Adaptive digital notch filter design on the unit circle for theremoval of powerline noise from biomedical signals

Investigates adaptive digital notch filters for the elimination of powerline noise from biomedical signals. Since the distribution of the frequency variation of the powerline noise may or may not be centered at 60 Hz. Three different adaptive digital notch filters are considered. For the first case, an adaptive FIR second-order digital notch filter is designed to track the center frequency variation. For the second case, the zeroes of an adaptive IIR second-order digital notch filter are fixed on the unit circle and the poles are adapted to find an optimum bandwidth to eliminate the noise to a pre-defined attenuation level. In the third case, both the poles and zeroes of the adaptive IIR second-order filter are adapted to track the center frequency variation within an optimum bandwidth. The adaptive process is considerably simplified by designing the notch filters by pole-zero placement on the unit circle using some suggested rules. A constrained least mean-squared algorithm is used for the adaptive process. To evaluate their performance, the three adaptive notch filters are applied to a powerline noise sample and to a noisy EEG as an illustration of a biomedical signal     

On-line estimation of signal and noise parameters with application to adaptive Kalman filtering

This paper presents two algorithms for on-line estimation of the optimal gain of the Kalman filter applied to sensor signals when the signal-to-noise ratio is unknown. First-order spectra of a pure signal and colored measurement noise have been assumed. The proposed adaptive Kalman filtering algorithms have been tested for various spectra of the pure signal and noise, and for various signal-to-noise ratios. The effect of the length of an adaptation step and a sampling frequency on the mean square errors of the pure signal estimation has also been examined. Although the test have been performed for stationary signals, the algorithms presented can also be used successfully for time-varying sensor signals when the signal-to-noise ratios vary very slowly in comparison with the length of the adaptation step.The results are helpful for designers who synthesize optimal linear digital filters for sensor signals with first-order spectra and colored measurement noise. The estimation error curves presented enable designers to determine the noise reduction attainable for particular applications of the adaptive Kalman filtering algorithms.     

CPT铷原子钟锁相环频率合成器设计和分析

基于CPT(相干布局囚禁)87铷原子钟设计出输出频率为3417 MHz的锁相环频率合成器,通过ADIsimPLL仿真出最佳环路带宽,环路滤波器参数以及相位噪声等,并通过STM32对锁相环芯片进行控制。对频率合成器进行了测试,电路尺寸为40 mm×40 mm,输出信号功率范围为-4 dBm^+5 dBm可调,输出信号噪声满足要求-88.65 dBc/Hz@1 kHz,-92.31 dBc/Hz@10 kHz,-104.63 dBc/Hz@100 kHz,杂散和谐波得到抑制,设计的频率合成器能很好的应用于原子钟的射频信号源。     

Local polynomial modeling of time-varying autoregressive models with application to time-frequency analysis of event-related EEG

This paper proposes a new local polynomial modeling (LPM) method for identification of time-varying autoregressive (TVAR) models and applies it to time-frequency analysis (TFA) of event-related electroencephalogram (ER-EEG). The LPM method models the TVAR coefficients locally by polynomials and estimates the polynomial coefficients using weighted least-squares with a window having a certain bandwidth. A data-driven variable bandwidth selection method is developed to determine the optimal bandwidth that minimizes the mean squared error. The resultant time-varying power spectral density estimation of the signal is capable of achieving both high time resolution and high frequency resolution in the time-frequency domain, making it a powerful TFA technique for nonstationary biomedical signals like ER-EEG. Experimental results on synthesized signals and real EEG data show that the LPM method can achieve a more accurate and complete time-frequency representation of the signal.     

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     

Nonuniform sampling and antialiasing in image representation

A unified approach to the representation and processing of a class of images which are not bandlimited but belong to the space of locally bandlimited signals is presented. A nonuniform sampling theorem (Clark et al, 1985) for functions belonging to this space is extended, and a class of nonstationary stochastic processes is considered. The space of locally bandlimited signals is shown to be a reproducing-kernel space. A generalized projection theorem can therefore be applied, yielding either a continuous or a discrete projection filter. The former can be used for image conditioning prior to nonuniform sampling, while the latter provides a general tool for image representation by nonuniform sampling schemes. The problem of finding the local bandwidth of a given signal, in order to generate an optimal sampling scheme, is addressed in the context of signal representation in the combined position-frequency space. The stochastic estimation of parameters which characterize the local bandwidth is discussed. Bounds on the error resulting from the utilization of nonexact position-varying signal parameters are derived     

A frequency steered phase-locked loop

Narrow bandwidth phase-locked loops (PLLs) can have difficulty acquiring lock reliably when there is a significant difference between the input signal and the free run frequency of the PLL's voltage-controlled oscillator (VCO). The new technique presented here incorporates an accurate local reference frequency into the PLL structure. The range of frequencies to which the new PLL structure can lock can be confined to a desired small region around the accurate local reference frequency. The new PLL structure also provides other benefits such as reduction of VCO phase noise. The new technique does not require any monitoring nor any switching of the local frequency reference signal which is always acting. The key parameters of the new PLL structure are identified and the performance characterized     

Bandwidth-efficient coded modulation with optimized linearpartial-response signals

We study the design of optimal signals for bandwidth-efficient linear coded modulation. Previous results show that for linear channels with intersymbol interference (ISI), reduced-search decoding algorithms have near-maximum-likelihood error performance, but with much smaller complexity than the Viterbi decoder. Consequently, the controlled ISI introduced by a lowpass filter can be practically used for bandwidth reduction. Such spectrum shaping filters comprise an explicit coded modulation, for which we seek the optimal design. We simultaneously constrain the bandwidth and maximize the minimum Euclidean distance between signals. We show that under quite general assumptions the problem can be formulated as a linear program, and solved with well-known efficient optimization techniques. Numerical results are presented, and the performance of the optimal signals, measured by their combined bandwidth and noise immunity, is analyzed. The new codes are comparable to set-partition (TCM) trellis codes. Tests of an M-algorithm decoder confirm this and show that the performance occurs at small detection complexity     

Statistical AM-FM models, extended Kalman filter demodulation,Cramer-Rao bounds, and speech analysis

A stochastic dynamical system model for describing time signals that are jointly amplitude (AM) and frequency (FM) modulated is presented. The signal is assumed to be bandpass, perhaps originating from a filter bank applied to a broadband signal, and includes the constraint that the magnitude of the complex baseband signal is positive. Motivated by speech processing and the desire for narrowband modulating signals, time is divided into frames, and the modulating signals are smoothly interpolated across each frame. The model allows a detailed characterization of the bandwidth of the modulating signals and the statistical character of the measurement noise. An adaptive estimation algorithm based on extended Kalman filtering ideas for extracting the modulating signals from the measured signal is described and demonstrated on both voiced and unvoiced speech signals. The Cramer-Rao bound on the performance of any estimator is computed     

Low-bandwidth binaural beamforming

An efficient beamforming scheme for wireless binaural hearing aids is proposed that provides a trade-off between the transmission bit rate and the amount of noise reduction. It is proposed to transmit only the lowfrequency part of the signal from one hearing aid to the other, which is used in a binaural beamformer to generate the low-frequency part of the output. The high-frequency part is generated by a monaural beamformer using only the locally available microphone signals. The trade-off can be attained by adjusting the cutoff frequency of the lowpass filter. For speech sources with a 8 kHz bandwidth in the presence of an interfering source, it is shown that good performance can be achieved with a cutoff frequency of 4 kHz.     

Short-time Fourier analysis via optimal harmonic FIR filters

The Fourier coefficients (FCs) of quasiperiodic signals are assumed to be in random walk motion in order to represent a broader class. A state model for such quasiperiodic signals is derived. The optimal short-time estimate of the Fourier coefficients is obtained via the suggested optimal harmonic FIR filter (OHFF) based on this state-space signal model. The optimal harmonic FIR filter can be considered to be a generalization of the discrete Fourier transform (DFT) in the sense that it becomes the same as the DFT when the state model is for periodic signals and the filter length is equal to the order of the state model. The optimal harmonic FIR filter derived from the model, even with nonzero state noise and measurement noise, gives an exact harmonic estimate when an incoming signal is periodic and noiseless. It is shown by examples that the ability to suppress noise and the ability to resolve changes of the Fourier coefficients can be adjusted by the filter length and the noise covariance of the state model. Finally, the suggested scheme is compared with existing short-time Fourier analysis methods in a test signal that has time-varying Fourier coefficients     

Etalonnage de l’analyse spectrale par la méthode du modèle autorégressif

The authors give the general formulas for the amplitude calibration of the autoregressive spectral analysis method of a pure frequency in additive white noise. These calibrations are given versus the autoregressive filter order and the input signal to noise ratio. They show that this spectral analysis method can be characterized by a bandwidth depending of the autoregressive filter order and the input signal to noise ratio. This bandwidth is calculated in the general case.     

On‐line wavelet filtering of narrowband noise in signal detection of spread spectrum system for location tracking

Spread spectrum signal transmitted by wireless channel for location tracking can be severely corrupted by noise due to external disturbances. Narrowband noise is the most effective interference that can make measurement signal undetected. However, the current methods for narrowband interference (NBI) suppression are either very time‐consuming or add distortion to the signal received. In this paper, an adaptive Gaussian wavelet filter with optimal time–frequency localization and variable notch depth is proposed to suppress a large number of NBIs with additive white Gaussian noise and pulsed noise that interfere with the spread spectrum communication system. The filtering of both continuous and time‐varying NBIs with fast resampling is performed in conjunction with the fast Fourier transform‐based correlation for peak detection, and is computationally efficient for real‐time operation of signal detection. The performance of the adaptive filter has been evaluated by experiments employing a reliable noise detector. Experimental results demonstrate that the proposed wavelet filter isolates the signals from the NBI in accordance with the corrupted frequency contents while preserving the desired spread spectrum signal, and improves signal to noise ratio for peak detection leading to higher accuracy of timing measurement for real‐time wireless location. Copyright © 2011 John Wiley & Sons, Ltd.     

基于数字滤波的低频随机信号实时功率谱分析仪的实现

对于非平稳随机信号的功率谱分析,采用自相关函数傅里叶变换和直接傅里叶变换分析时,由于存在数据截断,二者从概念上都不能很好地反映随机信号的功率谱.采用参数谱估计方法,则不能实现等百分比带宽分析.对于噪声和结构振动等信号,需要进行等百分比带宽分析.采用滤波法进行功率谱分析,不存在数据截断带来的误差,还可方便地用于等百分比带宽的谱分析.利用数字滤波器可以实现时分和频分复用的特点,结合重抽样技术来实现整个频率轴上的实时功率谱分析.上述算法可以通过高速数字信号处理器(DSP)芯片实时地完成.文中介绍了基于数字滤波的低频随机信号实时功率谱分析仪的实现方法,并给出了实时算法的设计要点.     

Minimax estimation of unknown deterministic signals in colorednoise

The estimation of a deterministic signal corrupted by random noise is considered. The strategy is to find a linear noncausal estimator which minimizes the maximum mean square error over an a priori set of signals. This signal set is specified in terms of frequency/energy constraints via the discrete Fourier transform. Exact filter expressions are given for the case of additive white noise. For the case of additive colored noise possessing a continuous power spectral density, a suboptimal filter is derived whose asymptotic performance is optimal. Asymptotic expressions for the minimax estimator error are developed for both cases. The minimax filter is applied to random data and is shown to solve asymptotically a certain worst-case Wiener filter problem     

GSVD-based optimal filtering for single and multimicrophone speech enhancement

A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.     

Adaptive Separation of Subcarrier for Wireless Link of Satellite Communication

Currently, the subcarrier on the satellite communication wireless link has uncertain signal number and bandwidth and non-overlapped frequency spectra of mixed signals, and thus can hardly be separated and identified. Through analysis, a simple and effective estimation algorithm for subcarrier frequency was proposed and the code rate was estimated based on the instantaneous characteristics of the modulated signal. Results show that, using the proposed adaptive separation and recognition method, multiple signals can be effectively separated from the mixed signal, with high precision and strong noise immunity. Moreover, after partition, each subcarrier can be separated by the filter for modulation. The method is characterized by simple principle and ease of implementation.     

噪声调频信号对宽带线性调频雷达的干扰机理

研究了噪声调频信号中调制噪声方差及带宽的选择对宽带线性调频匹配滤波器的影响。通过观察噪声调频信号通过线性调频匹配滤波器之后的时域输出包络,分析了其起伏特性,推导出了在最大包络起伏指标下的调制噪声最优带宽应该为发射线性调频信号的时宽的倒数量级。同时,通过误差分析表明:要在实际中达到此干扰最优带宽,对侦察接收机的指标要求无需过高。     

一种基于互补谐振结构的宽带共模噪声滤波器

提出了一种用于高速差分信号传输的宽带共模噪声滤波器,采用在差分线正下方参考地平面上刻蚀内外互补的共面波导1/4波长谐振器和Z字形短路枝节线来实现。滤波器采用内外互补耦合λ/4开路枝节线谐振器结构,有效减小了横向尺寸,利用Z字形枝节线增大互感以改善滤波器的带内增益平坦度,最后用级联实现了共模噪声抑制阻带的展宽。仿真和测试结果表明,该滤波器在4.1~12.5 GHz频率范围内实现了20 dB的共模噪声抑制,共模阻带相对带宽(FBW)为101%,尺寸仅为0.78λ_g×0.18λ_g(15.8 mm×3.6 mm),其中λ_g为阻带中心频率处对应的波长。且该结构在实现共模噪声宽带抑制的同时,还可有效保证差分信号传输特性良好。     

Fuzzy rule-based signal processing and its application to imagerestoration

A novel signal processing technique based on fuzzy rules is proposed for estimating nonstationary signals, such as image signals, contaminated with additive random noises. In this filter, fuzzy rules concerning the relationship between signal characteristics and filter design are utilized to set the filter parameters, taking the local characteristics of the signal into consideration. The fuzzy rules are found to be quite effective, since the rules to set the filter parameters are usually expressed in an ambiguous style. The high performance of this filter is demonstrated in noise reduction of a 1-D test signal and a natural image with various training signals