rate, which in turn minimizes the cost of retransmission.

Bandpass filters (BPFs) are very important to extract target signals and eliminate noise from the received signals. A BPF of which frequency characteristics is a sum of Gaussian functions is called the Gaussian mixture BPF (GMBPF). In this research, we propose to implement the GMBPF approximately by the sum of several frequency components of the sliding Fourier transform (SFT) or the attenuated SFT (ASFT). Because a component of the SFT/ASFT can be approximately realized using the finite impulse response (FIR) recursive filters, its calculation complexity does not depend on the length of the impulse response. The property makes GMBPF ideal for narrow bandpass filtering applications. We conducted experiments to demonstrate the advantages of the proposed GMBPF over FIR filters designed by a MATLAB function with regard to the computational complexity.

With the emergence of a large quantity of data in science and industry, it is urgent to improve the prediction accuracy and reduce the high complexity of Gaussian process regression (GPR). However, the traditional global approximation and local approximation have corresponding shortcomings, such as global approximation tends to ignore local features, and local approximation has the problem of over-fitting. In order to solve these problems, a large-scale Gaussian process regression algorithm (RFFLT) combining random Fourier features (RFF) and local approximation is proposed. 1) In order to speed up the training time, we use the random Fourier feature map input data mapped to the random low-dimensional feature space for processing. The main innovation of the algorithm is to design features by using existing fast linear processing methods, so that the inner product of the transformed data is approximately equal to the inner product in the feature space of the shift invariant kernel specified by the user. 2) The generalized robust Bayesian committee machine (GRBCM) based on Tsallis mutual information method is used in local approximation, which enhances the flexibility of the model and generates a sparse representation of the expert weight distribution compared with previous work. The algorithm RFFLT was tested on six real data sets, which greatly shortened the time of regression prediction and improved the prediction accuracy.

In this study, a blind carrier frequency offset (CFO) estimation method is proposed using the time-frequency symmetry of the transmitted signals of a weighted Fourier transform (WFrFT) communication system. Blind CFO estimation is achieved by focusing on the property that results in matching the signal waveforms before and after the Fourier transform when the WFrFT parameter is set to a certain value. Numerical simulations confirm that the proposed method is more resistant to Rayleigh fading than the conventional estimation methods.

In this paper, we propose an interpretation method on amplitude intensities for response waveforms of backward transient scattered field components for both E- and H-polarizations by a 2-D coated metal cylinder. A time-domain (TD) asymptotic solution, which is referred to as a TD Fourier transform method (TD-FTM), is derived by applying the FTM to a backward transient scattered field expressed by an integral form. The TD-FTM is represented by a combination of a direct geometric optical ray (DGO) and a reflected GO (RGO) series. We use the TD-FTM to derive amplitude intensity ratios (AIRs) between adjacent backward transient scattered field components. By comparing the numerical values of the AIRs with those of the influence factors that compose the AIRs, major factor(s) can be identified, thereby allowing detailed interpretation method on the amplitude intensities for the response waveforms of backward transient scattered field components. The accuracy and practicality of the TD-FTM are evaluated by comparing it with three reference solutions. The effectiveness of an interpretation method on the amplitude intensities for response waveforms of backward transient scattered field components is revealed by identifying major factor(s) affecting the amplitude intensities.

In various studies of attacks on autonomous vehicles (AVs), a phantom attack in which advanced driver assistance system (ADAS) misclassifies a fake object created by an adversary as a real object has been proposed. In this paper, we propose F-GhostBusters, which is an improved version of GhostBusters that detects phantom attacks. The proposed model uses a new feature, i.e, frequency of images. Experimental results show that F-GhostBusters not only improves the detection performance of GhostBusters but also can complement the accuracy against adversarial examples.

Long-term coherent integration can significantly improve the ability to detect maneuvering targets by radar. Especially for weak targets, longer integration times are needed to improve. But for non-radially moving targets, the time-varying angle between target moving direction and radar line of sight will cause non-linear range migration (NLRM) and non-linear Doppler frequency migration (NLDFM) within long-time coherent processing, which precludes existing methods that ignore angle changes, and seriously degrades the performance of coherent integration. To solve this problem, an efficient method based on Radon Fourier transform (RFT) with modified variant angle model (ARFT) is proposed. In this method, a new parameter angle is introduced to optimize the target motion model, and the NLRM and NLDFM are eliminated by range-velocity-angle joint three-dimensional searching of ARFT. Compared with conventional algorithms, the proposed method can more accurately compensate for the NLRM and NLDFM, thus achieving better integration performance and detection probability for non-radial moving weak targets. Numerical simulations verify the effectiveness and advantages of the proposed method.

The present paper proposes orthogonal variable spreading factor codes over finite fields for multi-rate communications. The proposed codes have layered structures that combine sequences generated by discrete Fourier transforms over finite fields, and have various code lengths. The design method for the proposed codes and examples of the codes are shown.

Observations of gravity waves based on High Frequency Surface Wave Radar can make contributions to a better understanding of the energy transfer process between the ocean and the ionosphere. In this paper, through processing the observed data of the ionospheric clutter from HFSWR during the period of the Typhoon Rumbia with short-time Fourier transform method, HFSWR was proven to have the capability of gravity wave detection.

Multiple-valued bent functions are functions with highest nonlinearity which makes them interesting for multiple-valued cryptography. Since the general structure of bent functions is still unknown, methods for construction of bent functions are often based on some deterministic criteria. For practical applications, it is often necessary to be able to construct a bent function that does not belong to any specific class of functions. Thus, the criteria for constructions are combined with exhaustive search over all possible functions which can be very CPU time consuming. A solution is to restrict the search space by some conditions that should be satisfied by the produced bent functions. In this paper, we proposed the construction method based on spectral subsets of multiple-valued bent functions satisfying certain appropriately formulated restrictions in Galois field (GF) and Reed-Muller-Fourier (RMF) domains. Experimental results show that the proposed method efficiently constructs ternary and quaternary bent functions by using these restrictions.

The frequency of uterine peristalsis is closely related to the success rate of pregnancy. An ultrasonic imaging is almost always employed for the measure of the frequency. The physician subjectively evaluates the frequency from the ultrasound image by the naked eyes. This paper aims to measure the frequency of uterine peristalsis from the ultrasound image. The ultrasound image consists of relative amounts in the brightness, and the contour of the uterine is not clear. It was not possible to measure the frequency by using the inter-frame difference and optical flow, which are the representative methods of motion detection, since uterine peristaltic movement is too small to apply them. This paper proposes a measurement method of the frequency of the uterine peristalsis from the ultrasound image in the implantation phase. First, traces of uterine peristalsis are semi-automatically done from the images with location-axis and time-axis. Second, frequency analysis of the uterine peristalsis is done by Fourier transform for 3 minutes. As a result, the frequency of uterine peristalsis was known as the frequency with the dominant frequency ingredient with maximum value among the frequency spectrums. Thereby, we evaluate the number of the frequency of uterine peristalsis quantitatively from the ultrasound image. Finally, the success rate of pregnancy is calculated from the frequency based on Fuzzy logic. This enabled us to evaluate the success rate of pregnancy by measuring the uterine peristalsis from the ultrasound image.

Binary bent functions have a strictly specified number of non-zero values. In the same way, ternary bent functions satisfy certain requirements on the elements of their value vectors. These requirements can be used to specify six classes of ternary bent functions. Classes are mutually related by encoding of function values. Given a basic ternary bent function, other functions in the same class can be constructed by permutation matrices having a block structure similar to that of the factor matrices appearing in the Good-Thomas decomposition of Cooley-Tukey Fast Fourier transform and related algorithms.

Expectation propagation (EP) decoding is proposed for sparse superposition coding in orthogonal frequency division multiplexing (OFDM) systems. When a randomized discrete Fourier transform (DFT) dictionary matrix is used, the EP decoding has the same complexity as approximate message-passing (AMP) decoding, which is a low-complexity and powerful decoding algorithm for the additive white Gaussian noise (AWGN) channel. Numerical simulations show that the EP decoding achieves comparable performance to AMP decoding for the AWGN channel. For OFDM systems, on the other hand, the EP decoding is much superior to the AMP decoding while the AMP decoding has an error-floor in high signal-to-noise ratio regime.

A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).

In this letter, an efficient hybrid direction-of-arrival (DOA) estimation scheme is devised for massive uniform rectangular array. In this scheme, the DOA estimator based on a two-dimensional (2D) discrete Fourier transform is first applied to acquire coarse initial DOA estimates for single data snapshot. Then, the fine DOA is accurately estimated through using the iterative search estimator within a very small region. Meanwhile, a Nyström-based method is utilized to correctly compute the required noise-subspace projection matrix, avoiding the direct computation of full-dimensional sample correlation matrix and its eigenvalue decomposition. Therefore, the proposed scheme not only can estimate DOA, but also save computational cost, especially in massive antenna arrays scenarios. Simulation results are included to demonstrate the effectiveness of the proposed hybrid estimate scheme.

A light field, which is equivalent to a dense set of multi-view images, has various applications such as depth estimation and 3D display. One of the essential problems in light field applications is light field interpolation, i.e., view interpolation. The interpolation accuracy is enhanced by exploiting an inherent property of a light field. One example is that an epipolar plane image (EPI), which is a 2D subset of the 4D light field, consists of many lines, and these lines have almost the same slope in a local region. This structure induces a sparse representation in the frequency domain, where most of the energy resides on a line passing through the origin. On the basis of this observation, we propose a group sparsity prior suitable for light fields to exploit their line structure fully for interpolation. Specifically, we designed the directional groups in the discrete Fourier transform (DFT) domain so that the groups can represent the concentration of the energy, and we thereby formulated an LF interpolation problem as an overlapping group lasso. We also introduce several techniques to improve the interpolation accuracy such as applying a window function, determining group weights, expanding processing blocks, and merging blocks. Our experimental results show that the proposed method can achieve better or comparable quality as compared to state-of-the-art LF interpolation methods such as convolutional neural network (CNN)-based methods.

This letter presents an improved hybrid direction of arrival (DOA) estimation scheme with computational efficiency for massive uniform linear array. In order to enhance the resolution of DOA estimation, the initial estimator based on the discrete Fourier transform is applied to obtain coarse DOA estimates by a virtual array extension for one snapshot. Then, by means of a first-order Taylor series approximation to the direction vector with the one initially estimated in a very small region, the iterative fine estimator can find a new direction vector which raises the searching efficiency. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.