Deception jammer suppression in fractional Fourier transformation domain with random chirp rate modulation

The issue addressed here is deception jammer suppression in radar systems. Advances in electronic countermeasure (ECM) technology are likely to change the requirements for electronic counter-countermeasures (ECCM), and the original specifications from which the systems were designed may no longer be appropriate. Here, the fraction Fourier transformation (FrFT) is used as a means of signal representation and filtering. A two-phase process is proposed based on random chirp rate modulation. First, the jamming signal is focused and excised. Second, the target echo is then focalized and refined. The approach yields to a two-block device in an actual radar system.     

AN EXACT METHOD FOR ANALYSING ELASTODYNAMIC RESPONSE OF ANISOTROPIC LAMINATES TO LINE LOADS

SUMMARY

An exact matrix formulation for analysing the responses of anisotropic laminated plates subjected to line loads is presented. In this formulation, a Fourier transform with respect to the horizontal spatial co-ordinate is employed and wave modes for a layer are obtained from an eigenvalue equation. Displacements in the wavenumber domain are obtained by using boundary conditions. A complex path is used and a new adaptive quadrature scheme is proposed to evaluate the inverse Fourier integration to obtain the displacement in the frequency domain. An exponential window method is used to compute responses in the time domain. Complex paths are investigated in detail to improve the efficiency for computing the responses of the plates for both pure and viscoelastic materials in both time and frequency domains. Numerical examples are presented to illustrate the present method.     

Generalized CAZA sequences

ABSTRACT

Constant amplitude zero auto-correlation (CAZA) sequences and periodic sequences have been widely used as preambles for synchronization and channel estimation in the literature. In this paper, we first construct generalized CAZA (GCAZA) sequences in the time domain. Then, their Cramer-Rao bounds containing no matrix inversion for the purpose of joint carrier frequency offset and channel impulse response estimation are derived. The properties of auto-correlation and the discrete Fourier transform of a GCAZA are then presented analytically. The latter also explains the relationship between the conventional frequency-domain CAZA and the proposed time-domain GCAZA. Finally, we conduct numerical simulations and compare the results with existing sequences in the literature for fading channels.     

Digital transform processing of carrier fringe patterns from speckle-shearing interferometry

Abstract

The Fourier transform (FT) and the wavelet transform (WT) methods are used to process the fringe carrier pattern resulting from speckle-shearing inteferometry, in which the carrier frequency is modulated by deformation of a bending plate. Both the amount and the sign of the first derivative of the out-of-plane displacement can be obtained by these two transform techniques in the whole field. Phase distributions of the deflection slope are compared, which shows the wavelet analysis gives a better solution with noise reduction and without deficiency of filter window choice as for that in the Fourier transform. Meanwhile, the phase values in the path along the maximum WT amplitudes give a direct map of the second derivative patterns of the deflection, which presents the same image as that given by the shearing subtraction of the phase patterns from the inverse Fourier transformation but avoids the processing of unwrapping for the phase reconstruction.     

Research on identification of nonlinear damping based on time frequency analysis

Abstract

According to the relationship between damping, strain and time, the piecewise linear wavelet transform and the piecewise linear short time Fourier transform methods are put forward to identify the nonlinear damping of alloy material. The overall nonlinear property of damping is derived from the piecewise local linearisation. The satisfied results obtained from simulations demonstrate that the methods presented are effective. Usually, damping measured in the non-uniform stress field is only a volumetric average. To overcome this deficiency, a trapezoid specimen with quasi-uniform stress field is developed on the basis of the traditional damping experimental equipment. The damping measurement experiment is carried out. The measurement signal is analysed by the two methods presented. The relation curve of damping versus strain has shown that the damping capacity of the alloy Al–33Zn–6Si increases with the increasing strain. The relationship between damping and strain appears obviously nonlinear.     

DFT Domain Characterization of Quasi-Cyclic Codes

 The transform domain characterization of linear cyclic codes over finite fields using Discrete Fourier Transform (DFT) over an appropriate extension field is well known. In this paper, we extend this transform domain characterization for linear quasi-cyclic codes over finite fields. We show how one can derive a lower bound on the minimum Hamming distance of a quasi-cyclic code and decode the code upto that minimum Hamming distance using this characterization. Received: January 17, 2002; revised version: November 30, 2002 RID="*" ID="*" This work was partly supported by CSIR, India, through Research Grant (22(0298)/99/EMR-II) to B. S. Rajan Keywords: Quasi-cyclic codes, Discrete Fourier transform, Cyclotomic cosets. Part of this work was presented in ICCCD 2000, Kharagpur, India and ISIT 2001, Washington D.C., USA     

Frequency Spectral Measurements of a Pulsed,TE CO2

Abstract

Experimental measurements of the intra-pulse chirp and temporal coherence from a Joule class TE CO₂ laser incorporating LAWS transmitter design features are presented. Digitized quadrature data (I and Q) from our ground-based coherent Doppler lidar system utilizing return signals off a hard target in the telescope far field are processed using fast Fourier transform and pulse pair techniques to obtain laser pulse frequency spectral components (offset frequency and spectral width) and high-resolution (～ 50 ns/sample) frequency chirp profiles. Less than 300 kHz of frequency chirp is observed in the first 3·5 μs of the laser pulse which contains approximately 90% of the pulse energy. Spectral width of the laser pulse, including both chirp and transform limited components, are measured to be less than 300 kHz full width at half maximum.     

Enhancing time-stamp counter phase modulation measurements

This paper demonstrates that digital signal processing techniques can enhance the quality of phase modulation measurements produced by a time-stamp (phase digitizing) frequency counter. A typical time-stamp counter utilizes a digital divider to reduce signal frequency to the desired sample rate. Unfortunately, division also reduces phase modulation to the point where useful information may be obscured by counter measurement uncertainty (jitter). An analogy between an analog-to-digital converter (ADC) and a time-stamp counter predicts that the counter induced modulation can be modeled as random noise which is white in phase. The noise magnitude is directly related to the instrument's resolution specification. Fourier analysis, subject to some restrictions, can compute the power spectra of phase or frequency modulation, revealing even low level responses. A number of techniques can be used to reduce the amount of counter induced noise that appears on time domain plots of phase and frequency modulation. Experimental data, generated by a prototype counter, illustrates the type of results that can be expected from Fourier analysis and various noise reduction techniques     

Multiscale windowed Fourier transform for phase extraction of fringe patterns

A multiscale windowed Fourier transform for phase extraction of fringe patterns is presented. A local stationary length of signal is used to control the window width of a windowed Fourier transform automatically, which is measured by an instantaneous frequency gradient. The instantaneous frequency of the fringe pattern is obtained by detecting the ridge of the wavelet transform. The numerical simulation and experiment have proved the validity of this method. The combination of the windowed Fourier transform and the wavelet transform makes the extracted phase more precise than other methods.     

免疫算法在分数阶Fourier变换域极值优化中的应用

利用线性调频(Linear Frequency Modulation,LFM)信号在分数阶Fourier域上的聚焦性,通过搜索可实现LFM信号的检测和参数估计。通常采用步进式搜索法,效率低下。为了克服该缺点,通过对分数阶Fourier域优化问题的研究,将免疫算法引入到分数阶Fourier变换极值搜索中。仿真结果表明:该方法优于传统的步进式搜索法。     

Photography by Infra-red

A novel approach to frequency multiplexing of images is presented. By modulating each image pixel at a different (temporal) frequency, the entire image can be transformed into an electrical signal utilizing a single detector. The electrical current of the detector is proportional to the spatial Fourier transform of the image, allowing one to perform spatial frequency manipulations in the time domain. The multiplexing is obtained by using a two-dimensional array of piezoelectric-elasto-optic modulators. By utilizing these effects one makes use of the mechanical resonance of the crystals simplifying the electrical signals needed for excitation. It is shown that a similar (or the same) modulator can be used for image reconstructions; i.e. performing the inverse Fourier transform. Preliminary results obtained with quartz crystals prove the feasibility of this approach.     

An improved computation of the pseudo Wigner‐Ville distribution and its applications

Abstract

The Wigner‐Ville distribution (WVD), generally calculated by the fast Fourier transform (FFT), is a useful tool for time‐frequency signal analysis. However, for nonstationary multicomponent signals, the inherent bilinear structure of the WVD causes undesirable interfering cross terms, and becomes troublesome to many applications. The FFT requires complex arithmetic computations, but the fast Hartley transform (FHT) only requires real arithmetic computations. Therefore, the FHT performs much faster than the FFT. An improved WVD computation using the FHT and running windowed exponential distribution is proposed in this paper. The cross‐terms of nonstationary multicomponent signals can be completely eliminated, and the result is favorable for pattern recognition and signal classification. The derived algorithm is also applied to building up a real‐time processing scheme for conducting experiments in an anechoic chamber.     

Time-frequency-based non-stationary interference suppression for noise radar systems

The problem addressed here is non-stationary interference suppression in noise radar systems. Towards this aim, two linear time ?frequency (TF) transforms, short-time Fourier transform and local polynomial Fourier transform are used as a means of signal representation and filtering. The noise radar return signal is a wideband random signal occupying the whole TF plane, whereas the interference signal is well concentrated in the TF plane. This implies that the filtering of the received signal can be performed by using a binary mask to excise only a portion of the TF plane corrupted by the interference. Simulations carried out on the radar return signal corrupted by extremely strong non-stationary interferences confirm the effectiveness of the proposed method.     

Peak-to-average power ratio reduction in OFDM using cyclically shifted phase sequences

Two approaches for reducing peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) are proposed that are relied on a set of cyclically shifted phase sequences (CSPS) and implemented using the time domain circular convolution. After multiplying CSPS with the frequency domain data, the signal candidates can be expressed as weighted sum of the circularly shifted OFDM time domain data in the first method, which is called CSPS method. In the second method, weighted coefficients for generating the signal candidates in CSPS method are optimally selected to improve its performance; thus, the second method is referred to as optimised CSPS (OCSPS) method. The performances of the CSPS and OCSPS methods are evaluated using simulated data and compared with those of selective mapping (SLM) and partial transmit sequences (PTS). The simulation results show that both the CSPS and OCSPS methods can reduce the PAPR effectively, and that the OCSPS performs even better than the CSPS. The OCSPS can achieve the same performance as compared to the PTS. A distinct feature of the proposed methods is that only one inverse discrete Fourier transform is needed, and thus, the candidates can be calculated in time domain directly.     

遗传算法在分数阶Fourier变换域极值优化中的应用

分数阶Fourier变换采用线性调频基,因此,线性调频（Linear Frequency Modulation,LFM）信号在分数阶Fourier域平面能够聚焦,并形成峰值。为了克服传统步进式搜索法在LFM信号峰值搜索中效率低下的缺点,将遗传算法引入到分数阶Fourier变换极值搜索中。仿真结果表明,该方法优于传统的步进式搜索法。     

Multiple fractional fourier transform hologram by use of holographic lens

Abstract

A new method is presented to record multiple fractional Fourier transform holograms by use of a holographic lens. With holographic lenses, several fractional Fourier transform holograms of different objects can be recorded in a simple way, and images of these recorded objects can be reconstructed in different positions and directions in three-dimensional space. In this paper, the theory and characteristics of the hologram recorded using the holographic lens are analysed. Using this method, a multiple fractional Fourier transform hologram was fabricated, with satisfactory results.     

ESTIMATION Of PARTICLE SIZE bY DRIFTS and FTIR-PAS

ABSTRACT

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) were used to study particle size and distribution of sucrose powder. Partial least squares (PLS) regression was used to correlate spectral data with particle size. FTIR-PAS spectra were similar to the spectra obtained using DRIFTS when the sample is mixed with 95% potassium bromide (KBr). Both DRIFTS and FTIR-PAS methods can successfully predict the mean panicle size and concentration in binary and quaternary mixtures. R-square values for both DRIFTS and FTIR-PAS are greater than 0.9.     

基于卡尔曼滤波的STFT域回声抵消算法

提出了一种低复杂度的短时傅里叶变换域卡尔曼滤波算法来解决声学回声抵消问题。首先在短时傅里叶变换域建立了基于频域卷积传递函数的观测方程,并利用一阶马尔科夫模型对频域回声路径进行建模,给出了精确的卡尔曼滤波方程,并讨论了过程噪声和观测噪声的估计问题。为降低算法计算复杂度,提出了低复杂度卡尔曼滤波算法。另外,在更新滤波器时加入远端信号邻近频点的信息来进一步提高回声抵消性能。实验结果表明,所提算法对近端干扰不敏感,不需要额外的双端对讲检测算法,且比传统的频域自适应滤波算法具有更快的收敛速度。     

Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform

Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with ±0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.     

Reconstruction of Scattering Potentials from Incomplete Data

Abstract

In many situations encountered in physics and in other fields, one can frequently experimentally determine some but not all the Fourier components of a scattering potential. In this paper we present an integral equation which makes it possible to reconstruct any square-integrable function f(r) of finite support from the knowledge of its Fourier transform j (K) over any finite three-dimensional domain of K space. We illustrate the use of this integral equation by application to potential scattering at fixed energy and we show how it can be used to reconstruct details of the scattering potential beyond the usual resolution limit from measurements of the scattered field in the far zone of the scatterer.