Sinusoidal Signals In Noise Research Articles

A Robust Feedback Active Noise Control System With Online Secondary-Path Modeling

In this letter, a robust feedback active noise control (FBANC) system with an online secondary-path modeling (OSPM) subsystem is proposed for suppressing sinusoidal noise signals. First, a decoupling scheme is proposed by using of an adaptive linear prediction filter (LPF) that takes the FBANC residual noise as its input and separates the remaining sinusoidal noise from the broadband noise that includes an inherent additive noise within the primary noise as well as a broadband component due to an auxiliary white Gaussian noise (AWGN). The remaining sinusoidal noise (LPF output) is used effectively not only to update the FIR controller but also to scale the AWGN, while the broadband noise (LPF error) serves as a desired signal for the OSPM. In this way, the hostile coupling between the FIR controller and the OSPM subsystem is significantly mitigated, leading to both faster system convergence and improved noise reduction performance (NRP). Second, a simple and practical scheme for refreshing the proposed FBANC system is also developed to enhance its robustness against even abrupt changes with the SP and/or the primary noise signal. Extensive simulations with synthetic and real secondary paths and noise signals are conducted to demonstrate the effectiveness of the proposed FBANC system.

A Frequency-Time Algorithm of Parameter Estimation for Sinusoidal Signal in Noise

Abstract In this paper, a computationally efficient and high precision parameter estimation algorithm with frequency-time combination is proposed to improve the estimation performance for sinusoidal signal in noise, which takes the advantages of frequency- and time-domain algorithms. The noise influence is suppressed through spectrum analysis to get coarse frequency, and the fine frequency is obtained by denoising filtering and using linear prediction property. Then, estimation values of the amplitude and initial phase are obtained. The numerical results indicate that the proposed algorithm makes up for the shortcomings of frequency- and time-domain algorithms and improves the anti-interference performance and parameter estimation accuracy for sinusoidal signal.

Frequency determination from truly sub-Nyquist samplers based on robust Chinese remainder theorem

Abstract In this paper, a truly sub-Nyquist sampling method for frequency estimation of sinusoidal signals in noise is presented. Basically speaking, sinusoidal signals are first sampled at multiple sampling rates lower than the Nyquist rate, and then a robust Chinese remainder theorem (CRT) is proposed to estimate the frequencies of interest from the aliased frequencies obtained by taking the discrete Fourier transform of the collected samples in each undersampled waveform. Compared with compressed sensing, this method can be easily implemented from the hardware point of view. This paper provides a thorough overview of the existing research results on the robust CRT during the last decade, and discusses some related open problems as well.

Development of two-input adaptive noise canceller for wideband and narrowband noise signals

In this paper, the development of the single-stage two-input adaptive noise canceller that proposed by Widrow et al. is investigated. It is shown that the use of multi-stage cancellers instead of a single stage improves the performance of the conventional two-input adaptive noise canceller in a real life high-noise environment. In such environment, the background noise may contain both the wideband and narrowband (sinusoidal) noise components. In this contribution, the wideband noise and sinusoidal noise signals can be significantly suppressed using a new multi-stage adaptive noise cancellation scheme based on adaptive line enhancer (ALE) and Least Mean Square (LMS) filter. The proposed scheme is comprised of two stages. The first stage uses ALE filters, which are used to cancel the sinusoidal noise from the primary and reference input signals, whereas the wideband noise is cancelled using LMS adaptive filter in the second stage. The good performance of the proposed scheme has been verified via real-time implementation on the Texas Instruments TMS320C6713DSK.

On the Estimation of the Parameters of a Real Sinusoid in Noise

We propose and comprehensively analyze a computationally efficient algorithm to estimate the parameters of a real sinusoidal signal in noise. This method uses the fast Fourier Transform and is, therefore, computationally efficient. Accounting for the interference due to the negative spectral component allows the frequency to be estimated very accurately. Estimates of the amplitude and phase are derived in the process and are necessary for the suppression of the leakage. Theoretical analysis establishes that the estimator is asymptotically unbiased and achieves the Cramer–Rao lower bound. Simulation results are presented to verify the theory and demonstrate that the estimation performance is superior to other estimators in the literature.

Efficient Iterative Frequency Estimator of Sinusoidal Signal in Noise

The frequency estimation of the sinusoidal signal in noise is a problem of prime importance. A usual estimation method uses the Discrete Fourier transform to obtain the coarse estimation which is improved by a fine estimation stage. In this paper, we propose an efficient iterative estimation algorithm using the phase shift Fourier interpolation. We derive the performance of the new estimator. We show that the estimator is asymptotically unbiased and its mean squared error is slightly above the asymptotical Cramer-Rao bound over the whole frequency estimation range. To reduce the calculation, we study the estimation errors of the coarse estimation caused by finite data bits and short signal sequence. An approximate model is proposed by which we can obtain the estimation errors of different data bits and sequence length. Then we choose the proper sequence length and data bits to achieve the coarse search. This allows for a dramatic reduction in the calculation of coarse estimation, while still attaining the same performance comparable to that of a full length and data bits. In the numerical results we show that, in the proposed framework, when the signal to noise ratio is bigger than 11 dB, the computation speed is 13.45 times of the original with 512 sampling points.

Implementation of LMS-ALE Filter Using Vedic Algorithm

ALE or adaptive line Enhancers are special kinds of adaptive filters widely used in noise cancellation circuits. In circuits where we don’t have any prior knowledge of signal and noise, fixed filters unit never works good. Among adaptive filter ring algorithms LMS algorithm is very common, in our work also we use LMS algorithm. LMS-ALE filters removes the sinusoidal noise signals present in the channel by calculating the filter coefficients in every iteration. LMSALE filter has large number of multiplier units. FFT or Fast Fourier Transform blocks present in LMS algorithm again consist of large array of multiplier units. Optimization of LMS-ALE filter lies must start from optimization of multiplier blocks. Here we use Vedic “Vertical and crosswise algorithm” for multiplier design. When compared to conventional booth multiplier based LMS-ALE filter units, Vedic multipliers gives more performance in areas like resource utilization, power requirement, delay etc. The work includes designing Vedic multipliers, complex Vedic multipliers, redesigning Radix-8 FFT using Vedic multipliers, redesigning LMS block using Vedic FFT, redesigning LMS ALE filter using Vedic multipliers and Vedic LMS blocks. Major part of design is done in verilog using Xilinx ISE design suite. ADC block present in LMS-ALE filter is done in Matlab version 2013.

Implementation of LMS-ALE Filter using Vedic Algorithm

ALE or adaptive line Enhancers are special kinds of adaptive filters widely used in noise cancellation circuits. In circuits where we don’t have any prior knowledge of signal and noise, fixed filters unit never works good. Among adaptive filter ring algorithms LMS algorithm is very common, in our work also we use LMS algorithm. LMS-ALE filters removes the sinusoidal noise signals present in the channel by calculating the filter coefficients in every iteration. LMS-ALE filter has large number of multiplier units. FFT or Fast Fourier Transform blocks present in LMS algorithm again consist of large array of multiplier units. Optimization of LMS-ALE filter lies must start from optimization of multiplier blocks. Here we use Vedic “Vertical and crosswise algorithm” for multiplier design. When compared to conventional booth multiplier based LMS-ALE filter units, Vedic multipliers gives more performance in areas like resource utilization, power requirement, delay etc. The work includes designing Vedic multipliers, complex Vedic multipliers, redesigning Radix-8 FFT using Vedic multipliers, redesigning LMS block using Vedic FFT, redesigning LMS ALE filter using Vedic multipliers and Vedic LMS blocks. Major part of design is done in Verilog using Xilinx ISE design suite. ADC block present in LMS-ALE filter is done in Matlab version 2013.

Two dimensional autoregressive estimation from noisy observations as a quadratic eigenvalue problem

We consider the problem of two dimensional (2-D) autoregressive (AR) parameter estimation in the presence of observation noise. The proposed method is based on Yule-Walker Equations. We express the Yule Walker equations as a quadratic eigenvalue problem then by solving these equations, the parameters of the signal and noise are estimated. We also apply the proposed method to (2-D) spectrum estimation of the sinusoidal signals in noise. The performance of the proposed method is evaluated by computer simulation examples.

Properties of FXLMS-Based Narrowband Active Noise Control With Online Secondary-Path Modeling

Rotating machines such as diesel engines, cutting machines, fans, motors, etc., generate sinusoidal noise signals that may be effectively reduced by narrowband active noise control (ANC) systems. In this paper, a typical filtered-X LMS (FXLMS) based narrowband ANC system equipped with an online secondary-path modeling subsystem is analyzed in detail. First, difference equations governing the dynamics of the FXLMS algorithm for secondary source synthesis and the LMS algorithm for secondary-path estimation are derived in terms of convergence in both mean and mean square. Steady-state expressions for mean-square error (MSE) as well as the residual noise power are then developed in closed form. Extensive simulations are performed to demonstrate the validity of the analytical results.

LISA source confusion: identification and characterization of signals

The Laser Interferometer Space Antenna (LISA) is expected to detect gravitational radiation from a large number of compact binary systems. We present a method by which these signals can be identified and have their parameters estimated. Our approach uses Bayesian inference, specifically the application of a Markov chain Monte Carlo method. The simulation study that we present here considers a large number of sinusoidal signals in noise, and our method estimates the number of periodic signals present in the data, the parameters for these signals and the noise level. The method is significantly better than classical spectral techniques at performing these tasks and does not use stopping criteria for estimating the number of signals present.

Bayesian modeling of source confusion in LISA data

One of the greatest data analysis challenges for the Laser Interferometer Space Antenna (LISA) is the need to account for a large number of gravitational wave signals from compact binary systems expected to be present in the data. We introduce the basis of a Bayesian method that we believe can address this challenge, and demonstrate its effectiveness on a simplified problem involving one hundred synthetic sinusoidal signals in noise. We use a reversible jump Markov chain Monte Carlo technique to infer simultaneously the number of signals present, the parameters of each identified signal, and the noise level. Our approach therefore tackles the detection and parameter estimation problems simultaneously, without the need to evaluate formal model selection criteria, such as the Akaike Information Criterion or explicit Bayes factors. The method does not require a stopping criterion to determine the number of signals, and produces results which compare very favorably with classical spectral techniques.

Design of detectors based on stochastic resonance

This paper presents a study of the phenomenon of stochastic resonance in quantizers, and discusses the use of this phenomenon for the detection of weak sinusoidal signals in noise. Stochastic resonance in 2-level, symmetric 3-level, and symmetric multilevel quantizers is investigated. Expressions are derived for the signal-to-noise ratio (SNR) gain of the quantizers driven by a small amplitude sinsuoidal signal and i.i.d. noise. The gain depends on the probability density function (PDF) of the input noise, and for a given noise PDF, the gain can be maximized by a proper choice of the quantizer thresholds. The maximum gain G SR is less than unity if the input noise is Gaussian, but several non-Gaussian noise PDFs yield values of G SR exceeding unity. Thus, the quantizers provide an effective enhancement in the SNR, which can be utilized to design a nonlinear signal detector whose performance is better than that of the matched filter. The nonlinear detector in consideration consists of a stochastically resonating (SR) quantizer followed by a correlator. An asymptotic expression for the probability of detection of the SR detector is derived. It is shown that the detection performance of the SR detector is better than that of the matched filter for a large class of noise distributions belonging to the generalized Gaussian and the mixture-of-Gaussian families.

Exponential Modeling with Unknown Model Order Using Structured Nonlinear Total Least Norm

A new algorithm called Structured Nonlinear Total Least Norm (SNTLN) has recently been developed for obtaining an approximate solution to the structured overdetermined nonlinear system. Both theoretical justification and computational testing show that SNTLN is an efficient method for solving structured overdetermined systems. In this paper, we present a method based on SNTLN for estimating the parameters of exponentially damped sinusoidal signals in noise when the model order is unknown. It is compared to two other existing methods to show its robustness in recovering correct values of parameters when the model order is unknown, in spite of some large errors in the measured data.

LMS-based notch filter for the estimation of sinusoidal signals in noise

In this paper, the problem of estimating the discrete Fourier coefficients of sinusoidal signals with known arbitrary frequencies in additive noise using a least mean square (LMS) adaptive algorithm is treated in some detail. Frequency response analysis reveals that the LMS algorithm proposed for a single-frequency case possesses the characteristics of an IIR notch filter. The estimator is analyzed for its convergence and mean square error (MSE) due to the additive noise and the mismatch between the signal and the designated frequencies. Difference equations governing the dynamic behavior of the estimator are also derived. The analyses of a single-frequency case are extended to a multifrequency case. Simulations are performed to confirm the theoretical results.

A new adaptive technique for on-line partial discharge monitoring

The insulation system of HV apparatus deteriorates due to partial discharges (PD). PD tests are carried out successfully in shielded laboratories to verify the insulation quality and to rectify defects left during the manufacturing process. A variety of techniques exists for this purpose. It is also desired to monitor the insulation when equipment is in operation. Unfortunately, the performance of PD test equipment is adversely affected by interference signals. The sinusoidal signals of low and high frequency, due to their correlation, make the measurement difficult and sometimes even impossible. This paper describes the design of an adaptive digital filtering technique and its successful application to the on-line/on-site detection of PD current pulses generated in HV insulation in the presence of sinusoidal noise signals. The technique is based on Wiener optimal filtering theory and its characteristics are investigated. The adaptive filter of this system has a time-varying response and is self-tuning to each low and high frequency noise component. The filter remains active until the signal-to-noise ratio is significantly increased and it can be used for weak PD pulse integration. Theoretical background of the technique and the results of laboratory and field tests are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Co-modulation masking release: Spectro-temporal pattern analysis in hearing

The peripheral auditory system is often modelled as containing an array of bandpass filters (called the auditory filters), each tuned to a different centre frequency. When a subject tries to detect a sinusoidal signal in noise, it has traditionally been assumed that performance is based on the output of the single auditory filter which gives the highest signal-to-masker ratio. However, recent experiments demonstrate the ability to compare the outputs of different auditory filters to enhance signal detection. This enhancement takes place especially when the envelope of the masker fluctuates over time, and when the fluctuations are coherent or correlated across different frequency bands. This phenomenon is called comodulation masking release (CMR) and it demonstrates the ability of the auditory system to perform a highly flexible spectro-temporal pattern analysis. CMR appears to be reduced or absent in persons with cochlear hearing loss, and this may partly account for the difficulties experienced by these persons in understanding speech in noisy backgrounds.

Applications of fast orthogonal search: time-series analysis and resolution of signals in noise.

In this paper a technique is examined for obtaining accurate and parsimonious sinusoidal series representations of biological time-series data, and for resolving sinusoidal signals in noise. The technique operates via a fast orthogonal search method discussed in the paper, and achieves economy of representation by finding the most significant sinusoidal frequencies first, in a least squares fit sense. Another reason for the parsimony in representation is that the identified sinusoidal series model is not restricted to frequencies which are commensurate or integral multiples of the fundamental frequency corresponding to the record length. Biological applications relate to spectral analysis of noisy time-series data such as EEG, ECG, EMG, EOG, and to speech analysis. Simulations are provided to demonstrate precise detection of component frequencies and weights in short data records, coping with missing or unequally spaced data, and recovery of signals heavily contaminated with noise. The technique is also shown to be capable of higher frequency resolution than is achievable by conventional Fourier series analysis.

A robust orthogonal algorithm for system identification and time-series analysis.

We describe and illustrate methods for obtaining a parsimonious sinusoidal series representation or model of biological time-series data. The methods are also used to identify nonlinear systems with unknown structure. A key aspect is a rapid search for significant terms to include in the model for the system or the time-series. For example, the methods use fast and robust orthogonal searches for significant frequencies in the time-series, and differ from conventional Fourier series analysis in several important respects. In particular, the frequencies in our resulting sinusoidal series need not be commensurate, nor integral multiples of the fundamental frequency corresponding to the record length. Freed of these restrictions, the methods produce a more economical sinusoidal series representation (than a Fourier series), finding the most significant frequencies first, and automatically determine model order. The methods are also capable of higher resolution than a conventional Fourier series analysis. In addition, the methods can cope with unequally-spaced or missing data, and are applicable to time-series corrupted by noise. Finally, we compare one of our methods with a well-known technique for resolving sinusoidal signals in noise using published data for the test time-series.

Maximum-likelihood estimation of parameters of exponentially damped sinusoids

Maximum-likelihood estimates of the parameters of exponentially damped sinusoidal signals in noise can be found by using an iterative procedure based on Newton's method. The initial estimate is obtained by an improved linear-prediction method. The properties of the Newton estimates obtained from short data records is experimentally studied.