Short-time fractional Fourier methods for the time-frequency representation of chirp signals

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.     

线性调频信号激励过阻尼双稳系统的随机共振现象研究

线性调频信号是工程中常见的一种信号, 由于其为非周期信号, 无法以频域信噪比作为衡量其是否产生随机共振的测量手段, 故鲜有文献研究以线性调频信号为激励信号的随机共振现象. 本文利用线性调频信号在最优分数阶Fourier变换域上的能量聚集性, 首次提出以最优分数阶Fourier变换域上定义的信噪比作为测量手段, 研究了线性调频信号叠加高斯白噪声激励过阻尼双稳系统的随机共振现象, 且发现了以线性调频信号为激励信号时产生的新现象, 即随着信号频率的增大, 随机共振将逐渐减弱, 并给出了合理的解释.仿真的结果与理论分析一致, 验证了本文所提出方法的有效性. 关键词： 线性调频信号 分数阶Fourier变换 随机共振     

Convolution and Filtering in Fractional Fourier Domains

Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.     

Generalized fractional S-transform and its application to discriminate environmental background acoustic noise signals

We propose a modification of S-transform (ST) by changing the kernel of Fourier transform (FT) with that of fractional Fourier transform (FRFT) and call it generalized fractional ST (GFST). The FRFT is a generalization of FT and it has been shown more useful than the FT for signals with changing frequencies such as chirp signals. The proposed GFST is applied to analyze and classify different environmental background sound mixed with speech signal in the form of additive noise. The simulation results demonstrate that Euclidean distance between the feature vectors computed from generalized fractional ST corresponding to different background noise is increased as compared to ST for the same set of feature vectors and signals.     

Bio-inspired wideband sonar signals based on observations of the bottlenose dolphin (Tursiops truncatus)

This paper uses advanced time-frequency signal analysis techniques to generate new models for bio-inspired sonar signals. The inspiration comes from the analysis of bottlenose dolphin clicks. These pulses are very short duration, between 50 and 80 micros, but for certain examples we can delineate a double down-chirp structure using fractional Fourier methods. The majority of clicks have energy distributed between two main frequency bands with the higher frequencies delayed in time by 5-20 micros. Signal syntheses using a multiple chirp model based on these observations are able to reproduce much of the spectral variation seen in earlier studies on natural dolphin echolocation pulses. Six synthetic signals are generated and used to drive the dolphin based sonar (DBS) developed through the Biosonar Program office at the SPAWAR Systems Center, San Diego, CA. Analyses of the detailed echo structure for these pulses ensonifying two solid copper spherical targets indicate differences in discriminatory potential between the signals. It is suggested that target discrimination could be improved through the transmission of a signal packet in which the chirp structure is varied between pulses. Evidence that dolphins may use such a strategy themselves comes from observations of variations in the transmissions of dolphins carrying out target detection and identification tasks.     

基于多项式调频Fourier变换的信号分量提取方法

为了从含有噪声的混合信号中有效提取各个信号分量, 提出一种基于多项式调频Fourier变换的分量提取方法. 通过研究Fourier变换和分数阶Fourier变换的信号能量积累方式及变换基函数的时频表示, 提出利用时频平面上的多项式调频曲线族代替Fourier变换和分数阶Fourier 变换的调频直线族, 将变换的适用范围扩展到非线性调频信号. 采用粒子群智能优化算法搜索调频曲线族的最优多项式参数, 使混合信号中的某一分量在多项式调频Fourier域上能量谱集中. 最后对能量谱集中的分量进行窄带滤波, 并利用多项式调频逆Fourier变换重构信号分量. 仿真实验结果表明, 该方法不仅能够提取混合信号中的线性调频分量, 还能够实现非线性调频分量的能量谱集中、信号分离和时频特征提取.     

分数傅里叶变换啁啾滤波

针对常规傅里叶变换所不能解决的啁啾噪声滤除问题，利用Wigner分布函数分析分数傅里叶变换的空域和频域特性，提出在分数傅里叶变换域进行啁啾滤波的方法。并将该方法应用到图像处理中，对分数傅里叶变换滤除一维和二维图像的啁啾噪声进行了计算机仿真，获得了满意的效果，结果表明该方法在图像处理中的有效性。     

Intensity analysis methods for transient signals

Conventionally, the Fourier transform is applied for sound intensity analysis of stationary signals, but this method can be applied for analyzing non-stationary transient signals. Instead of the Fourier transform analysis, instantaneous spectrum analysis methods such as the Wigner-Ville distribution and the wavelet transform are proposed. By using the mathematical example as a transient signal, advantages and disadvantages of these methods including the short-time Fourier transform are compared. From calculation results, it is considered that the STFT method is the most suitable for the accurate measurement of sound intensity levels, but the WT method is also recommended from its higher resolution of transient signals.     

Confusion effects with sinusoidal and narrow-band noise forward maskers

In some forward-masking conditions, signal thresholds may be elevated by the listener's inability to distinguish the signal from the preceding masker. In this study, such "confusion" effects are investigated for both sinusoidal and narrow-band noise forward maskers combined with sinusoidal signals of varying duration. Results for the sinusoidal maskers show effects of off-frequency listening for brief signals and possibly small effects of confusion for longer signals. Results for the narrow-band noise maskers show a marked influence of confusion over a wide range of signal durations. This range is in good agreement with that predicted from previous work with "pulsing" maskers [D. Neff, J. Acoust. Soc. Am. 78, 1966-1976 (1985)]. These results suggest that studies using narrow-band noise forward maskers or studies of psychophysical suppression should include direct tests for confusion effects in key conditions.     

Acoustic features based on auditory model and adaptive fractional Fourier transform for speech recognition

It is well known that auditory system of human beings has excellent performance which automatic speech recognition(ASR) systems can’t match,and fractional Fourier transform (FrFT) has unique advantages in non-stationary signal processing.In this paper,the Gammatone filterbank is applied to speech signals for front-end temporal filtering,and then acoustic features of the output subband signals are extracted based on fractional Fourier transform. Considering the critical effect of transform order for FrFT,an order adaptation method based on the instantaneous frequency is proposed,and its performance is compared with the method based on ambiguity function.ASR experiments are conducted on clean and noisy Putonghua digits,and the results show that the proposed features achieve significantly higher recognition rate than the MFCC baseline,and the order adaptation method based on instantaneous frequency has much lower complexity than that based on ambiguity function.Further more,the FrFT-based features achieve the highest recognition rate using the proposed order adaptation method.     

Echolocation behavior of franciscana dolphins (Pontoporia blainvillei) in the wild

Franciscana dolphins are small odontocetes hard to study in the field. In particular, little is known on their echolocation behavior in the wild. In this study we recorded 357 min and analyzed 1019 echolocation signals in the Rio Negro Estuary, Argentina. The clicks had a peak frequency at 139 kHz, and a bandwidth of 19 kHz, ranging from 130 to 149 kHz. This is the first study describing echolocation signals of franciscana dolphins in the wild, showing the presence of narrow-band high frequency signals in these dolphins. Whether they use other vocalizations to communicate or not remains uncertain.     

Libera数字束流位置处理器在工作点测量中的应用

 数字信号处理技术在现代束流诊断中有成熟的应用，特别是在束流位置检测器信号分析和工作点测量时有优越的性能。在合肥光源工作点测量中,采用高斯白噪声激励起束流横向振荡，再利用Libera数字束流位置处理器采集激励后的束流位置信号，并进行幅度解调得到束流横向振荡频率，再利用Matlab进行快速傅里叶分析处理，得到工作点的小数部分，从而实现工作点测量。在合肥光源上进行实验，测量得到其水平工作点是3.535 2，垂直工作点是2.629 9。     

非高斯环境下的深度学习脉冲信号去噪与重构*

侧扫声呐进行沉底小目标探测时,底混响是主要背景干扰。底混响通常是一种非平稳、非高斯的带限噪声,它使得白噪声条件下的滤波器性能受到限制。在混响背景下常利用自回归模型对接收信号进预行白化处理,但对于实际侧扫声呐应用,白化后直接匹配滤波的处理效果不甚理想。针对此问题,在自回归模型预白化的基础上,提出采用一种次最佳检测与多分辨二分奇异值分解相结合的改进方法。该方法首先对接收信号进行分段处理,利用改进Burg算法估计每段数据自回归模型的系数及阶数;然后构造白化滤波器对分段数据预白化,并对白化后的数据进行多分辨二分奇异值分解;最后应用ostu方法对原始声图和处理后的声图进行目标检测。仿真与实验结果表明,该方法明显提高了信混比,改善了侧扫声呐沉底静态小目标的成图质量,有利于后期实现基于图像的目标自动检测。     

一阶光学系统分数傅里叶变换的相空间分析

在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件.     

Fractional Fourier transform in information processing, tomography of optical signal, and Green function of harmonic oscillator

A review of the properties of the fractional Fourier transform, which is used in information processing, is presented in connection with the symplectic tomography transform of optical signals. The relationship between the Green function of the quantum harmonic oscillator and the fractional Fourier transform is elucidated. An analysis of electromagnetic signals which uses an invertible map of analytic signal onto the tomographic probability distribution is made. The formal connection of the analysis with the tomography method of measuring quantum states is considered. The relation to other methods of time-frequency quasidistributions (for example, the Ville-Wigner quasidistribution) characterizing a signal is studied. Paper submitted by author in English February 15, 1999.     

S变换轮廓术中消除条纹非线性影响的方法

S变换是短时傅里叶变换和小波变换的延伸和推广,是一种无损可逆的非平稳信号时频分析方法.它不仅具有线性、多分辨性和逆变换唯一性等特点,而且其反变换与傅里叶变换保持着直接的联系.在S变换中,以简谐波作为基波,以可以同时进行伸缩和平移的高斯函数作为窗函数.同短时傅里叶变换相比,S变换的时频分辨率可以同时达到最佳,同小波变换相...     

Modeling the recorded spectrum and reconstructing the transfer function of the wideband ionospheric HF radio channel in the case of chirp sounding

We model theoretically the received spectrum in the case of sounding of the ionospheric HF radio channel by a chirp signal. It is shown that the result of processing of an individual time sample of the received signal is equivalent to the sounding of the radio channel by a complex narrow-band pulsed signal such that the group delays of its propagation modes determine the maxima in the received spectrum. We analyze the quadrature components of realizations of the received signal at the intermediate frequency at the bandpass-filter output in the receiving channel of the chirp ionosonde. The results of our analysis show the possibility of reconstructing the transfer function of a HF radio channel in the sounding-frequency band for the delay range determined by the characteristics of the intermediate-frequency bandpass filter. We propose a method for reconstructing the transfer function of the ionospheric radio channel, which involves supplementing the circuit of primary processing of the signal by a corrective digital filter with specified amplitude-frequency and phase-frequency characteristics. The proposed method can be used for all operating regimes of the chirp ionosonde in the case of digital recording and processing of signals. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 5, pp. 387–395, May 2007.     

针对磁共振射频脉冲的时频域分析方法比较研究

射频脉冲可实现样本自旋体系的精确操控,进而产生预期的核磁共振(NMR)信号,在NMR信号产生过程中扮演重要角色.该文分别采用短时傅里叶变换(STFT)、连续小波变换(CWT)和维格纳-威利分布(WVD)几种时频域分析方法对射频脉冲(优化形状脉冲)进行特性分析和比较.结果表明,三种方法各自具有优缺点,结合各自优势对射频脉冲进行各种方法分析,可以更好地理解复杂脉冲的幅度、相位特性在时频域的分布情况.该文的研究方法将为直观理解复杂射频脉冲对自旋体系的作用机制提供参考.