The extended Fourier transform for 2D spectral estimation.

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals.     

Compression and reconstruction of MRI images using 2D DCT.

In magnetic resonance imaging (MRI), the original data are sampled in the spatial frequency domain. The sampled data thus constitute a set of discrete Fourier transform (DFT) coefficients. The image is usually reconstructed by taking inverse DFT. The image data may then be compressed using the discrete cosine transform (DCT). We present here a method of treating the data that combines two procedures, image reconstruction and data compression. This method may be particularly useful in medical picture archiving and communication systems (PACS) where both image reconstruction and compression are important issues.     

Application of maximum entropy methods in NQR data processing

The superiority of maximum entropy method (MEM) over the traditional fast Fourier transform (FFT) method is demonstrated in NQR spectral analyses. Using computersimulated and real spectral data, a comparative study was made between the maximum entropy and the conventional discrete Fourier transform methods. It is concluded that use of MEM in NQR spectroscopy can lead to sensitivity improvements, reduction of instrumental artifacts and truncation errors, shortened data acquisition times and automatic suppression of noise, while at the same time increasing the resolution. A property of MEM which is particularly significant for two-dimensional NQR spectroscopy is its ability to produce spectral estimates from the short data records, free of truncation artifacts. The use of MEM in two-dimensional NQR studies can lead to reduction of the time necessary to acquire two-dimensional set.     

基于相位相关性的傅里叶变换光谱数据的相位误差修正方法

 相位误差的校正是傅里叶变换成像光谱仪数据处理的重要环节之一。针对干涉曲线的对称性特征,利用相位相关性计算方法,提出一种新的傅里叶变换光谱数据的相位校正的方法。将相位相关性拟合为Sinc函数,计算亚像素的偏移量,采用离散余弦变换转换到光谱域。使用标准光谱库中的源光谱数据作为原始数据,将通过离散余弦变换仿真的干涉数据与该方法得到的结果进行比较和验证,并与Mertz方法进行了对比。结果表明：该方法精度优于Mertz方法,并且计算简单。     

Discrete Transforms and Matrix Rotation Based Cancelable Face and Fingerprint Recognition for Biometric Security Applications

The security of information is necessary for the success of any system. So, there is a need to have a robust mechanism to ensure the verification of any person before allowing him to access the stored data. So, for purposes of increasing the security level and privacy of users against attacks, cancelable biometrics can be utilized. The principal objective of cancelable biometrics is to generate new distorted biometric templates to be stored in biometric databases instead of the original ones. This paper presents effective methods based on different discrete transforms, such as Discrete Fourier Transform (DFT), Fractional Fourier Transform (FrFT), Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT), in addition to matrix rotation to generate cancelable biometric templates, in order to meet revocability and prevent the restoration of the original templates from the generated cancelable ones. Rotated versions of the images are generated in either spatial or transform domains and added together to eliminate the ability to recover the original biometric templates. The cancelability performance is evaluated and tested through extensive simulation results for all proposed methods on a different face and fingerprint datasets. Low Equal Error Rate (EER) values with high AROC values reflect the efficiency of the proposed methods, especially those dependent on DCT and DFrFT. Moreover, a comparative study is performed to evaluate the proposed method with all transformations to select the best one from the security perspective. Furthermore, a comparative analysis is carried out to test the performance of the proposed schemes with the existing schemes. The obtained outcomes reveal the efficiency of the proposed cancelable biometric schemes by introducing an average AROC of 0.998, EER of 0.0023, FAR of 0.008, and FRR of 0.003.     

On BER assessment of conventional- and wavelet-OFDM over AWGN channel

Orthogonal wavelets enclose more potential of dropping the ISI- and ICI-sway amid the carriers due to multipath propagation over the free-space fading channels. Moreover, wavelet-OFDM is more bandwidth efficient as compared to conventional OFDM and is less affected by Doppler shift. Accordingly, a BER estimation of discrete Fourier transform (DFT) based OFDM system and discrete wavelet transform (DWT) based OFDM system is carried out in this work. The assessment is demonstrated by means of diverse modulation schemes explicitly BPSK, QPSK, 8-PSK, QAM, 8-QAM, 16-QAM for both conventional- and wavelet-OFDM wireless system over AWGN channels. Higher orders of PSK schemes involve more SNR requirement to target an acceptable BER of 10⁻⁵ over AWGN channels in both the cases. Furthermore, the efficiency of W-OFDM increases with decreasing the required value of BER.     

Fourier analysis for rotating-element ellipsometers

We introduce a Fourier analysis of the waveform of periodic light-irradiance variation to capture Fourier coefficients for multichannel rotating-element ellipsometers. In this analysis, the Fourier coefficients for a sample are obtained using a discrete Fourier transform on the exposures. The analysis gives a generic function that encompasses the discrete Fourier transform or the Hadamard transform, depending on the specific conditions. Unlike the Hadamard transform, a well-known data acquisition method that is used only for conventional multichannel rotating-element ellipsometers with line arrays with specific readout-mode timing, this Fourier analysis is applicable to various line arrays with either nonoverlap or overlap readout-mode timing. To assess the effects of the novel Fourier analysis, the Fourier coefficients for a sample were measured with a custom-built rotating-polarizer ellipsometer, using this Fourier analysis with various numbers of scans, integration times, and rotational speeds of the polarizer.     

Detection of pseudoperiodic patterns using partial acquisition of magnetic resonance images

Improving the resolution of magnetic resonance imaging (MRI), or, alternatively, reducing the acquisition time, can be quite beneficial for many applications. The main motivation of this work is the assumption that any information that is a priori available on the target image could be used to achieve this goal. In order to demonstrate this approach, we present a novel partial acquisition strategy and reconstruction algorithm, suitable for the special case of detection of pseudoperiodic patterns. Pseudoperiodic patterns are frequently encountered in the cerebral cortex due to its columnar functional organization (best exemplified by orientation columns and ocular dominance columns of the visual cortex). We present a new MRI research methodology, in which we seek an activity pattern, and a pattern-specific experiment is devised to detect it. Such specialized experiments extend the limits of conventional MRI experiments by substantially reducing the scan time. Using the fact that pseudoperiodic patterns are localized in the Fourier domain, we present an optimality criterion for partial acquisition of the MR signal and a strategy for obtaining the optimal discrete Fourier transform (DFT) coefficients. A by-product of this strategy is an optimal linear extrapolation estimate. We also present a nonlinear spectral extrapolation algorithm, based on projections onto convex sets (POCSs), used to perform the actual reconstruction. The proposed strategy was tested and analyzed on simulated signals and in MRI phantom experiments.     

玉米品种近红外光谱的DFT特征分析方法

提出了一种基于离散傅里叶变换(discrete Fourier transform,DFT)的玉米品种特征分析新方法.实验数据为37个玉米晶种种子的近红外漫反射光谱数据,波段范围为4 000～12 000 cm-1.文中通过对原始数据进行分析,发现扫描频率较高的部分噪声也比较大.文中首先定义了一种类间、类内差异度Qm的...     

A quantum search algorithm of two entangled registers to realize quantum discrete Fouriertransform of signal processing

The discrete Fourier transform （DFT） is the base of modern signal processing. 1-dimensional fast Fourier transform （1D FFT） and 2D FFT have time complexity O（N log N） and O（N^2 log N） respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover＇s iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT （1D QDFT） and two-dimensional quantum DFT （2D QDFT） are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, 1D and 2D QDFT have time complexity O（v/N） and O（N） respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.     

Estimation of generalized frequency response functions for quadratically and cubically nonlinear systems

A new method of estimating the Volterra kernels in the frequency-domain is introduced based on a non-parametric algorithm. Unlike the traditional non-parametric methods using the frequency-domain formulations based on discrete Fourier transform (DFT) data, this new approach uses the time-domain measurements directly to estimate the frequency-domain response functions.     

抽样对傅里叶变换轮廓术的影响

以变形结构光场为研究对象,分析抽样对傅里叶变换轮廓术测量范围的影响,提出了实际测量中抽机频率选择的判断依据,计算机模拟和初步实验证明了理论的可靠性和可行性。     

Generalized fiber Fourier optics

A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.     

基于背景信息的磁共振成像尖峰噪声消除

磁共振成像扫描过程中如果在K空间中出现尖峰噪声,将会严重影响图像质量. 该文提出了一种利用磁共振图像背景信息来定位并修复尖峰噪声的方法. 首先将K空间数据沿着频率编码k_x和相位编码k_y 2个方向分别进行一维傅立叶变换,然后在获得的2个中间域数据中,分别截取出背景区域, 进行一维反傅立叶变换得到与背景对应的频率域数据,通过对背景频率域数据的分析,获得尖峰噪声的k_x和k_y坐标,最后对异常点进行修复. 该算法可以很好地消除各种模式的尖峰噪声,与已有的算法相比,能够更好地处理K空间中连续多个相位编码行上出现尖峰噪声的情况,有效地消除图像伪影.     

Thin-film thickness profile measurement using wavelet transform in wavelength-scanning interferometry

We proposed a new method for retrieving the phase from wavelength-scanning interferogram by wavelet transform. We demonstrate, with both theoretical and experimental data, that this method provides a reliable technique for retrieving phase in the wavelength-scanning interferometry. We show that the proposed method by wavelet transform can reconstruct the nonlinear phase better than the conventional Fourier transform and direct spectral phase calculation method by simulation. The patterned thin film is measured to get the thickness and surface profile simultaneously with the developed wavelength-scanning interferometry.     

Narrow peaks and high dimensionalities: Exploiting the advantages of random sampling

Level of artifacts in spectra obtained by Multidimensional Fourier Transform has been studied, considering randomly sampled signals of high dimensionality and long evolution times. It has been shown theoretically and experimentally, that this level is dependent on the number of time domain samples, but not on its relation to the number of points required in appropriate conventional experiment. Independence of the evolution time domain size (in the terms of both: dimensionality and evolution time reached), suggests that random sampling should be used rather to design new techniques with large time domain than to accelerate standard experiments. 5D HC(CC-TOCSY)CONH has been presented as the example of such approach. The feature of Multidimensional Fourier Transform, namely the possibility of calculating spectral values at arbitrary chosen frequency points, allowed easy examination of resulting spectrum. We present the example of such approach, referred to as Sparse Multidimensional Fourier Transform.     

Modification of the discrete spectral parameters of optical solitons in fibers with variable dispersion

The spectral parameters of solitons result from the nonlinear Fourier transform for a pulse propagating in a fiber. A new approach for controlling the discrete component of spectral parameters is proposed. In the presence of a resonance between field oscillations and fiber dispersion, the real part of spectral parameters change, which leads to multisoliton pulse separation into fundamental solitons. It is proposed to use this effect for signal decoding in communication lines operating based on the nonlinear Fourier transform.     

空间调制干涉光谱成像仪光谱定标技术研究

为了对干涉光谱成像仪进行光谱定标,针对空间调制该仪器的原理,得出了其光程差和光谱分辨率的计算方法,并分析了仪器的线型函数.在实验中使用多种单色光源(波长范围:450～950 nm)和扩束准直镜(焦距120 mm、口径50 mm)进行光谱定标测试.结果表明:影响实验室光谱定标不确定度的主要因素为d/f的测量误差和标准光谱的误差.     

塑料挥发物长光程FTIR测量方法

塑料产品除了在自然环境中可降解为微塑料污染环境之外,还会产生挥发性有机物,同样对环境造成巨大的污染和危害,因此对塑料挥发物的测量就显得尤为重要。目前传统挥发物的测量方法,如环境质谱法和色谱法等,存在测量过程复杂,成本高,无法实时测量等缺点,因而需要一种快速有效的针对塑料挥发物的测量方法。采用傅里叶变换红外光谱仪（Fourier transform infrared spectrometer,FTIR Spectrometer）结合怀特池对塑料挥发物进行测量,但是由于抽取式傅里叶变换红外光谱仪本身灵敏度有限,很难实现微量的塑料挥发物的测量,所以针对这一问题,尝试通过长光程气体池提高常规傅里叶变换红外光谱仪的灵敏度从而实现不同种类塑料挥发物的测量。选取了5种塑料产品,分别是低密度聚乙烯（LDPE）,高密度聚乙烯（HDPE）,聚乙烯（PE）,聚对苯二甲酸乙二醇酯（PET）,聚丙烯（PP）,利用光程长为20 m的怀特池结合傅里叶变换红外光谱仪实现了其中一些挥发物的光谱特征观测,实验观察到所有种类的塑料在2个光谱波数段具有明显的光谱特征,分别为800~850和1 050~1 150 cm-1。除聚对苯二甲酸乙二醇酯（PET）外,其余4种塑料挥发物在2 800~3 000 cm-1还存在明显的光谱吸收波段。进一步又研究了不同温度条件下塑料产生的挥发物,通过分析不同温度条件下的塑料产生的挥发物的红外光谱,发现除低密度聚乙烯（LDPE）在两种温度条件下光谱差异较大外,其他种类的塑料挥发物红外光谱差异较小。该研究提出了一种新型的基于长光程FTIR的塑料挥发物的测量方法,证实了其在塑料挥发物测量方面的有效性,这种方法具有测量成本低,可连续观测,实时在线等优点,为实现连续在线的塑料挥发物排放通量监测奠定了基础。     

非相干光实现的二维复数离散傅里叶变换

本文给出了用非相干光束来实现二维复数离散傅里叶交换的方法.建立了一个多成像光学系统.此系统充分利用了光的平行处理特性,二维数据可同时处理.光学上的复数表示可采用二种编码方法来实现.我们选取了N=6二维输入数据来验证上述方法,实验所获得的结果与计算机模拟相一致.