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Showing papers in "IEEE Transactions on Acoustics, Speech, and Signal Processing in 1984"


Journal ArticleDOI
TL;DR: In this article, a system which utilizes a minimum mean square error (MMSE) estimator is proposed and then compared with other widely used systems which are based on Wiener filtering and the "spectral subtraction" algorithm.
Abstract: This paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short-time spectral amplitude (STSA) of the speech signal in its perception. A system which utilizes a minimum mean-square error (MMSE) STSA estimator is proposed and then compared with other widely used systems which are based on Wiener filtering and the "spectral subtraction" algorithm. In this paper we derive the MMSE STSA estimator, based on modeling speech and noise spectral components as statistically independent Gaussian random variables. We analyze the performance of the proposed STSA estimator and compare it with a STSA estimator derived from the Wiener estimator. We also examine the MMSE STSA estimator under uncertainty of signal presence in the noisy observations. In constructing the enhanced signal, the MMSE STSA estimator is combined with the complex exponential of the noisy phase. It is shown here that the latter is the MMSE estimator of the complex exponential of the original phase, which does not affect the STSA estimation. The proposed approach results in a significant reduction of the noise, and provides enhanced speech with colorless residual noise. The complexity of the proposed algorithm is approximately that of other systems in the discussed class.

3,905 citations


Journal Article
TL;DR: This paper derives a minimum mean-square error STSA estimator, based on modeling speech and noise spectral components as statistically independent Gaussian random variables, which results in a significant reduction of the noise, and provides enhanced speech with colorless residual noise.
Abstract: Absstroct-This paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short-time spectral amplitude (STSA) of the speech signal in its perception. A system which utilizes a minimum mean-square error (MMSE) STSA estimator is proposed and then compared with other widely used systems which are based on Wiener filtering and the \" spectral subtraction \" algorithm. In this paper we derive the MMSE STSA estimator, based on modeling speech and noise spectral components as statistically independent Gaussian random variables. We analyze the performance of the proposed STSA estimator and compare it with a STSA estimator derived from the Wiener estimator. We also examine the MMSE STSA estimator under uncertainty of signal presence in the noisy observations. In constructing the enhanced signal, the MMSE STSA estimator is combined with the complex exponential of the noisy phase. It is shown here that the latter is the MMSE estimator of the complex exponential of the original phase, which does not affect the STSA estimation. The proposed approach results in a significant reduction of the noise, and provides enhanced speech with colorless residual noise. The complexity of the proposed algorithm is approximately that of other systems in the discussed class.

2,714 citations


Journal ArticleDOI
TL;DR: An algorithm to estimate a signal from its modified short-time Fourier transform (STFT) by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT magnitude is presented.
Abstract: In this paper, we present an algorithm to estimate a signal from its modified short-time Fourier transform (STFT). This algorithm is computationally simple and is obtained by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT. Using this algorithm, we also develop an iterative algorithm to estimate a signal from its modified STFT magnitude. The iterative algorithm is shown to decrease, in each iteration, the mean squared error between the STFT magnitude of the estimated signal and the modified STFT magnitude. The major computation involved in the iterative algorithm is the discrete Fourier transform (DFT) computation, and the algorithm appears to be real-time implementable with current hardware technology. The algorithm developed in this paper has been applied to the time-scale modification of speech. The resulting system generates very high-quality speech, and appears to be better in performance than any existing method.

1,899 citations


Journal ArticleDOI
TL;DR: Fast transversal filter (FTF) implementations of recursive-least-squares (RLS) adaptive-filtering algorithms are presented in this paper and substantial improvements in transient behavior in comparison to stochastic-gradient or LMS adaptive algorithms are efficiently achieved by the presented algorithms.
Abstract: Fast transversal filter (FTF) implementations of recursive-least-squares (RLS) adaptive-filtering algorithms are presented in this paper. Substantial improvements in transient behavior in comparison to stochastic-gradient or LMS adaptive algorithms are efficiently achieved by the presented algorithms. The true, not approximate, solution of the RLS problem is always obtained by the FTF algorithms even during the critical initialization period (first N iterations) of the adaptive filter. This true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic-gradient algorithms (factor of 1.6 to 3.5, depending upon application). Additionally, the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing, fast-RLS algorithms, such as the fast Kalman algorithms of Morf, Ljung, and Falconer (1976) and the fast ladder (lattice) algorithms of Morf and Lee (1977-1981). They are further shown to attain (steady-state unnormalized), or improve upon (first N initialization steps), the very low computational requirements of the efficient RLS solutions of Carayannis, Manolakis, and Kalouptsidis (1983). Finally, several efficient procedures are presented by which to ensure the numerical Stability of the transversal-filter algorithms, including the incorporation of soft-constraints into the performance criteria, internal bounding and rescuing procedures, and dynamic-range-increasing, square-root (normalized) variations of the transversal filters.

724 citations


Journal ArticleDOI
TL;DR: A new algorithm is introduced for the 2m-point discrete cosine transform that reduces the number of multiplications to about half of those required by the existing efficient algorithms, and it makes the system simpler.
Abstract: A new algorithm is introduced for the 2m-point discrete cosine transform. This algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms, and it makes the system simpler.

661 citations


Journal ArticleDOI
TL;DR: A systematic method of sparse matrix factorization is developed for all four versions of the discrete W transform, the discrete cosine transform, and the discrete sine transform as well as for the discrete Fourier transform, which makes new algorithms more efficient than conventional algorithms.
Abstract: A systematic method of sparse matrix factorization is developed for all four versions of the discrete W transform, the discrete cosine transform, and the discrete sine transform, as well as for the discrete Fourier transform. The factorization leads to fast algorithms in which only real arithmetic is involved. A scheme for reducing multiplications and a convenient index system are introduced. This makes new algorithms more efficient than conventional algorithms for the discrete Fourier transform, the discrete cosine transform, and the discrete sine transform.

597 citations


Journal ArticleDOI
TL;DR: In this paper, the eigenstructure of the covariance and spectral density matrices of the received signals is used for estimating the spatio-temporal spectrum of the signals received by a passive array.
Abstract: This paper presents new algorithms for estimating the spatio-temporal spectrum of the signals received by a passive array. The algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals. They allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems. Simulation results that illustrate the performance of the new algorithms are presented.

508 citations


Journal ArticleDOI
TL;DR: In this article, a cascade of two sections is proposed for finite impulse response (FIR) digital filters, where the first section generates a sparse set of impulse response samples and the other section generates the remaining samples by using interpolation.
Abstract: A new approach to implement computationally efficient finite impulse response (FIR) digital filters is presented. The filter structure is a cascade of two sections. The first section generates a sparse set of impulse response samples and the other section generates the remaining samples by using interpolation. The method can be used to implement most practical FIR filters with significant savings in the number of arithmetic operations. Typically 1/2 to 1/8 of the number of multipliers and adders of conventional FIR filters are required in the implementation. The saving is achieved both in the linear phase and the non-linear phase cases. In addition, the new implementation gives smaller coefficient sensitivities and better roundoff noise properties than conventional implementations.

440 citations


Journal ArticleDOI
TL;DR: The relationship between α-trimmed means and median filters is explained, a simple straightforward and fast algorithm for applying a median filter is derived, and a new explanation of the convergence of repeated median filtering to the root signal is provided.
Abstract: Suppose that X is a finite set of N numbers, The α-trimmed mean of X is obtained by sorting X into ascending order, removing (trimming) a fixed fraction \alpha(0 \leq \alpha \leq 0.5) from the high and low ends of the sorted set, and computing the average of the remaining values. When applied to a sliding window of length LW, the α-trimming process is called α-trim filtering. For α = 0.5, the α-trimmed mean of a set is the median of the set and the filtering operation is called median filtering. Repeated application of a median filter to the output of a previous median filter of the same length LW eventually produces a signal which is invariant to median filtering. This final signal is called the root signal. This paper explains the relationship between α-trimmed means and median filters, derives a simple straightforward and fast algorithm for applying a median filter, and provides a new explanation of the convergence of repeated median filtering to the root signal. The latter result incorporates an approach which permits generalization of the associated concepts to a larger class of "index map" filters.

430 citations


Journal ArticleDOI
Hermann Ney1
TL;DR: The algorithm to be developed is essentially identical to one presented by Vintsyuk and later by Bridle and Brown, but the notation and the presentation have been clarified and the computational expenditure per word is independent of the number of words in the input string.
Abstract: This paper is of tutorial nature and describes a one-stage dynamic programming algorithm for file problem of connected word recognition. The algorithm to be developed is essentially identical to one presented by Vintsyuk [1] and later by Bridle and Brown [2] ; but the notation and the presentation have been clarified. The derivation used for optimally time synchronizing a test pattern, consisting of a sequence of connected words, is straightforward and simple in comparison with other approaches decomposing the pattern matching problem into several levels. The approach presented relies basically on parameterizing the time warping path by a single index and on exploiting certain path constraints both in the word interior and at the word boundaries. The resulting algorithm turns out to be significantly more efficient than those proposed by Sakoe [3] as well as Myers and Rabiner [4], while providing the same accuracy in estimating the best possible matching string. Its most important feature is that the computational expenditure per word is independent of the number of words in the input string. Thus, it is well suited for recognizing comparatively long word sequences and for real-time operation. Furthermore, there is no need to specify the maximum number of words in the input string. The practical implementation of the algorithm is discussed; it requires no heuristic rules and no overhead. The algorithm can be modified to deal with syntactic constraints in terms of a finite state syntax.

364 citations


Journal ArticleDOI
TL;DR: It is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals, filtering each binary signal to a root with a binary median filter, and then reversing the decomposition.
Abstract: Median filters are a special class of ranked order filters used for smoothing signals Repeated application of the filter on a quantized signal of finite length ultimately results in a sequence, termed a root signal, which is invariant to further passes of the median filter In this paper, it is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals, filtering each binary signal to a root with a binary median filter, and then reversing the decomposition This equivalence allows problems in the analysis and the implementation of median filters for arbitrary level signals to be reduced to the equivalent problems for binary signals Since the effects of median filters on binary signals are well understood, this technique is a powerful new tool

Journal ArticleDOI
TL;DR: Several algorithms are presented for the design of shape-gain vector quantizers based on a traning sequence of data or a probabilistic model, and their performance is compared to that of previously reported vector quantization systems.
Abstract: Memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding (LPC). One approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the Cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy. Such shape-gain vector quantizers can be applied both to waveform coding using a quadratic-error distortion measure and to voice coding using an Itakura-Saito distortion measure. In each case, the minimum distortion reproduction vector can be found by first selecting a shape code-word, and then, based on that choice, selecting a gain codeword. Several algorithms are presented for the design of shape-gain vector quantizers based on a traning sequence of data or a probabilistic model. The algorithms are used to design shape-gain vector quantizers for both the waveform coding and voice coding application. The quantizers are simulated, and their performance is compared to that of previously reported vector quantization systems.

Journal ArticleDOI
TL;DR: In this paper, the authors define a feasible solution to the signal restoration problem as the one which satisfies all constraints which can be imposed on the true solution, which are described as closed convex sets.
Abstract: The feasible solution to the signal restoration problem is defined as the one which satisfies all constraints which can be imposed on the true solution. A very important set of constraints can be obtained by examining the statistics of the noise. These and other constraints can be described as closed convex sets. Thus, projection onto closed convex sets is the numerical method used to obtain a feasible solution. Examples of this method demonstrate its usefulness in one-and two-dimensional signal restoration. The limitations of the method are discussed.

Journal ArticleDOI
TL;DR: In this article, an adaptive notch filter is developed for the enhancement and tracking of sinusoids in additive noise, colored or white, using a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter.
Abstract: In this paper, an adaptive notch filter is developed (employing a frequency domain and time domain analysis) for the enhancement and tracking of sinusoids in additive noise, colored or white. The notch filter is implemented as a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter. The resulting notch filter requires few parameters, facilitates the formation of the desired band rejection filter response, and also leads to various useful implementations (cascade, parallel). For the adaptation of the filter coefficients, the stochastic Gauss-Newton algorithm is used. The convergence of this updating procedure is established by studying the associated differential equation. Also, it is shown that the structure present in the problem enables truncation of the gradient, thereby reducing the complexity of adapting the filter coefficients. Simulation results are presented to substantiate the analysis, and to demonstrate the potential of the notch filtering technique.

Journal ArticleDOI
R. Mucci1
TL;DR: Time domain and frequency domain concepts which aid in the design and efficient implementation of a digital beamformer have been described at various times in the literature and the numerous beam-former structures that result are discussed.
Abstract: Time domain and frequency domain concepts which aid in the design and efficient implementation of a digital beamformer have been described at various times in the literature. The numerous beam-former structures that result are discussed with an emphasis on hardware requirements and spectral areas of application. Time domain procedures which include delay-sum, partial-sum, interpolation and shifted-sideband beamforming, and frequency domain techniques which include the application of discrete Fourier transforms and phase shift beam-forming are considered. Hardware considerations are primarily in the areas of analog-to-digital conversion, data storage, and computational throughput requirements.

Journal ArticleDOI
TL;DR: In this article, the steady state output error of the least mean square (LMS) adaptive algorithm due to the finite precision arithmetic of a digital processor is analyzed and the relation between the quantization error and the error that occurs when adaptation possibly ceases due to quantization is also investigated.
Abstract: The steady state output error of the least mean square (LMS) adaptive algorithm due to the finite precision arithmetic of a digital processor is analyzed. It is found to consist of three terms: 1) the error due to the input data quantization, 2) the error due to the rounding of the arithmetic operations in calculating the filter's output, and 3) the error due to the deviation of the filter's coefficients from the values they take when infinite precision arithmetic is used. The last term is of paricular interest because its mean squared value is inversely proportional to the adaptation step size μ. Both fixed and floating point arithmetics are examined and the expressions for the final mean square error are found to be similar. The relation between the quantization error and the error that occurs when adaptation possibly ceases due to quantization is also investigated.

Journal ArticleDOI
TL;DR: The problem of estimating time delay by cross correlation methods is reexamined for the whole class of stationary signals and expressions are derived for the estimation mean square error by the cross correlation method, and are shown to be identical to previously published results for Gaussian signals.
Abstract: The problem of estimating time delay by cross correlation methods is reexamined for the whole class of stationary signals. Expressions are derived for the estimation mean square error (MSE) by the cross correlation method, and are shown to be identical to previously published results for Gaussian signals. The generalized cross correlation method is also analyzed, and the optimal weight function for this method is derived. It is shown to be identical to that derived for Gaussian signals by the maximum likelihood method. For the cross correlation method a simplified MSE expression is derived, which is to be used instead of a previously published result.

Journal ArticleDOI
TL;DR: It is shown that optimal restoration must take place in the Karhunen-Loeve domain and that high quality approximate multispectral restorations must be achieved at less computational cost than exact restoration.
Abstract: The theory of optimal image restoration is well established for monochrome imagery. However, a variety of sensors acquire multi-spectral or polychrome imagery. The restoration of multispectral imagery by optimal (Wiener) methods is developed in this paper. It is shown that optimal restoration must take place in the Karhunen-Loeve domain. It is further shown that high quality approximate multispectral restorations must be achieved at less computational cost than exact restoration. This latter point is applied to the development of a fast approximate procedure for restoration of conventional color photography.

Journal ArticleDOI
TL;DR: In this article, a new technique for designing quadrature mirror filters is described, which is carried out in the time domain and results in an optimization problem requiring minimization of a quartic multinomial.
Abstract: A new technique for designing quadrature mirror filters is described. The formulation, carried out in the time domain, is shown to result in an optimization problem requiring minimization of a quartic multinomial. An iterative solution is suggested which involves (computation of) the eigenvector of a matrix with a dimensionality equal to one half the number of filter taps. Our experiments show that convergence to the optimum tap weights is stable, and the accuracy of the final solution is limited only by the accuracy of the eigenvalue-eigenvector routine. As in an earlier technique, the user can specify the stop: band frequency the relative weights of the passband ripple energy and the stopband residual energy, and, of course, the number of filter taps.

Journal ArticleDOI
TL;DR: In this article, the authors present filtering methods for interfacing time-discrete systems with different sampling frequencies, which are applicable for sampling rate conversion between any two sampling frequencies; the conversion ratio may even be irrational or slowly time varying.
Abstract: The paper presents filtering methods for interfacing time-discrete systems with different sampling frequencies. The methods are applicable for sampling rate conversion between any two sampling frequencies; the conversion ratio may even be irrational or slowly time varying. Interpolation by irrational factors requires digital filters with nonperiodically varying coefficients. This is dealt with in two ways. 1) All possible coefficient values are precalculated. This is, in a sense, possible because of the finite resolution needed. Or 2), the coefficients can be updated in real time using either FIR or IIR filters. The first solution requires a huge coefficient memory; the second scheme, on the other hand, is computationally intensive. While discussing both of these solutions, more practical intermediate schemes incorporating both FIR-and IIR-type filters are suggested. The suggested practical implementations are either based on analog reconstruction filters where the derived digital filter coefficients are functions of the distances between current input and output samples or digital interpolators combined with simple analog interpolation schemes for finding the desired values in between the uniform output samples from the digital interpolator.

Journal ArticleDOI
TL;DR: This study shows that the relative importance of spectral magnitude and phase depends on the nature of signals, and explains the convergence behavior of the existing iterative algorithms for signal reconstruction.
Abstract: In this paper we discuss the problem of signal reconstruction from spectral magnitude or phase using group delay functions. We define two separate group delay functions for a signal, one is derived from the magnitude and the other from the phase of the Fourier transform of the signal. The group delay functions offer insight into the problem of signal reconstruction and suggest methods for reconstructing signals from partial information such as spectral magnitude or phase. We examine the problem of signal reconstruction from spectral magnitude or phase on the basis of these two group delay functions and derive the conditions for signal reconstruction. Based on existing iterative and noniterative algorithms for signal reconstruction, we propose new algorithms for some special classes of signals. The algorithms are illustrated with several examples. Our study shows that the relative importance of spectral magnitude and phase depends on the nature of signals. Speech signals are used to illustrate the importance of spectral magnitude and picture signals are used to illustrate the importance of phase in signal reconstruction problems. Using the group delay functions, we explain the convergence behavior of the existing iterative algorithms for signal reconstruction.

Journal ArticleDOI
TL;DR: It is shown that a muitichannel LS estimation algorithm with a different number of parameters to be estimated in each channel can be implemented by cascading lattice stages of nondescending dimension to form a generalized lattice structure.
Abstract: A generalized multichannel least squares (LS) lattice algorithm which is appropriate for multichannel adaptive filtering and estimation is presented in this paper. It is shown that a muitichannel LS estimation algorithm with a different number of parameters to be estimated in each channel can be implemented by cascading lattice stages of nondescending dimension to form a generalized lattice structure. A new realization of a multichannel lattice stage is also presented. This realization employs only scalar operations and has a computational complexity of 0(p2) for each p-channel lattice stage.


Journal ArticleDOI
TL;DR: Results of this research indicate that by using adaptive prediction and quantization, intensity and density coded images of high quality can be obtained at information rates as low as 0.7 bits/pixel.
Abstract: This paper summarizes a study on two-dimensional linear prediction of images and its application to adaptive predictive coding of monochrome images. The study was focused on three major areas: two-dimensional linear prediction of images and its performance, implementation of an adaptive predictor and adaptive quantizer for use in image coding, and linear prediction and adaptive predictive coding of density (logarithm of intensity) images. Among the issues investigated are: autoregressive modeling of 2-D image sequences, estimation of the nonzero average bias of the image samples, stability of the inverse prediction error filter, and estimation of the parameters of a 2-D separable linear predictor. The implementation of the adaptive predictor is based on the results of linear predictive analysis. The adaptive quantization of the prediction error signal is done by using a flexible three-level quantizer for code words of fixed or variable length. The above ideas are further applied to density images for exploiting the multiplicative structure of images. The results of this research indicate that by using adaptive prediction and quantization, intensity and density coded images of high quality can be obtained at information rates as low as 0.7 bits/pixel.

Journal ArticleDOI
TL;DR: In this paper, the problem of reconstructing a multidimensional field from noisy, limited projection measurements is approached using an object-based stochastic field model, where objects within a cross section are characterized by a finite-dimensional set of parameters.
Abstract: The problem of reconstructing a multidimensional field from noisy, limited projection measurements is approached using an object-based stochastic field model. Objects within a cross section are characterized by a finite-dimensional set of parameters, which are estimated directly from limited, noisy projection measurements using maximum likelihood estimation. In Part I, the computational structure and performance of the ML estimation procedure are investigated for the problem of locating a single object in a deterministic background; simulations are also presented. In Part II, the issue of robustness to modeling errors is addressed.

Journal ArticleDOI
TL;DR: New quadrature mirror filter structures for the frequency domain analysis and synthesis of digital signals are introduced and a new scheme which reduces the computational complexity by about a factor of two over conventional QMF implementations is proposed.
Abstract: This paper introduces new quadrature mirror filter (QMF) structures for the frequency domain analysis and synthesis of digital signals. The conventional QMF technique is first extended to cover complex quadrature mirror filters (CQMF) in which a digital signal is split into N adjacent complex subbands where the real and imaginary parts are subsampled by 1/2N with respect to the original signal. The computational complexity of QMF banks is then analyzed and a new scheme which reduces the computational complexity by about a factor of two over conventional QMF implementations is proposed. Finally, the filter design tradeoffs are discussed and the microprogramed implementation of QMF banks is evaluated.

Journal ArticleDOI
Roman Kuc1
TL;DR: In this article, two approaches for estimating the attenuation coefficient of soft biological tissue have been examined: the spectral shift approach, which estimates β from the downward shift experienced by the propagating pulse spectrum with penetration into the liver, and the spectral-difference approach (SDA) which estimates α from the slope of the log spectral differences.
Abstract: The acoustic attenuation coefficient of soft biological tissue has been observed to have an increasing linear-with-frequency attenuation characteristic with a slope, denoted by β, that varies with the disease condition of the liver. Hence, it would be diagnostically useful to estimate the value of β from reflected ultrasound signals. Two approaches for estimating β are examined: the spectral-shift approach, which estimates β from the downward shift experienced by the propagating pulse spectrum with penetration into the liver, and the spectral-difference approach, which estimates β from the slope of the log spectral differences. While the spectral-shift approach requires the propagating pulse to have a Gaussian-shaped spectrum, the spectral-difference method does not require a specific spectral form. A mathematical model is developed to simulate the random ultrasound signals reflected from the liver. The bias and variance properties of the β estimators are determined by using the simulated signals and compared as a function of the data window size. The results indicate that, while the accuracy of both approaches is equivalent for large data windows, the frequency-shift approach is more accurate than the spectral-difference approach for most practical cases.

Journal ArticleDOI
TL;DR: In this paper, a new method for removing impulse noises from images is proposed, which is based on replacing the central pixel value by the generalized mean value of all pixels inside a sliding window.
Abstract: A new method for removing impulse noises from images is proposed. The filtering scheme is based on replacing the central pixel value by the generalized mean value of all pixels inside a sliding window. The concepts of thresholding and complementation which are shown to improve the performance of the generalized mean filter are introduced. The threshold is derived using a statistical theory. The actual performance of the proposed filter is compared with that of file commonly used median filter by filtering noise corrupted real images. The hardware complexity of the two types of filters are also compared indicating the advantages of the generalized mean filter.

Journal ArticleDOI
TL;DR: In this paper, an adaptative filter whose main feature is to preserve edges and impulses present in the signal is analyzed by the computation of the mean-square error (MSE) of its output sequence.
Abstract: An adaptative filter whose main feature is to preserve edges and impulses present in the signal is analyzed by the computation of the mean-square error (MSE) of its output sequence. The filter in its more general form is highly nonlinear, resembling the M-type estimators used in robust statistics. A simplified form used here allows the exact computation of the MSE when the filter length is finite. This MSE can be compared to the ones obtained for a median filter and a mean filter. It is shown that for a wide range of the filter and signal parameters such as filter length, edge heights, and impulse width, the performance of the filter proposed in this paper is superior to the other filters mentioned above. An additional advantage of the simplified version of the filter is that in most cases, its computation amounts to a linear adaptative averaging. This contrasts with the amount of calculation required to implement the median filter and any other filter based on the order statistics of the measured samples.

Journal ArticleDOI
TL;DR: Although both estimates lead to intelligible speech, speech based on the MESA estimate is qualitatively superior, and the empirical investigation is based on speech synthesized using the different spectral estimates.
Abstract: In maximum entropy spectral analysis (MESA), one maximizes the integral of \logS(f) , where S(f) is a power spectrum. The resulting spectral estimate, which is equivalent to that obtained by linear prediction and other methods, is popular in speech processing applications. An alternative expression, -S(f)\logS(f) , is used in optical processing and elsewhere. This paper considers whether the alternative expression leads to spectral estimates useful in speech processing. We investigate the question both theoretically and empirically. The theoretical investigation is based on generalizations of file two estimates-the generalizations take into account prior estimates of the unknown power spectrum. It is shown that both estimates result from applying a generalized version of the principle of maximum entropy, but they differ concerning the quantities that are treated as random variables. The empirical investigation is based on speech synthesized using the different spectral estimates. Although both estimates lead to intelligible speech, speech based on the MESA estimate is qualitatively superior.