Estimating the length of a compact function from a noisy measurement of the modulus of its Fourier transform

Consider f, zero outside an interval of length L, and its Fourier transform F. It is known that, if arg F is unknown, L can be found from (a) the Fourier transform of |F|2 or (b) the Fourier transform of |F| exp(j?), where ? = Hilbert transfrom of In|F|. It appears that method (b) may be superior if |F| is measured in the presence of noise.     

Fourier transform of a polygonal shape function and its application in electromagnetics

The shape functions(x, y)of a planar apertureSigmais defined ashaving value one insideSigmaand zero outside. The two-dimensional Fourier transform ofs(x, y)whenSigmais anN-sided polygon is considered, and a closed-form exact solution is presented. Applications of these results are described for 1) the calculation of the secondary pattern of a reflector antenna with a noncircular aperture, and 2) high-frequency transmission through a periodic frequency selective surface.     

Examples of bivariate nonseparable compactly supported orthonormalcontinuous wavelets

We give many examples of bivariate nonseparable compactly supported orthonormal wavelets whose scaling functions are supported over [0,3]x[0,3]. The Holder continuity properties of these wavelets are studied.     

Precise expression relating the Fourier transform of a continuoussignal to the fast Fourier transform of signal samples

The fast Fourier transform (FFT) signature of a finite duration, constant frequency, time signal displays sidebands which are a sampling artifact. An analytical expression is derived which precisely predicts artifact behavior. Using this expression, a precise spectral estimate (PSE) is derived. It is demonstrated that this method outperforms the FFT with and without Hamming weighting both in estimating the magnitudes and phases of the spectral components of a time series. Furthermore, PSE is capable of resolving frequency to a fraction of an FFT frequency resolution cell     

一类长度为4的紧支撑正交小波基构造

根据紧支撑正交小波基的构造方法,由滤波器出发,构造满足Lawton充分条件的长度为4带参数的滤波器,它是文献[7]和[8]的一个推广。找到更一般化的具有紧支撑的正交小波基,并进行一维信号仿真实验,得到当m=2,a=5及m=3,a=10的正交小波在阈值=1的情况下,无论是用软阈值函数还是硬阈值函数,其信噪比都大于db2小波。     

基于变换域的IMS信号处理方法及其改进

讨论了一种基于变换域的离子迁移谱(IMS)信号处理方法-傅立叶变换离子迁移谱(FT-IMS)技术,通过离子门开关频率的改变实现信号的调制,得到频域的IMS信号.该技术使离子利用率由百分之一提高到了百分之二十五,信噪比(SNR)提高了14 dB以上;通过增加离子门开关频率的范围可以进一步提高分辨率,解决了IMS技术中SNR和分辨率相矛盾的问题.在此基础上,改进了FT-IMS算法,减弱了FT-IMS技术中镜像脉冲的干扰.经对FT-IMS算法和改进算法的数值仿真验证,证明了其有效性.     

Analysis of Chirp as windowing function through fractional Fourier transform

This article presents a new mathematical model for obtaining the fractional Fourier transform (FrFT) of Chirp function. FrFT is a parameterised transform having an adjustable transform parameter which makes it more flexible and superior over ordinary FT in several applications. It is an important tool used in signal processing for spectral analysis. The closed-form expression derived for FrFT of finite duration Chirp establishes the dependence of FrFT of Chirp on the order of FrFT and the Chirp parameter. The mathematical model obtained shows that the Chirp function can be used as an adjustable window function in the fractional Fourier domain. The main-lobe width, side-lobe level and side-lobe fall-off rate of a Chirp window can be controlled by changing the adjustable transform parameter to different values. For some particular values of fractional angle, Chirp can give better spectral parameters than the existing window functions. By varying the order of FrFT, the variations in spectral parameters of the Chirp window are obtained and studied. The performance of the Chirp window in fractional domain is also compared with some of the existing windows.     

Relationship between the ambiguity function coordinate transformations and the fractional Fourier transform

It has been shown that the fractional Fourier transform, recently very intensively investigated in mathematics, quantum mechanics, optics and signal processing, can be obtained as a special case of the earlier introduced linear coordinate transformations of the ambiguity function or Wigner distribution. Some applications of the generalized fractional transform on the time-frequency analysis are presented.     

傅里叶变换光谱仪探测器非线性的影响及其校正方法

针对傅里叶变换光谱仪探测器引起的非线性进行研究,阐述了非线性的产生、分析了非线性对光谱的影响以及介绍了两种校正二次项非线性的方法:卷积法和迭代法。并采用这两种方法对干涉图进行二次非线性校正,然后在卷积法与迭代法的基础上提出一种更适用于实际数据的新方法。最后采用这三种方法对模拟数据以及实际采集数据分别进行非线性校正,实验数据说明校正后非线性能得到抑制。并且通过对比发现,新的校正方法有较好的精度及更快的速度。     

Fourier transform of a linear distribution with triangular supportand its applications in electromagnetics

A three-dimensional Fourier transform (FT) of a linear function with triangular support is derived in its coordinate-free representation. The Fourier transform of this distribution is derived in three steps. First, the 2-D FT of a constant (top hat) function is obtained. Next, the distribution is generalized to a linearly varying function. Finally, the formulation is extended to a coordinate-free representation which is the 3-D FT of the 2-D function defined over a surface. This formulation is applied to the near-field computation, yielding accurate numerical solutions     

On the transform property of a band-limited function and its samples

Sampling and reconstruction of band-limited functions are fundamental problems in communications and signal processing. This correspondence introduces a new transform pair for any well behaved but arbitrary function f(t) and, thereafter, establishes two transform relationships between a band-limited function and its sample values. This work can be viewed as yet another comment and extension on the sampling theorem.     

Display of microwave pulse response via the real-time Fourier transform of the transfer function

It has been shown that the locating reflectometer evaluates, in real time, the Fourier transform of a signal applied to it. If a swept signal transmitted through a microwave 2-port (i.e. the transfer function) is applied to the instrument, it will display the pulse response. Transient phenomena taking just a few cycles of an X band carrier may be displayed, yet only low-frequency electronic circuitry is needed.     

Bayesian reconstruction of signals invariant under a space-groupsymmetry from Fourier transform magnitudes

A Bayesian signal reconstruction problem, motivated by X-ray crystallography, which includes magnitude of Fourier transform measurements and a Markov random field a priori model was approximately solved by Doerschuk (see J. Opt. Soc. Amer. A, vol.8, no.8, p.1222-1232 and p.1207-1221, 1991). These ideas are extended to signals that obey a space-group symmetry, which is a crucial extension for X-ray crystallography application. Performance statistics based on simulated data are presented.     

Real-time Fourier transform with a surface-wave convolver

The generation of Fourier transforms of electronic signals in real time with an acoustic-surface-wave convolver is demonstrated. Two matched chirps propagating through each other behave as a narrowband filter in wavevector space, with the filter centre moving at a rate proportional to the acoustic velocity and the chirp rate.     

Derivation of Fourier transform of discrete series from z-transform

The relationship between z-transform and Fourier transform of a discrete series is presented. The Fourier transform of a discrete series whose z-transform has poles on the unit circle can be derived using these results.<>     

基于分数阶Fourier变换的模糊函数及其在二次调频信号参数估计应用中的研究

作为处理非平稳信号的一种重要工具,模糊函数(ambiguity function,AF)已经被广泛应用于雷达信号处理、声纳技术等领域,并对线性调频信号信号的参数估计具有极好的处理能力。但对应用于众多领域的二次调频信号,模糊函数就显得无能为力了。作为Fourier变换的更广义形式,分数阶Fourier变换(Fractional Fourier transform)近年来受到了广泛关注。为解决二次调频信号的估计问题,本文研究了基于分数阶Fourier变换的模糊函数,给出了这种变换的一些新的重要性质,如共轭对称性、Moyal公式、时移性等,推导出了它与经典模糊函数、基于分数阶Fourier变换的Wigner分布、短时Fourier变换、小波变换等其他时频变换的关系。作为应用,最后本文用这种分数阶模糊函数来估计二次调频信号,应用实例的仿真结果表明了分数阶模糊函数在估计二次调频信号参数方面的可行性和有效性。      

Quality of signals reconstructed from degraded Fourier transform phase

Through a series of simulations with one dimensional real digital signals, the effects of various degrees of phase degradation for different lengths of sequences and for different choices in the set of sampling frequencies on the quality (as measured by normalised mean-square-error-NMSE) of signals reconstructed from noisy Fourier transform (FT) phases is established.<>     

Performance of a Fourier transform data transmission system

Results on the performance of a Fourier transform data transmission system in white Gaussian noise are presented for various quantisation widths and transform sizes.