Showing papers on "Fourier transform published in 2019"

Laguerre-Gaussian mode sorter.

Abstract: Multi-plane light conversion is a method of performing spatial basis transformations using cascaded phase plates separated by Fourier transforms or free-space propagation. In general, the number of phase plates required scales with the dimensionality (total number of modes) in the transformation. This is a practical limitation of the technique as it relates to scaling to large mode counts. Firstly, requiring many planes increases the complexity of the optical system itself making it difficult to implement, but also because even a very small loss per plane will grow exponentially as more and more planes are added, causing a theoretically lossless optical system, to be far from lossless in practice. Spatial basis transformations of particular interest are those which take a set of spatial modes which exist in the same or similar space, and transform them into an array of spatially separated spots. Analogous to the operation performed by a diffraction grating in the wavelength domain, or a polarizing beamsplitting in the polarization domain. Decomposing the Laguerre-Gaussian, Hermite-Gaussian or related bases to an array of spots are examples of this and are relevant to many areas of light propagation in free-space and optical fibre. In this paper we present our work on designing multi-plane light conversion devices capable or operating on large numbers of spatial modes in a scalable fashion.

Fourier-space Diffractive Deep Neural Network.

Abstract: In this Letter we propose the Fourier-space diffractive deep neural network (F-D^{2}NN) for all-optical image processing that performs advanced computer vision tasks at the speed of light. The F-D^{2}NN is achieved by placing the extremely compact diffractive modulation layers at the Fourier plane or both Fourier and imaging planes of an optical system, where the optical nonlinearity is introduced from ferroelectric thin films. We demonstrated that F-D^{2}NN can be trained with deep learning algorithms for all-optical saliency detection and high-accuracy object classification.

Hyperspectral Anomaly Detection by Fractional Fourier Entropy

Abstract: Anomaly detection is an important task in hyperspectral remote sensing. Most widely used detectors, such as Reed–Xiaoli (RX), have been developed only using original spectral signatures, which may lack the capability of signal enhancement and noise suppression. In this article, an effective alternative approach, fractional Fourier entropy (FrFE)-based hyperspectral anomaly detection method, is proposed. First, fractional Fourier transform (FrFT) is employed as preprocessing, which obtains features in an intermediate domain between the original reflectance spectrum and its Fourier transform with complementary strengths by space-frequency representations. It is desirable for noise removal so as to enhance the discrimination between anomalies and background. Furthermore, an FrFE-based step is developed to automatically determine an optimal fractional transform order. With a more flexible constraint, i.e., Shannon entropy uncertainty principle on FrFT, the proposed method can significantly distinguish signal from background and noise. Finally, the proposed FrFE-based anomaly detection method is implemented in the optimal fractional domain. Experimental results obtained on real hyperspectral datasets demonstrate that the proposed method is quite competitive.

Cycle-by-cycle analysis of neural oscillations

Abstract: We introduce a fully documented, open-source Python package, bycycle, for analyzing neural oscillations on a cycle-by-cycle basis. This approach is complementary to traditional Fourier- and Hilbert...

Low complexity LMMSE Receiver for OTFS

Abstract: Orthogonal time frequency space modulation is a two dimensional (2D) delay-Doppler domain waveform. It uses inverse symplectic Fourier transform (ISFFT) to spread the signal in time-frequency domain. To extract diversity gain from 2D spreaded signal, advanced receivers are required. In this work, we investigate a low complexity linear minimum mean square error receiver which exploits sparsity and quasi-banded structure of matrices involved in the demodulation process which results in a log-linear order of complexity without any performance degradation of BER.

Deep Learning Based Phase Reconstruction for Speaker Separation: A Trigonometric Perspective

Abstract: This study investigates phase reconstruction for deep learning based monaural talker-independent speaker separation in the short-time Fourier transform (STFT) domain. The key observation is that, for a mixture oftwo sources, with their magnitudes accurately estimated and under a geometric constraint, the absolute phase difference between each source and the mixture can be uniquely determined; in addition, the source phases at each time-frequency $({\text{T}} - {{\Gamma }})$ unit can be narrowed down to only two candidates. To pick the right candidate, we propose three algorithms based on iterative phase reconstruction, group delay estimation, and phase-difference sign prediction. State-of-the-art results are obtained on the publicly available wsj0-2mix and 3 mix corpus.

Universal optimality of the $E_8$ and Leech lattices and interpolation formulas

Abstract: We prove that the $E_8$ root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions $8$ and $24$, respectively. In other words, they minimize energy for every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians), which is a strong form of robustness not previously known for any configuration in more than one dimension. This theorem implies their recently shown optimality as sphere packings, and broadly generalizes it to allow for long-range interactions. The proof uses sharp linear programming bounds for energy. To construct the optimal auxiliary functions used to attain these bounds, we prove a new interpolation theorem, which is of independent interest. It reconstructs a radial Schwartz function $f$ from the values and radial derivatives of $f$ and its Fourier transform $\widehat{f}$ at the radii $\sqrt{2n}$ for integers $n\ge1$ in $\mathbb{R}^8$ and $n \ge 2$ in $\mathbb{R}^{24}$. To prove this theorem, we construct an interpolation basis using integral transforms of quasimodular forms, generalizing Viazovska's work on sphere packing and placing it in the context of a more conceptual theory.

An Interference Mitigation Technique for FMCW Radar Using Beat-Frequencies Interpolation in the STFT Domain

Abstract: A frequency-modulated continuous-wave (FMCW) radar interference mitigation technique using the interpolation of beat frequencies in the short-time Fourier transform (STFT) domain, phase matching, and reconfigurable linear prediction coefficients estimation for Coherent Processing Interval processing is proposed. The technique is noniterative and does not rely on algorithm convergence. It allows the usage of the fast Fourier transform (FFT) as the radar’s beat-frequency estimation tool, for reasons such as real-time implementation, noise linearity after the FFT, and compatibility with legacy receiver architectures. Verification is done in range and in range-Doppler using radar experimental data in two ways: first by removing interferences from interference-contaminated data and second by using interference-free data as the reference data, and processing it—as if it had interferences—using the proposed technique, inverse cosine windowing and zeroing for comparison. We found that processing with the proposed technique closely matches the reference-data and outperforms the inverse cosine windowing and zeroing techniques in 2-D cross correlation, amplitude, and phase average errors and phase root-mean-square error. It is expected that the proposed technique will be operationally deployed on the TU Delft simultaneous-polarimetric PARSAX radar.

Low Complexity LMMSE Receiver for OTFS

Abstract: Orthogonal time frequency space modulation is a two dimensional (2D) delay-Doppler domain waveform. It uses inverse symplectic Fourier transform (ISFFT) to spread the signal in time-frequency domain. To extract diversity gain from 2D spreaded signal, advanced receivers are required. In this work, we investigate a low complexity linear minimum mean square error receiver which exploits sparsity and quasi-banded structure of matrices involved in the demodulation process which results in a log-linear order of complexity without any performance degradation of BER.

Convolution and Multichannel Sampling for the Offset Linear Canonical Transform and Their Applications

Abstract: The offset linear canonical transform (OLCT) plays an important role in many fields of optics and signal processing. In this paper, we address the problem of signal filtering and reconstruction in the OLCT domain based on new convolution theorems. Firstly, we propose new convolution and product theorems for the OLCT, which state that a modified ordinary convolution in the time domain is equivalent to simple multiplication operations for the OLCT and the Fourier transform (FT). Moreover, it is expressible by a one dimensional integral and is easy to implement in designing filters. The classical convolution theorem in the FT domain is shown to be a special case of our derived results. Then, a practical multichannel sampling expansion for band-limited signal with the OLCT is introduced. This sampling expansion constructed by the new convolution structure can reduce the effect of spectral leakage and is easy to implement. By designing OLCT filters, we can obtain derivative sampling and second-order derivative interpolation. Furthermore, potential applications of the multichannel sampling are discussed. Last, based on the new convolution structure, we investigate and discuss several applications, including swept-frequency filter analysis, image denosing and image encryption. Some illustrations and simulations are presented to verify the validity and effectiveness of the proposed method.

Improved Damage Localization and Quantification of CFRP Using Lamb Waves and Convolution Neural Network

Abstract: A novel method is proposed in this paper for simultaneously locating and quantifying damage in composite plates by employing Lamb waves and the algorithm of convolution neural network. The interaction between Lamb wave and damage of different degrees is also studied by simulation. The experiments on Lamb wave are carried out by employing a square array which is composed of four piezoelectric wafers. First of all, the sensor array collects response signals of Lamb wave as training data, and then de-noises them adopting the method of the wavelet transform. In the process, the damage caused to the composite can be realized through mass blocks. Besides, the Fourier transform is applied for the extraction of the characteristics shown by the signals. After that, the spectrum with the characteristics of damage and corresponding damage modes are employed as input and output of the convolutional neural network, respectively, and accordingly, the model of damage identification is established. Finally, 191 samples (from a total of 192) were identified accurately and the correct recognition rate achieved is 99.5%, which consequently demonstrates that the convolution neural network can be employed to establish the complex mapping relationship between signal and damage, and further proves that the proposed method performs well in high accuracy and great potential in simultaneous localization and quantitative identification of damage existing in composite plate.

Defect Detection in Electronic Surfaces Using Template-Based Fourier Image Reconstruction

Abstract: For defect detection in nonperiodical pattern images, such as printed circuit boards or integrated circuit dies found in the electronic industry, template matching could be the only applicable method to tackle the problem. The traditional template matching techniques work in the spatial domain and rely on the local pixel information. They are sensitive to geometric and lighting changes, and random product variations. The currently available Fourier-based methods mainly work for plain and periodical texture surfaces. In this paper, we propose a global Fourier image reconstruction method to detect and localize small defects in nonperiodical pattern images. It is based on the comparison of the whole Fourier spectra between the template and the inspection image. It retains only the frequency components associated with the local spatial anomaly. The inverse Fourier transform is then applied to reconstruct the test image, where the local anomaly will be restored and the common pattern will be removed as a uniform surface. The proposed method is invariant to translation and illumination, and can detect subtle defects as small as 1-pixel wide in a wide variety of nonperiodical patterns found in the electronic industry.

A GN model on photothermal interactions in a two-dimensions semiconductor half space

Abstract: The model of coupled plasma and thermo-elastic wave were used to investigate the wave propagation in a two-dimensional semiconducting half space by using eigenvalues approach. By using Fourier and Laplace transformations with the eigenvalues techniques methodology, the exact solution of all physical quantities is obtained. The boundary edge of the plane is due to a heat flux with a pulse that decays exponentially and is taken as free of tractions. A semiconductor media such as silicon has been studied. The outcomes have been verified numerically and are represented graphically.

New Rapid and Robust Color Image Watermarking Technique in Spatial Domain

Abstract: In this paper, a novel spatial domain color image watermarking technique is proposed to rapidly and effectively protect the copyright of the color image. First, the direct current (DC) coefficient of 2D-DFT obtained in the spatial domain is discussed, and the relationship between the change of each pixel in the spatial domain and the change of the DC coefficient in the Fourier transform is proved. Then, the DC coefficient is used to embed and extract watermark in the spatial domain by the proposed quantization technique. The novelties of this paper include three points: 1) the DC coefficient of 2D-DFT is obtained in the spatial domain without of the true 2D-DFT; 2) the relationship between the change of each pixel in the image block and the change of the DC coefficient of 2D-DFT is found, and; 3) the proposed method has the short running time and strong robustness. The experimental results on two publicly available image databases (CVG-UGR and USC-SIPI) have shown that the proposed method not only has satisfied the needs of invisibility but also has better performance in terms of robustness and real-time feature, which show the proposed method has both advantages of spatial domain and frequency domain.

Research and Application of Acoustic Emission Signal Processing Technology

Abstract: Acoustic emission signal processing has always been a key problem in damage assessment of components and materials, and parameter analysis and waveform analysis are two important means of acoustic emission signal processing. In this paper, the parameter analysis method in signal processing and the meaning and characteristics of each parameter are introduced. Then, the waveform analysis method is introduced and the basic theory of wavelet transform and its spectrum analysis in waveform analysis method are mainly analyzed. The comparison between wavelet transform and Fourier transform is made: traditional Fourier transform signal processing methods can only be used to process transient stationary signals, and the transient non-stationary signals cannot be analyzed locally. The wavelet transform can take into account the characteristics of both the time and frequency domains, and it can also reflect the local signal well. Through the analysis of the signals in the process of concrete damage, it is found that the two signal processing methods mentioned above can well characterize the damage evolution of materials and damage precursors.

Thermal effects of magnetohydrodynamic micropolar fluid embedded in porous medium with Fourier sine transform technique

Abstract: This paper investigates the thermal effects of magnetohydrodynamic micropolar fluid with hidden phenomenon of heat and mass transfer via Caputo–Fabrizio fractional derivative. Analytical solutions are obtained for velocity field, mass concentration, microrotation and temperature distribution by implementing Fourier Sine and Laplace transform. The general solutions have been expressed in terms of simple elementary functions involving the convolution theorem for the Laplace transform. The graphical illustration is depicted in order to explore the influence of rheological parameters, i.e., Grashof, Prandtl, Schmidt numbers, transverse magnetic field, microrotation parameter, porosity and few other parameters on micropolar fluid flow.

A Fourier Disparity Layer Representation for Light Fields

Abstract: In this paper, we present a new Light Field representation for efficient Light Field processing and rendering called Fourier Disparity Layers (FDL). The proposed FDL representation samples the Light Field in the depth (or equivalently the disparity) dimension by decomposing the scene as a discrete sum of layers. The layers can be constructed from various types of Light Field inputs, including a set of sub-aperture images, a focal stack, or even a combination of both. From our derivations in the Fourier domain, the layers are simply obtained by a regularized least square regression performed independently at each spatial frequency, which is efficiently parallelized in a GPU implementation. Our model is also used to derive a gradient descent-based calibration step that estimates the input view positions and an optimal set of disparity values required for the layer construction. Once the layers are known, they can be simply shifted and filtered to produce different viewpoints of the scene while controlling the focus and simulating a camera aperture of arbitrary shape and size. Our implementation in the Fourier domain allows real-time Light Field rendering. Finally, direct applications such as view interpolation or extrapolation and denoising are presented and evaluated.

Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings

Abstract: We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in one-dimensional periodic guided-mode resonant gratings consisting of a slab waveguide layer with a binary grating attached to one or both of its interfaces. Using these models, we obtain simple closed-form expressions predicting the locations of the BICs and quasi-BICs in the $\ensuremath{\omega}\text{\ensuremath{-}}{k}_{x}$ parameter space. We study two mechanisms of the BIC formation: coupling between two counterpropagating guided modes and coupling between a guided mode and a Fabry-P\'erot mode. The BIC conditions corresponding to the considered mechanisms are formulated in terms of the scattering coefficients of the binary grating. The predictions of the presented models are in excellent agreement with the results of full-wave simulations obtained using the Fourier modal method.

Sparse Fourier single-pixel imaging.

Abstract: Fourier single-pixel imaging is one of the main single-pixel imaging techniques. To improve the imaging efficiency, some of the recent method typically select the low-frequency and discard the high-frequency information to reduce the number of acquired samples. However, sampling only a small amount of low-frequency components will lead to the loss of object details and will reduce the imaging resolution. At the same time, the ringing effect of the restored image due to frequency truncation is significant. In this paper, a new sparse Fourier single-pixel imaging method is proposed that reduces the number of samples explorations while maintaining increased image quality. The proposed method makes a special use of the characteristics of the Fourier spectrum distribution based on which the power of image information decreases gradually from low to high frequencies in the Fourier space. A variable density random sampling matrix is employed to achieve random sampling with Fourier single-pixel imaging technology, followed by the processing of the sparse Fourier spectra using compressive sensing algorithms to recover the high-quality information of the object. The new algorithm can effectively improve the quality of object restoration comparing with the existing Fourier single-pixel imaging methods which only acquire the low-frequency parts. Additionally, considering that the resolution of the system is diffraction limited, super-resolution imaging can also be achieved. Experimental results demonstrate the mainly correctness but also effectiveness of the proposed method.

Fingerprint analysis of FTIR spectra of polymers containing vinyl acetate

Abstract: The analysis of materials using Fourier transform infrared (FTIR) spectroscopy has a unique area called the fingerprint region for each compound. However, this area is almost never discussed because of its complexity due to the large number of signals that appear in it. In this work, the fingerprint region analysis of the ethylene–vinyl acetate copolymer (EVA) with different percentages of vinyl acetate (VA) (18%, 28%, 40%) was performed. In comparison with other instrumental techniques, the crystallinity and structural arrangement of the EVA copolymers were determined simply and economically. The crystallinities for EVA18, EVA28 and EVA40 were 24.39%, 6.95% and1.03%, respectively. In terms of structural ordering, the number of linear chains of EVA copolymer decreases as the concentration of VA increases, which favors the reduction of degrees of freedom and the formation of hydrogen bonds.