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Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available works on distributed non-convex optimization problems focus on the deterministic setting where exact gradients are available at each agent. In this work and its Part II, we consider stochastic cost functions, where exact gradients are replaced by stochastic approximations and the resulting gradient noise persistently seeps into the dynamics of the algorithm. We establish that the diffusion learning strategy continues to yield meaningful estimates non-convex scenarios in the sense that the iterates by the individual agents will cluster in a small region around the network centroid. We use this insight to motivate a short-term model for network evolution over a finite-horizon. In Part II of this work, we leverage this model to establish descent of the diffusion strategy through saddle points in $O(1/\mu)$ steps, where $\mu$ denotes the step-size, and the return of approximately second-order stationary points in a polynomial number of iterations.

Seismic noise cross correlation studies are of increasing importance in the seismological research community due to the ubiquity of noise sources and advances on how to use the seismic noise wave field for structural imaging and monitoring purposes. Stacks of noise cross correlations are now routinely used to extract empirical Green's functions between station pairs. In regional and global scale studies, mostly surface waves are extracted due to their dominance in seismic noise wave fields. Group arrival times measured from the time-frequency representation of frequency dispersive surface waves are further used in tomographic inversions to image seismic structure. Often, the group arrivals are not clearly identified or ambiguous depending on the signal and noise characteristics. Here, we present a procedure to robustly measure group velocities using the time-frequency domain phase-weighted stack (PWS) combined with data resampling and decision strategies. The time-frequency PWS improves signal extraction through incoherent signal attenuation during the stack of the noise cross correlations. Resampling strategies help to identify signals robust against data variations and to assess their errors. We have gathered these ingredients in an algorithm where the decision strategies and tuning parameters are reduced for semiautomated processing schemes. Our numerical and field data examples show a robust assignment of surface-wave group arrivals. The method is computational efficient thanks to an implementation based on pseudoanalytic frames of wavelets and enables processing large amounts of data., This work was supported in part by the Project MISTERIOS under Grant CGL2013-48601-C2-1-R, in part by the MIMOSA under Grant ANR-14-CE01-0012, in part by the COST Action ES1401 TIDES, in part by AGAUR, and in part by the FP7 Marie Curie Project through SV's Beatriu de Pinos Fellowship under Contract 600385. This is IPGP contribution 3814.

In this paper, we present a new technique for the estimation of short-term linear predictive parameters of speech and noise from noisy data and their subsequent use in waveform enhancement schemes. The method exploits a priori information about speech and noise spectral shapes stored in trained codebooks, parameterized as linear predictive coefficients. The method also uses information about noise statistics estimated from the noisy observation. Maximum-likelihood estimates of the speech and noise short-term predictor parameters are obtained by searching for the combination of codebook entries that optimizes the likelihood. The estimation involves the computation of the excitation variances of the speech and noise auto-regressive models on a frame-by-frame basis, using the a priori information and the noisy observation. The high computational complexity resulting from a full search of the joint speech and noise codebooks is avoided through an iterative optimization procedure. We introduce a classified noise codebook scheme that uses different noise codebooks for different noise types. Experimental results show that the use of a priori information and the calculation of the instantaneous speech and noise excitation variances on a frame-by-frame basis result in good performance in both stationary and nonstationary noise conditions.

The problem of detecting a signal known except for amplitude in incompletely characterized non-Gaussian noise is addressed. The use of a generalized likelihood ratio test or its asymptotically equivalent form, the Rao test, is shown to produce a detector that has the identical asymptotic performance as a generalized likelihood ratio test designed with a priori knowledge of the unknown noise parameters. Since the latter clairvoyant detector always produces an upper bound on performance, the generalized likelihood ratio test is optimum. An example is given in which the noise is modeled as an autoregressive process with a mixed-Gaussian noise excitation. Results of a computer simulation are described which verify the theory.

LMS adaptive filtering in the spectrum domain is addressed and applied to noise cancelling. The spectrum domain noise cancellor minimizes the noise power at each spectral bin of the primary input. It requires, however, the power spectra of the input data to be estimated prior to cancelling. The paper discusses the function of the proposed cancellor and describes its general structure.

We present an approach to the problem of estimating the frequency and phase of a sinusoid in the presence of noise. Analytical expressions for the discrete Fourier Transform (DFT) of a finite sequence containing a sinusoid are first obtained for each frequency component. With noise, these DFT components are functions of frequency, amplitude and phase of the sinusoid and of the noise power as well as the number of samples. Nonlinear operations (multiplication and division) on the DFT components to eliminate certain variables then yield an estimator for the frequency and phase. Means and variances of the estimator are derived and simulation results are presented.

The spectrum of additive noise was systematically varied according to three variables: correspondance between the noise and speech spectrum (4 levels), equal weighting or weighting according to the width of the Articulation Index bands, SNR of the output signal (2 levels). All combinations of these 16 noise conditions were added to high quality speech sampled at 8kHz, and presented to listeners for judgment. Difference judgments were analyzed by a multidimensional scaling procedure to gain information about the number and nature of the important subjective variables. Overall quality ratings were obtained as a measure of the improvement in perceived quality due to the spectral shaping of the additive noise. Several objective measures were also tested for their sensitivity in predicting the overall quality ratings.

AR (autoregressive) modelling of a given time series usually yields high-resolution spectral estimates when the observed process is free from noise. Presence of noise however results in biased frequency estimates. In this paper, an adaptive bias elimination technique (ABET) is proposed which first estimates adaptively the noise power and uses it in a new algorithm which reduces the bias, resulting in improved spectral estimation. ABET is particularly suited for tracking the frequencies of sinusoids in a stationary white noise.

An important problem in speaker verification systems arises, when the speech inputs are noise corrupted with signal to noise ratios in the range of 10 to 30 dB (noise assumed to be zero mean and white). This paper deals with the accuracy of speaker verification algorithms derived from an orthogonal parameter representation of speech. Initially, the investigations are directed to evaluate the sensitivity of orthogonal parameters to the level of noise in the speech signal. The accuracy of verification is then determined, using only those parameters that are least sensitive to additive noise. The influence of the order of the linear prediction model on verification is also studied. The verification algorithm is based on the distance measure used by Sambur. Finally thresholds are established to determine the proper choice of orthogonal parameters (used in distance computation) and the order of the linear prediction model for a given signal to noise ratio in the speech signal. The above study is then used to evaluate the accuracy of verification when speech inputs are obtained from a noisy telephone channel.

A method of recovering sinusoids from additive arbitrary colored noise is presented. It was a Hankel matrix formulation to recover the frequencies, and reduces to the Pisarenko decomposition for the case of white noise.

High-order Yule-Walker equations are a, theoretically, correct tool for the computation of the AR parameters of an ARMA process. Unfortunatelly, in practical applications, working with sample data, one frequently obtain unreliable results. The high variance (in contrast with the small bias) exhibited by the corresponding AR parameter estimates is the main reason of having such a performance. Here, we propose a class of high-order Yule-Walker estimates that allow variance control in an easy form. The proposed methods, although simple to apply, are the result of a rather elaborated analysis, which also gives, as intermediate results, new insights into the practical problems of the high-order Yule-Walker equations. Although we have concentrated on ARMA processes of the AR plus white noise type, the results could be probably extended to more general cases.

For the class of digital filters described by the state equations, a new expression for the roundoff noise and the dynamic range constraint equations have been established. Then, minimization of the roundoff noise subject to the l 2 norm dynamic range constraint is considered. In particular, a lower bound and the global minimum of the unit noise, i.e., the noise generated under the assumption that each state equation contains exactly one noise source, have been obtained. A method of realizing the minimum unit noise filter, along with a numerical example is also given.

We present a general framework for the coding of signals with a time-varying short-term spectrum. The total quantization distortion is minimized by a dynamic bit allocation in time and in frequency. The resulting distortion is then white noise with fixed power. Such noise, however, is not optimal perceptually when coding speech signals. Spectral and temporal noise shaping are then used to minimize the perception of noise in frequency and in time. Initial experiments at 16 kb/s demonstrate the validity of shaping the noise in time as well as in frequency.

This paper describes a method for enhancing speech corrupted by broadband noise. The method is based on the spectral noise subtraction method. The original method entails subtracting an estimate of the noise power spectrum from the speech power spectrum, setting negative differences to zero, recombining the new power spectrum with the original phase, and then reconstructing the time waveform. While this method reduces the broadband noise, it also usually introduces an annoying "musical noise". We have devised a method that eliminates this "musical noise" while further reducing the background noise. The method consists in subtracting an overestimate of the noise power spectrum, and preventing the resultant spectral components from going below a preset minimum level (spectral floor). The method can automatically adapt to a wide range of signal-to-noise ratios, as long as a reasonable estimate of the noise spectrum can be obtained. Extensive listening tests were performed to determine the quality and intelligibility of speech enhanced by our method. Listeners unanimously preferred the quality of the processed speech. Also, for an input signal-to-noise ratio of 5 dB, there was no loss of intelligibility associated with the enhancement technique.

Spectral subtraction has been shown to be an effective approach for reducing ambient acoustic noise in order to improve the intelligibility and quality of digitally compressed speech. This paper presents a set of implementation specifications to improve algorithm performance and minimize algorithm computation and memory requirements. It is shown spectral subtraction can be implemented in terms of a nonstationary, multiplicative, frequency domain filter which changes with the time varying spectral characteristics of the speech. Using this filter a speech activity detector is defined and used to allow the algorithm to adapt automatically to changing ambient noise environments. Also the bandwidth information of this filter is used to further reduce the residual narrowband noise components which remain after spectral subtraction.

In digital adaptive echo cancellation, the sign algorithm is very attractive since it is multiplication free. However, when the residual echo undercrosses the useful signal level, the error sign is no longer significant of the canceller quality and the convergence stops. Introduction of extra noise into the error can eliminate this drawback. The system performances regarding the residual echo and the computational complexity are shown to be competitive with those of the classical gradient algorithm (not using the function sign).

The techniques for harmonic analysis in colored noise have attracted much more attentions in the last two years. This paper presents a novel approach, namely modified Yule -Walker equations method, to harmonic analysis in unknown colored noise, based on the fact that an ARMA model can be fitted to the time sequence consisting of harmonics plus a MA noise process. It shows that the present method can do without any prior knowledge about the noise model. New fixed-order fast algorithms, including both nonadaptive and adaptive situations, are presented for efficient solution of MYW equations. The performance of ours, FFT and maximum entropy are illustrated by simulation results.

Noise power spectra gained through discrete Fourier transform of sampled noise show the effects of aliasing and filtering at all frequencies, whatever the sampling rate and the filter cut-off frequencies. A self consistent method for the necessary correction of the spectra is developped, given the filter response. It is first shown that, with RLC filters, the uncorrected spectrum of white noise and 1/f - noise can be represented by Digamma functions, Polygamma functions, or by corresponding integrals. In certain cases the correction function can be calculated in simple form, and an example of dealiasing and defiltering of white noise is given. Finally, estimates of the truncation error of the sums representing the uncorrected spectra are given. In general, the spectra can be reconstituted all the way up to the folding frequency with tolerable computational effort.

Acoustic noise in speech can be suppressed by filtering a separately recorded correlated noise signal and subtracting it from the speech waveform. In the time domain this adaptive noise cancelling approach requires a computational rate which is linear with filter length. This paper describes how to implement the noise cancelling procedure in the frequency domain using the short-time Fourier transform. Using the efficiency of the FFT results in a computation rate which is proportional to the log of the filter length. For acoustic noise suppression where the filter length can be on the order of one thousand points, this approach offers a viable alternative for real time implementation, The performance of this method is compared with the time domain methods on noisy speech having a noise power equal to the signal power and is shown to be equally effective as a noise cancelling preprocessor.

An algorithm is presented in this paper which advances research in noisy background target recognition. This recognition process first uses an enhancement algorithm which extracts edges from an input scene. The edge enhanced target scene is searched with an edged object template and the correlation output displayed. High correlation peaks could be targets or high energy noise correlated with the edged template. To distinguish between these two conditions, the correlation peaks are used as centers for normalization of the input scene. An area equal to the size of the target is normalized to the template energy around each correlation center, the rest of the image being blanked, and the new scene is recorrelated with the template.

The optimum design of recursive digital filters in the cascade realization with respect to the output noise is healed here by taking into account the ordering, the pole-zero pairing, and the selection of configurations of the individual sections. In the first part of this paper, the output noise variances are derived for arbitrary realized cascaded configuration employing either the fixed-point or the floating-point arithmetics. The second part presents a simple algorithm to compute the output noise variance without direct evalution of complex integral. An example is presented in which the individual sections are allowed to take on different configurations.

Application of a Maximum A Posteriori (MAP) estimation procedure in estimating the LPC coefficients from speech waveforms degraded by additive random noise generally leads to solving a set of non-linear equations which are computationally undesirable. However, an attempt to approximate the true MAP estimation procedure leads to two iterative methods that require solving only sets of linear equations. These two methods have been applied to real speech data degraded by additive white Gaussian noise, and in this paper some preliminary results are discussed.

In this paper, the problem of signal detection in severe and/or changing noise environment is considered. The detector operates at near-optimum levels for a particular noise environment and is robust by maintaining high efficiency in other than nominal noise environments by adapting its optimum nonlinearity using an m-interval approximation of it. It is shown that the sequential MIPA detectors are asymptotically optimum, increase their transmission rate up to four times as compared to their fixed-sample size counterparts, and are highly insensitive to variation of noise if compared to detectors based on min-max theory.

The extraction of sinusoids in white noise, using least-squares predictors, has attracted a lot of attention in the past, mainly in the context of the adaptive line enhancer (ALE). However, very few results exist for the colored noise case, or for the whitening performance of the predictors. We use a matrix formulation to derive the optimal least-squares coefficients and frequency response of the ALE or the D-step predictor, for sinusoids (real or complex) in additive colored noise. Several cases are considered; in low-pass background noise the amplitude gain of the sinusoids becomes essentially a monotonically increasing function of their frequency, and a decreasing function for high-pass noise. For the whitening application, signal to noise ratio (SNR) bounds of the output are derived when the input is a white signal plus a sinusoidal interference. This performance is achievable using (possibly complex) exact least-squares recursions, such as our ladder form implementations.

The adaptative filter for real time noise cancelling applications is shown. The signal is corrupted by an additive noise which is a linear transformation of the noise "source" available as a reference input. To obtain the disturbing noise it is necessary to estimate this transformation. The difference between the input and the estimated noise gives an estimation of the signal. The system presented here is an open loop filter which is a different case from that proposed by Widrow. The theoretical study of the performance of the system (in the case where the disturbing noise is a non stationary process) is shown. To check the stationarity of the process we introduce a criterion which conpare the estimated transformation with the previous one (learning process) and decide if it is necessary or not to change the last estimated transformation. We studied typical cases of non stationarity as change of the power of the disturbing noise or in the impulse response of the linear system. The theoretical and computer calculated results are shown. We find a good agreement between the two approaches.

Nonstationary acoustic noise with energy possibly equal to or greater than the speech is suppressed using a two microphone implementation of adaptive noise cancellation. The primary noise added to the speech is reduced by subtracting a filtered version of the second microphone reference noise. The reference noise filter is adaptively up dated using the Widrow-Hoff LMS algorithm [1]. The effectiveness of noise suppression depends directly on the ability of the filter to estimate the transfer function relating the primary and reference noise channels. A study of the filter length required to achieve a desired noise reduction level in a hard-walled room is presented. Results demonstrating noise reduction in excess 10dB in an environment with 0dB signal noise ratio are presented.

Statistical error models for digital filter roundoff noise estimation are usally based on a set of noise sources interconnected according to the filter structure. The location of the noise sources depends on the location of the quantizers within the filter network. Roundoff noise analysis by both, simulation of digital filters and analysis of noise models yields the result that the entire roundoff noise behaviour even of multimesh digital filters can be described by exactly one quatizer if the noise power is not too great. In this contribution the assumptions for the conventional statistical noise analysis are discussed in detail Also practical methods for the determination of the characteristics of the one-quantizer-model are given. The applicability of the proposed simplified error model is demonstrated by the roundoff noise analysis of different filter structures utilizing various quantizers.

A family of algorithms is developed for adaptive parameter estimation of constrained autoregressive moving-average (ARMA) signals in the presence of noise. These algorithms utilize a priori information about the signal's properties, such as its spectral type (for example, low-pass, bandpass, etc.) or a spatial-domain characteristic. Special applications include modeling of autoregressions (AR) and signals of known spectral type in the presence of noise, signal deconvolution, image deblurring and multipath parameter estimation. Selected results of simulations are included to demonstrate the performance of the algorithms. >

Previous work has shown that increased frequency resolution is possible in the presence of impulsive noise utilizing an L 1 solution to a set of two-dimensional linear prediction equations. This research considers spectral estimation via an L 1 solution to a set of overdetermined linear prediction equations (1-D) for Gaussian and non-Gaussian noise. The resulting spectral estimator is evaluated for the case of two sinusoids in noise for a variety of noise types: Gaussian, uniform, Rayleigh, and impulsive.

A high resolution technique for estimating the frequencies, powers, and the number of sinusoids in noise is examined. Unlike the Pisarenko decomposition method which may only be applied to sinusoids in uncorrelated noise, the technique examined in this paper may be applied even when the noise is correlated. This technique consists of applying Prony's algorithm to a segment of the autocorrelation function, r(k), for which |k| is greater than Γ corr , where Γ corr is the decorrelation time of the noise.

The paper describes very recent and promising results on a new approach to noise correction for pole-zero modeling of signals by the pencil-of-functions method. In contradistinction to spectral subtraction techniques where only amplitude information is emphasized (and phase is ignored), we propose a method that (a) estimates the noise spectral density for the frame, and then (b) performs the subtraction of the noise correlation matrix from the correlation matrix of the information signals. The information signals are, of course, generated by processing the test signal by a cascade of first-order low pass signals, as described in earlier papers. Improvement resulting from this noise correction technique is particularly remarkable when judged by the pole-estimation accuracy, A comparison of the poles for multiple noise runs for three methods, namely, (a) Prony method, (b) Pencil-of-functions method, and (c) Pencil-of-functions method with noise correction, is given. The signal considered was the impulse response of a third order rational filter H(z), masked by noise with an SNR=12 dB.

We propose the application of modified recursive least-squares algorithms and least-squares lattice algorithms to echo cancellation problems to provide fast convergence and overcome the effects of the double-talking. The modified algorithms run continuously, but the gain updates become negligibly small during the double-talking intervals. Thus, detection of the double-talking and virtual freezing of the adaptive filter weights are both built into the algorithm. Simulations are used to verify the performance of the proposed algorithms, And the results confirm the theoretical predictions. A comparison of performances of different algorithms applied to real speech signals is also given in the paper.

This paper describes a very effective method for reducing framing noise associated with block-by-block speech coding algorithms. It is a post-coding speech enhancement procedure designed specifically to combat this type of noise. The procedure is based on a fully adaptive comb filter which is adapted in synchrony with the coding algorithm's frame boundary. An optimal (minimum mean-squared-error sense) linear prediction approach is applied to determine the filter coefficients and adapt them to the short-time statistics of the speech. A formal subjective listening trial has shown the method to significantly improve the perceived quality of block-coded speech.

A unified theoretical treatment of constrained optimisation methods for tomographic and spectral estimation from discrete data is given. The solution is shown to be equivalent to the unconstrained optimisation of a dual functional in which the image or spectrum is modelled in terms of a Lagrange multiplier vector and the kernel of the constraint integrals. In order to obtain the best possible solution it is important to consider the effects of noise in the constraints. The problem is reformulated using the above models and the exact data is replaced with the noise statistics as constraints; this is solved using a penalty method. A very fast direct algorithm is also introduced which matches the noise variance provided the signal to noise ratio is approximately known.

In this paper, we derive the detection performance of an optimally beamformed 3-D random array system, assuming known Gaussian signal, noise, and interference statistics, and compare it with the performance of a conventional beamformed system. The receiver operating characteristics (ROC) are straightforward, nonlinear functions of the particular array realization and the second-order signal, noise, and interference statistics. Thus, a determination of the average ROCs (over the array ensemble) appears intractable. However, by making a reasonable approximation, we are able to derive an analytical expression for the average ROC for both conventional and optimal processing.

The converging squares algorithm is a method for locating peaks in sampled data of 2 dimensions or higher. There are two primary advantages of this algorithm over other conventional methods. First, it is robust with respect to noise and data type. There are no empirical parameters to allow adjustment of the process, so results are completely objective. Secondly, the method is computationally efficient. The inherent structure of the algorithm is that of a resolution pyramid. This enhances computational efficiency as well as contributing to the quality of noise immunity of the method. The algorithm is detailed for 2-dimensional data. Quantitative comparisons of computation are made with two conventional peak picking methods.

This paper describes a general approach for reducing the level of broadband noise in speech. The method is derived by considering the probability density functions of the complex spectrum parameters corrupted by additive noise. This leads to a general formulatian of the problem and a class of speech spectral estimators is introduced, which include spectral subtraction as a special case. An optimum speech signal estimator is then derived from this class. Preliminary tests on spoken digit sequences with this estimator indicate a significant improvement in intelligibility at low signal-to-noise levels.

The analysis of speech using Linear Prediction is reformulated to account for the presence of acoustically added noise and a technique is presented for reducing its effect on parameter estimation. The method, called Predictive Noise Cancellation (PNC), modifies the noisy speech autocorrelations using an estimate of present background noise which is adaptively updated from an average all-pole noise spectrum. The all-pole noise spectrum is calculated by averaging autocorrelations during non-speech activity. The method uses procedures which are already available to the LPC analyzer, and thus is well suited for real time analysis of noisy speech. Preliminary results show signal to noise improvements on the order of 10 to 20 db.

Recursive computation can be used to generate sine waveforms. The waveforms are degraded by the round-off noise caused by rounding the results of multiplications. The variance of the round-off noise will increase during the computation if white noise model is assumed. However, in certain cases this will not happen. In this paper the so called 'locking' phenomenon is described. A measure is given to the locking sensitivity of a certain algorithm. Some results of computer simulations and hardware measurements are also given.

The application of an adaptive prediction error filter to autoregressive spectral analysis has been proposed by Lloyd Griffiths and is in use for the measurement of the frequencies of sinusoids It is well known that additive observation noise can bias these frequency estimates, thus limiting the useful applications of Griffiths technique to low noise environments. In the limit of white observation noise this paper develops a modified adaptive algorithm which incorporates a priori or measured noise power information so that the generated frequency estimates are unbiased. Unlike other bias removal techniques recently discussed, this technique can work with multiple sinusoids. The performance of this algorithm will be demonstrated through computer simulations and its convergence behavior will be discussed.

In this paper, a comparative study of adaptive predictive coders operating at 16 Kbps is reported. In the first part of the paper, the different architectures are described, assuming both recursive and transversal approaches and several implementations of noise shaping concept. The second part of the paper gives the detailed results of the study. For each coder, two configurations have been considered, either including a pitch loop (long term prediction), or not. For each of them, both objective measures -in terms of signal to noise ratio - and subjective evaluations - provided by listening tests - are given. Obtained results about noise shaping techniques applied to predictive coders are in good agreement with previously reported ones. Moreover, it is shown that similar performances can be reached by using a transversal structure.

A new method of estimating the parameters of a spectrum of a finite number of sinusoids of similar amplitudes and frequencies is presented. Basically the method makes the estimation of their amplitudes and phases and try to annihilating them by the addition of sinusoids of opposite sign. The residual is used to correct the estimators.

Because of the effect even additive Gaussian noise at the input has on the actual estimation of the attenuation parameter, Q, least squares estimation techniques make poor Q estimators. The errors in Q estimation may have a near Cauchy distribution. Maximum likelihood (ML) estimators based on Laplacian and Cauchy noise are derived and tested on various models. Simpler estimators, such as the median and alpha-trimmed mean (ATM) are also tested on the models. On very realistic models with noise, and on real data, the ML methods fail and the best methods appear to be the median and ATM.

A stand alone noise suppression algorithm is described for reducing the spectral effects of acoustically added noise in speech. A fundamental result is developed which shows that the spectral magnitude of speech plus noise can be effectively approximated as the sum of magnitudes of speech and noise. Using this simple phase independent additive model, the noise bias present in the short time spectrum is reduced by subtracting off the expected noise spectrum calculated during nonspeech activity. After bias removal, the time waveform is recalculated from the modified magnitude and saved phase. This Spectral Averaging for Bias Estimation and Removal, or SABER method requires only one FFT per time window for analysis and synthesis.

General matrix relations for computing the roundoff noise in nonrecursive and recursive estimators, implementid with fixed point and floating point arithmetic, are derived. The derived relations are verified by the statistical simulation procedure. A good agreement between the theory and experiment is obtained. The new method for determining the relative variance of the equivalent source of roudoff noise based on the mean square value of mantissas, in floating point case, is proposed. The cited example shows that frequently it is not correct to neglect the round-off noise end gives a justification of the whole analysis.

We will describe a noise reduction method which diffuses and suppresses the noise component, while concentrating and enhancing speech formant information. Two Dimensional Spectral Smoothing (TDSS) is applied over a time sequence of spectral envelope to diffuse noise and concentrate formant information. After consonant enhancement, Non-linear Spectral Amplitude Transformation (NSAT) is carried out to further suppress the noise component and enhance formant information. This noise reduction method has proven to be superior to the conventional frequency subtraction method.

The effect of receiver location uncertainty on all-pole superresoltion (SR) techniques that use aperiodic arrays will be analyzed in this paper. It will be shown that the effect of noise and element position errors on the target location estimates will be independent. An expression for the contribution of receiver location errors to the mean squared error in estimating the target locations will be derived. It will be shown that element position errors also raise the background level in the image. An expression for the rise in the background level will also be derived.

This paper describes, from a basic system-theoretical viewpoint, the state estimation for non-stationary vibratory structure system by observing the radiated noise from the vibrating object, disturbed by the background noise and/or other vibrations. The recursive estimation algorithm is newly derived by expanding the so-called Bayes' theorem in the form of an orthogonal expansion series. Accordingly, any kinds of statistics of state variables can be derived from it. The validity of the proposed method is confirmed especially by means of computer simulation, since the present study is yet in an early stage and we have focussed on only the methodological viewpoint in this paper.

The application of adaptive filters in noise cancelling often requires the relative placement of the two transducers at a distance that necessitates a large order filter in order to obtain an adequate output signal-to-noise ratio. A new adaptive filter structure is introduced that permits a closer placement of the transducers and that allows the cancellation of noise in the presence of crosstalk. Algorithms are developed for the new transversal and lattice structures. Simulations show considerable improvement in mean-square error over that obtained with standard noise cancelling algorithms.