Statistical properties of the LMS fourier analyzer in the presence of frequency mismatch

The statistical performances of the conventional adaptive Fourier analyzers, such as the least mean square (LMS), the recursive least square (RLS) algorithms, and so forth, may degenerate significantly, if the signal frequencies given to the analyzers are different from the true signal frequencies. This difference is referred to as frequency mismatch (FM). We analyze extensively the performance of the conventional LMS Fourier analyzer in the presence of FM. Difference equations governing the dynamics and closed-form steady-state expression for the estimation mean square error (MSE) of the algorithm are derived in detail. It is revealed that the discrete Fourier coefficient (DFC) estimation problem in the LMS eventually reduces to a DFC tracking one due to the FM, and an additional term derived from DFC tracking appears in the closed-form MSE expression, which essentially deteriorates the performance of the algorithm. How to derive the optimum step size parameters that minimize or mitigate the influence of the FM is also presented, which can be used to perform robust design of step size parameters for the LMS algorithm in the presence of FM. Extensive simulations are conducted to reveal the validity of the analytical results.     

一种可变步长傅里叶分析器的统计特性分析

可变步长最小均方(Variable step-size LMS,VSS-LMS)算法的傅里叶分析器在稳态误差、收敛速度及追踪能力方面具有优异性能,对其进行全面的统计特性分析具有重要意义.本文基于误差服从高斯分布等假设在平均及均方意义下,推导出描述系统动态特性的差分方程组,完成系统的动态数学建模,进而对系统进行稳态性能分析,给出系统稳态误差关于参考信号频率、系统参数和附加噪声的表达式,为系统应用中的参数选取提供有效指导.仿真表明,本文建立的统计模型与仿真结果具有一致性,验证了分析的有效性.     

LFM信号参数估计的插值FrFT修正算法

针对线性调频（LFM）信号参数估计插值FrFT算法在信噪比较低时性能下降而且针对不同参数估计性能不稳定的问题,提出了一种修正的插值FrFT算法。首先分析了现有插值FrFT算法问题出现的原因,然后定义了分数阶域量化频率,指出当信噪比较低时,若LFM信号初始频率接近分数阶域量化频率点,插值FrFT算法出现反向补偿的概率增大,性能下降。修正的插值FrFT算法改进了插值方向的判决条件以提高噪声免疫力,并通过频移LFM信号初始频率使其不在分数阶域量化频率点附近。最后,对不同初始频率的LFM信号进行仿真,结果表明,修正的插值FrFT算法提高了LFM信号参数估计精度,性能稳定,而计算量并没有明显增加。      

Bias correction and forward-backward averaging in frequency/DOA tracking problems

In this paper, we discuss some issues relevant to frequency and direction of arrival (DOA) tracking problems. First, we develop a linear Frequency Modulated (FM) signal model for accurately describing windowed, slowly time varying narrowband signals that typically occur in tracking problems. We then derive first order bias expressions for the peak locations of a Discrete Time Fourier Transform (DTFT) spectrum of a windowed, slowly time varying linear FM signal. We also show that Forward-Backward (FB) averaging is generally inappropriate for nonstationary data, but that it is appropriate when applied to tracking the frequencies of windowed, slowly time varying narrowband signals. A major motivation for using FB averaging is to increase the efficiency of subspace based frequency/DOA estimation in tracking problems. Finally, simulations confirm our first order bias expressions, and show that FB averaging does not significantly alter (or degrade) the time varying MUSIC based frequency estimation performance over that of Forward only averaging.This research was supported in part by the National Science Foundation Grant MIP-9203296 and Texas Advanced Research Program Grant 009741-022 and 009741-065.     

Analysis of Acoustic Events in Speech Signals Using Bessel Series Expansion

In this paper, we propose an approach for the analysis and detection of acoustic events in speech signals using the Bessel series expansion. The acoustic events analyzed are the voice onset time (VOT) and the glottal closure instants (GCIs). The hypothesis is that the Bessel functions with their damped sinusoid-like basis functions are better suited for representing the speech signals than the sinusoidal basis functions used in the conventional Fourier representation. The speech signal is band-pass filtered by choosing the appropriate range of Bessel coefficients to obtain a narrow-band signal, which is decomposed further into amplitude modulated (AM) and frequency modulated (FM) components. The discrete energy separation algorithm (DESA) is used to compute the amplitude envelope (AE) of the narrow-band AM-FM signal. Events such as the consonant and vowel beginnings in an unvoiced stop consonant vowel (SCV) and the GCIs are derived by processing the AE of the signal. The proposed approach for the detection of the VOT using the Bessel expansion is shown to perform better than the conventional Fourier representation. The performance of the proposed GCI detection method using the Bessel series expansion is compared against some of the existing methods for various noise environments and signal-to-noise ratios.     

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。      

基于时延估计算法的透明转发器的实现方法

讨论了转发器实现收发不间断的方法,提出了在自适应噪声相消的系统上,将简化的分数阶傅里叶变换理论应用于时延估计,进而将干扰信号重构抵消。推导了该算法,并提出基于该算法实现收发同时进行的转发器系统,即透明转发器。给出本系统模型框图,该透明转发器采用最小均方(LMS)算法建立自适应系统控制结构,能够通过自适应滤波器将自发干扰信号减除,并将不相关的背景噪声抵消。最后利用 MATLAB 软件仿真了基于该算法的透明转发器在具体信号上的运用,实验结果表明该方法实现了不间断转发功能,并且系统结构简单、易实现。     

Temporal tracking of spectral variations

We propose a data adaptive spectral estimation algorithm which is suitable for nonstationary estimation situations. This algorithm is based on the conventional Fourier transform of the estimated autocorrelation function. The data adaptive feature is implemented into the autocorrelation function estimation. The algorithm is computationally efficient due to its recursive nature. Its frequency tracking performance is tested against another adaptive algorithm based on the frequently used least mean square algorithm (LMS) of Widrow and Hoff (1960). The two algorithms demonstrate similar performance in many situations. Computer simulations indicate that, when applied to a signal composed of two sinusoids with different power levels, the proposed algorithm tracks the lower-powered sinusoid better than the LMS algorithm.     

Comparative tracking performance of the LMS and RLS algorithms forchirped narrowband signal recovery

This paper studies the comparative tracking performance of the recursive least squares (RLS) and least mean square (LMS) algorithms for time-varying inputs, specifically for linearly chirped narrowband input signals in additive white Gaussian noise. It is shown that the structural differences in the implementation of the LMS and RLS weight updates produce regions where the LMS performance exceeds that of the RLS and other regions where the converse occurs. These regions are shown to be a function of the signal bandwidth and signal-to-noise ratio (SNR). LMS is shown to place a notch in the signal band of the mean lag filter, thus reducing the lag error and improving the tracking performance. For the chirped signal, it is shown that this produces smaller tracking error for small SNR. For high SNR, there is a region of signal bandwidth for which RLS will provide lower error than LMS, but even for these high SNR inputs, LMS always provides superior performance for very narrowband signals     

LFM信号的分数阶傅里叶域自适应滤波算法研究

对于线性调频信号(LFM)的滤波,采用处理平稳信号的方法对其滤波往往得不到很好的效果。本文利用了线性调频信号在分数傅里叶变换域上具有很好的时频聚焦性的特点,来实现信号在分数阶傅里叶域的自适应滤波,自适应滤波算法采用改进的步长LMS方法,对传统的LMS算法做出了改进,算法中步长处理中引入了一个限制因子,可以较好地解决算法收敛速度和稳态失调量之间的矛盾。仿真结果表明,此算法在处理分数阶域的LFM信号滤波比传统的LMS算法有较好的滤波效果。      

Superresolution techniques for time-domain measurements with anetwork analyzer

Superresolution techniques for time delay estimation are proposed and applied to frequency-domain data measured with a network analyzer. A MUSIC (multiple signal classification) algorithm preprocessed by spatial smoothing is used. The spatial smoothing preprocessing is performed to destroy signal coherence, and the decorrelation performance is examined in detail. The expression which gives an individual response is given. Using this expression, it is possible to eliminate unwanted signals that appear as ripples in the frequency domain. Experimental results show that the frequency bandwidth required by the MUSIC algorithm to resolve distinct time-domain responses and eliminate unwanted signals is much narrower than that required by the FFT (fast Fourier transform). Thus, the MUSIC algorithm is applicable to the time-domain measurements with the network analyzer and has much higher resolution capability than the conventional FFT techniques. The MUSIC algorithm is one of the most promising methods of enhancing the accuracy of measurement for narrowband devices such as antennas     

Algorithmic Measurement of Digital Instantaneous Frequency

This paper presents an algorithmic method for measuring the instantaneous frequency of a uniformly sampled FM signal. The measured parameter, termed digital instantaneous frequency, is defined in a manner similar to that used to describe frequency-modulated, continuous-time signals. The measurements are derived from an adaptive linear prediction spectral estimates. The proposed algorithm is utilized in the development of a digital processor for FM demodulation which operates on a uniformly sampled FM signal, and its output is a sampled sequence of the estimated demodulated message. The performance of the digital processor is demonstrated and compared with that of a conventional FM discriminator.     

基于DS856的宽带波形产生技术

本文介绍了一种高速DDS芯片—DS856的工作原理和性能特点,利用FPGA对其进行配置产生宽带调频信号和点频连续波信号.该芯片能够直接产生L波段信号和更大带宽调频信号,为宽带波形产生提供了一种新途径.     

调频信号的数字合成方法

调频信号作为一种常见信号在电子技术的各个领域，特别是通信领域有着广泛的应用。因此调频信号的合成就成为了其中关键性的一项技术。传统的调频信号通常是通过模拟方法合成的。但是模拟合成有频率不稳定、参数设置不可量化等缺点，而用数字合成的方法就可以解决这些问题。数字频率合成通常采用DDS技术，调频信号的数字合成也基于这项技术。本文首先介绍了DDS的基本原理。然后提出用双DDS结构实现调频信号数字合成的方法。由于把调制波形的幅度量化成了频率字，构成了一个输出频率字的DDS。因此只要改变这个DDS波形RAM中的数据。就可以产生任意以周期信号为调制波形的调频信号，并且调制频率和深度都精确可调。     

Transmission scheme of high-capacity FM multiplex broadcastingsystem

FM multiplex broadcasting is a system for providing additional text and graphics, while maintaining compatibility with existing stereo sound broadcasting. The digital signals are multiplexed in a higher frequency band than baseband FM stereo signals. This paper describes a modulation method and an error correction method for a new high-capacity FM multiplex broadcasting system called DARC (Data Radio Channel), which has a bit rate of 16 kbit/s. Simulation results show that stereo sound signals interfere with a multiplexing signal under multipath conditions. LMSK (level controlled MSK) is proposed as a modulation scheme to ensure good transmission quality. It is shown that an error correction scheme using a product code of (272190) codes has a good performance for mobile reception. Field tests on the DARC for mobile reception are conducted in the service area of the NHK Tokyo FM station. These show that the correct reception rate can be obtained at more than 80% when transmitting information of 6 kbytes     

High-resolution direction finding of non-stationary signals using matching pursuit

One of the main goals of time–frequency (TF) signal representations in non-stationary array processing is to equip multi-antenna receivers with the ability to separate sources in the TF domain prior to direction finding. This permits high-resolution direction-of-arrival (DOA) estimation of individual sources and of more sources than sensors. In this paper, we use linear decomposition of sensor data based on matching pursuit (MP). The leading atoms of the MP, which capture most of the source TF signatures, can be different for different sources and, as such, provide the desired source discrimination. The MP coefficients with high signal-to-noise ratio (SNR) and corresponding to the leading decomposition atoms are used to develop the MP-MUSIC DOA estimation for non-stationary source signals. We demonstrate the source discriminatory capability of the proposed technique using linear FM, nonlinear FM, and other non-stationary signals. Further, we compare MP-MUSIC performance with conventional MUSIC and the time–frequency MUSIC, which incorporates bilinear transforms.     

A constrained notch Fourier transform

The paper presents a new sliding algorithm for estimating the amplitude and phase of the Fourier coefficients of noise corrupted harmonic signals given a priori knowledge of the signal frequencies. The proposed method is similar in principle to the notch Fourier transform (NFT) technique suggested by Tadokoro et al. [1987] except that it employs an infinite impulse response (IIR) rather than a finite impulse response (FIR) notch filter parameterization. This modification provides bandwidth controlled bandpass (BP) filters whose center frequencies are equally spaced in the frequency spectrum. In this sense, the proposed technique can be regarded as a constrained notch Fourier transform (CNFT). Sliding algorithms have been derived for both the NFT and CNFT for the purpose of estimating the Fourier coefficients of the sinusoidal components. The paper also proposes a similar algorithm to the CNFT for the signals containing sinusoids at arbitrary known frequencies. The main feature of the modified CNFT is that it uses second-order IIR BP filters whose bandwidth and center frequency can be adjusted independently. The bandwidth control aspect provides the user with an efficient means of achieving the required resolution as well as reducing spectral leakage. In general, the proposed approach leads to considerable reduction in terms of computational burden and memory storage     

Spectrum sensing and communication functionalities verification in cognitive radio

This paper is intended to discuss hardware setup implementation for realizing the spectrum sensing and communication functionalities of a five‐port integrated ultrawideband and narrowband antenna system. The five‐port integrated antenna system consists of one ultrawideband antenna and four narrowband antennas. The ultrawideband antenna is used for spectrum sensing in cognitive radio, whereas the four narrowband antennas are used for communication. In order to validate functionalities of the antennas, their spectrum sensing and communication performance is verified using an arbitrary waveform generator, real‐time signal analyzer, and Universal Software Radio Peripheral. The ultrawideband antenna is able to sense the various frequencies transmitted by the arbitrary waveform generator. These transmitted signals from the arbitrary waveform generator are treated as busy spectrum channels in the cognitive radio environment. The narrowband antennas are able to perform communication by transmitting the signals at identified spectrum holes. The sensed signals are observed on a real‐time signal analyzer, and the communication signals are viewed in LabVIEW software for which a real‐time signal reception algorithm is used. This signal reception is performed using Universal Software Radio Peripheral.     

一种稳定的变步长块LMS自适应算法

针对LMS自适应滤波算法在输入信号高度相关时.收敛速度下降导致性能下降,本文从基本的块LMS算法开始,简要介绍了块LMS算法的实现方法,在此基础上重点分析了在变步长块LMS算法中,影响步长因子的要素.提出了一种新的变步长因子迭代算法(SVBLMS),该迭代算法充分考虑输入信号和误差信号对变步长因子的影响.并且迭代的结构简单,计算量小.通过Matlab仿真.仿真结果表明.该迭代算法较其它块LMS算法有更快的收敛速度,更稳定的收敛过程.当输入为有色信号或输入噪声较大时,本算法都能保持良好的性能.     

LMS coefficient filtering for Time-varying chirped signals

This paper presents coefficient filtering techniques in the least mean squares (LMS) algorithm to improve adaptive predictor tracking performance for time-varying chirped signals. The example application used in this paper is an electronic support measure (ESM) receiver for detecting radar chirped pulses. The leakage LMS, momentum LMS, and the proposed future-state coefficient (FC-LMS) filtering algorithms have been studied. The leakage LMS algorithm has the ability to remove the memory effect of the initial converged time-varying frequency of the chirped signal, thus improving the radar pulse detection performance. The momentum LMS is able to search for the time-varying optimum weight solution more efficiently, and the FC-LMS uses a parallel technique to retain the LMS throughput while being able to show a better tracking performance for chirped signals compared with the standard LMS algorithm.