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Signal Processing, IEEE Transactions on

Issue 11 • Date Nov. 2001

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Displaying Results 1 - 25 of 42
  • Comments on "Least squares restoration of multichannel images"

    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (48 KB) |  | HTML iconHTML  

    For original article see Galatsanos et al. (IEEE Trans. Signal Processing, vol.39, p.2222-36, Oct. 1991). In this correspondence, we give the correct matrix formulation arising from the constrained optimization of the least squares restoration of multichannel images in Galatsanos et al. View full abstract»

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  • Integer DCTs and fast algorithms

    Page(s): 2774 - 2782
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (201 KB) |  | HTML iconHTML  

    A method is proposed to factor the type-II discrete cosine transform (DCT-II) into lifting steps and additions. After approximating the lifting matrices, we get a new type-II integer discrete cosine transform (IntDCT-II) that is float-point multiplication free. Based on the relationships among the various types of DCTs, we can generally factor any DCTs into lifting steps and additions and then get four types of integer DCTs, which need no float-point multiplications. By combining the polynomial transform and the one-dimensional (1-D) integer cosine transform, a two-dimensional (2-D) integer discrete cosine transform is proposed. The proposed transform needs only integer operations and shifts. Furthermore, it is nonseparable and requires a far fewer number of operations than that used by the corresponding row-column 2-D integer discrete cosine transform View full abstract»

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  • Mixed H2/H filtering design in multirate transmultiplexer systems: LMI approach

    Page(s): 2693 - 2701
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (233 KB)  

    A mixed H2/H filter design is proposed for multirate transmultiplexer systems with dispersive channel and additive noise. First, a multirate state-space representation is introduced for the transmultiplexer with the consideration of channel dispersion. Then, the problem of signal reconstruction can be regarded as a state estimation problem. In order to design an efficient separating filterbank for a transmultiplexer system with uncertain input signal and additive noise, the H filter is employed for robust signal reconstruction. The H2 filter design is considered to be a suboptimal approach to achieve the optimal signal reconstruction in transmultiplexer system under unitary noise power. Finally, a mixed H2/H filter is proposed to achieve a better signal reconstruction performance in transmultiplexer systems. These design problems can be transformed to solving the eigenvalue problems (EVP) under some linear matrix inequality (LMI) constraint. The LMI Matlab toolbox can be applied to efficiently solve the EVP by convex optimization technique View full abstract»

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  • New approaches to robust minimum variance filter design

    Page(s): 2620 - 2629
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (243 KB)  

    This paper is concerned with the design of robust filters that ensure minimum filtering error variance bounds for discrete-time systems with parametric uncertainty residing in a polytope. Two efficient methods for robust Kalman filter design are introduced. The first utilizes a recently introduced relaxation of the quadratic stability requirement of the stationary filter design. The second applies the new method of recursively solving a semidefinite program (SDP) subject to linear matrix inequalities (LMIs) constraints to obtain a robust finite horizon time-varying filter. The proposed design techniques are compared with other existing methods. It is shown, via two examples, that the results obtained by the new methods outperform all of the other designs View full abstract»

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  • On the parameterization of positive real sequences and MA parameter estimation

    Page(s): 2630 - 2639
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (245 KB)  

    An algorithm for moving average (MA) parameter estimation was proposed by Stoica et al. (see ibid. vol.48, p.1999-2012, 2000). Its key step (covariance fitting) is a semidefinite programming (SDP) problem with two convex constraints: one reflecting the real positiveness of the desired covariance sequence and the other having a second-order cone form. We analyze two parameterizations of a positive real sequence and show that there is a one-to-one correspondence between them. We also show that the dual of the covariance fitting problem has a significantly smaller number of variables and, thus, a much reduced computational complexity. We discuss in detail the formulations that are best suited for the currently available semidefinite quadratic programming packages. Experimental results show that the execution times of the newly proposed algorithms scale well with the MA order, which are therefore convenient for large-order MA signals View full abstract»

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  • Low-complexity multiuser channel estimation with aperiodic spreading codes

    Page(s): 2813 - 2822
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (294 KB)  

    Signal processing techniques for CDMA systems employing aperiodic spreading sequences have gained significant interest. Due to the time-varying nature of users' unknown signatures in a multipath communication environment, direct design of blind multiuser detectors is intractable. We focus on estimating the unknown multipath parameters for each active user in the system. The problem is solved in the correlation matching context based on correlations of both the directly received data and the outputs of a bank of matched filters. Three typical scenarios are discussed such as quasisynchronous uplink CDMA system with AWGN, with unknown interference, and downlink CDMA system with AWGN, leading to different solutions. We model the aperiodic spreading codes as random variables. For any priori-known distribution of the spreading codes, their statistics up to the fourth order can be evaluated, resulting in extremely low computational complexity of the methods. The identifiability of the channel parameters only depends on the nonsingularity of a deterministic matrix determined by known system parameters. In the case of unknown code statistics, the methods can be modified to be still applicable by estimating those code statistics from given spreading codes. However, in such a case, more computations are needed. Comparisons with other existing methods show that the proposed computationally efficient approaches can provide satisfactory results while requiring significantly less computations View full abstract»

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  • Support vector machines and the multiple hypothesis test problem

    Page(s): 2865 - 2872
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (212 KB)  

    Two enhancements are proposed to the application and theory of support vector machines. The first is a method of multicategory classification based on the binary classification version of the support vector machine (SVM). The method, which is called the M-ary SVM, represents each category in binary format, and to each bit of that representation is assigned a conventional SVM. This approach requires only [log2(K)] SVMs, where K is the number of classes. We give an example of classification on an octaphase-shift-keying (8-PSK) pattern space to illustrate the main concepts. The second enhancement is that of adding equality constraints to the conventional binary classification SVM. This allows pinning the classification boundary to points that are known a priori to lie on the boundary. Applications of this method often arise in problems having some type of symmetry, We present one such example where the M-ary SVM is used to classify symbols of a CDMA two-user, multiuser detection pattern space View full abstract»

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  • A state-space approach to QRD-LSL interpolation and QRD-LSL smoothing

    Page(s): 2880 - 2884
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (180 KB) |  | HTML iconHTML  

    Sayed and Kailath (1994) demonstrated the feasibility of directly deriving many known adaptive filtering algorithms in square-root forms by a proper reformulation of the original adaptive problem into a state-space form. This work employs this state-space form to develop adaptive interpolation and smoothing algorithms. In particular, a systematic and concise derivation of the QR-decomposition least-squares lattice (QRD-LSL) interpolation and smoothing algorithms using correspondences between Kalman filtering and LSL adaptive filtering is given View full abstract»

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  • RLS-Laguerre lattice adaptive filtering: error-feedback, normalized, and array-based algorithms

    Page(s): 2565 - 2576
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (351 KB)  

    This paper develops several lattice structures for RLS-Laguerre adaptive filtering including a posteriori and a priori based lattice filters with error-feedback, array-based lattice filters, and normalized lattice filters. All structures are efficient in that their computational cost is proportional to the number of taps, albeit some structures require more multiplications or divisions than others. The performance of all filters, however, can differ under practical considerations, such as finite-precision effects and regularization. Simulations are included to illustrate these facts View full abstract»

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  • A recursive variant of Mallows' filter class

    Page(s): 2745 - 2752
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (160 KB) |  | HTML iconHTML  

    Mallows' (1980) nonlinear FIR filter class includes most of the nonlinear digital filters in wide use today. This filter class is defined in terms of five axioms, and this paper modifies two of these axioms to obtain a class of symmetric recursive nonlinear filters. One of the main points considered in this paper is the consequence of Mallows' location invariance axiom A2, and general prescriptions are given for both Mallows' original FIR filter class and its recursive extension. This representation is also extremely useful in discussing the root sequences of both the recursive and nonrecursive structures. Since recursive filters can exhibit various forms of instability, a number of stability results are presented for this class of filters. Finally, some simple examples are considered that illustrate the potential utility of the results presented View full abstract»

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  • Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case

    Page(s): 2844 - 2852
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (244 KB)  

    The construction of Gabor's (1946) complex signal-which is also known as the analytic signal-provides direct access to a real one-dimensional (1-D) signal's local amplitude and phase. The complex signal is built from a real signal by adding its Hilbert transform-which is a phase-shifted version of the signal-as an imaginary part to the signal. Since its introduction, the complex signal has become an important tool in signal processing, with applications, for example, in narrowband communication. Different approaches to an n-D analytic or complex signal have been proposed in the past. We review these approaches and propose the hypercomplex signal as a novel extension of the complex signal to n-D. This extension leads to a new definition of local phase, which reveals information on the intrinsic dimensionality of the signal. The different approaches are unified by expressing all of them as combinations of the signal and its partial and total Hilbert transforms. Examples that clarify how the approaches differ in their definitions of local phase and amplitude are shown. An example is provided for the two-dimensional (2-D) hypercomplex signal, which shows how the novel phase concept can be used in texture segmentation View full abstract»

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  • An uncertainty principle for real signals in the fractional Fourier transform domain

    Page(s): 2545 - 2548
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (105 KB) |  | HTML iconHTML  

    The fractional Fourier transform (FrFT) can be thought of as a generalization of the Fourier transform to rotate a signal representation by an arbitrary angle α in the time-frequency plane. A lower bound on the uncertainty product of signal representations in two FrFT domains for real signals is obtained, and it is shown that a Gaussian signal achieves the lower bound. The effect of shifting and scaling the signal on the uncertainty relation is discussed. An example is given in which the uncertainty relation for a real signal is obtained, and it is shown that this relation matches with that given by the uncertainty relation derived View full abstract»

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  • Near-field/far-field azimuth and elevation angle estimation using a single vector hydrophone

    Page(s): 2498 - 2510
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (463 KB) |  | HTML iconHTML  

    This paper introduces a new underwater acoustic eigenstructure ESPRIT-based algorithm that yields closed-form direction-of-arrival (DOA) estimates using a single vector hydrophone. A vector hydrophone is composed of two or three spatially co-located but orthogonally oriented velocity hydrophones plus another optional co-located pressure hydrophone. This direction finding algorithm may (under most circumstances) resolve up to four uncorrelated monochromatic sources impinging from the near-field or the far-field, but it assumes that all signal frequencies are distinct. It requires no a priori knowledge of the signals' frequencies, suffers no frequency-DOA ambiguity, and pairs automatically the x-axis direction cosines with the y-axis direction cosines. It significantly outperforms an array of spatially displaced pressure hydrophones of comparable array-manifold size and computational load but may involve more complex hardware. This work also derives new Cramer-Rao bounds (CRBs) for various vector hydrophone constructions of arrival angle estimates for the incident uncorrelated sinusoidal signals corrupted by spatio-temporally correlated additive noise View full abstract»

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  • Sorting continuous-time signals: analog median and median-type filters

    Page(s): 2734 - 2744
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (254 KB) |  | HTML iconHTML  

    There are two natural orderings in signals: temporal order and rank order. There is no compelling reason to explore only one of these orderings, either in the discrete-time or in the continuous-time case. Nevertheless, the concept of rank order for continuous-time signals remains virtually neglected, which is in striking contrast to the discrete-time case: ranked order discrete-time filters, of which the running median is the most common example, have been intensively studied for three decades. The dependence of these nonlinear systems on the order statistics of the input samples stands in contrast with the tapped delay line filter, which depends on temporal order only. However, continuous-time signals can also be meaningfully sorted: a fact that is explored in this paper to define and study the analog median filter and other ranked-order filters. The paper introduces the basic tools needed to analyze and understand these continuous-time nonlinear filters (the distribution function and the sorting) and presents some of their properties in a tutorial way. The analog median filter is defined in terms of the (unique) nonincreasing left-continuous sorting. More general filters can also be defined, including filters similar to α-trimmed mean filters and L filters. These include filters that depend on one parameter and contain the running average and running median as special cases. The rate of convergence of the digital median filter to the analog median filter is discussed and related to the signal sampling period, the duration of the filter window, and the smoothness of the input signal. The paper introduces the concept of noise width and studies the effect of additive and multiplicative noise at the output of the analog median filter in terms of the noise width and the smoothness of the input signal View full abstract»

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  • Lattice structure for regular paraunitary linear-phase filterbanks and M-band orthogonal symmetric wavelets

    Page(s): 2659 - 2672
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (402 KB)  

    Parauninary linear-phase (PULP) M-channel uniform filterbanks, which are also known as the generalized lapped orthogonal transforms (GenLOTs), can be designed and implemented using lattice structures. This paper discusses how to impose regularity constraints onto the lattice structure of PULP filterbanks. These conditions are expressed in term of the rotation angles of the lattice components by which the resulting filterbanks are guaranteed to have one or two degrees of regularity, iterating these new regular filterbanks on the lowpass subband generates a large family of symmetric M-band orthonormal wavelets. Design procedures with many design examples are presented. Smooth interpolation using regular PULP filterbanks is illustrated through image coding experiments where the novel M-band wavelets consistently yield smoother reconstructed images and better perceptual quality View full abstract»

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  • Performance of multiple LMS adaptive filters in tandem

    Page(s): 2762 - 2773
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (315 KB) |  | HTML iconHTML  

    The tandem of adaptive filters can occur in practice such as in echo cancellation application for voice communications. This paper analyzes the performance of a number of adaptive filters in tandem. The adaptation algorithm is assumed to be least mean square (LMS). The analysis includes learning trajectory, steady-state excess error due to noise, tracking lag bias, and tracking lag variance. Recursive formulae for their computation are derived. The analysis is exact under Gaussian input and independency assumption. It does not restrict the step size of the filters in tandem to be identical. The validity of the theoretical development is corroborated by simulations. The results indicate that in the special case of equal and small step size, both the steady-state excess error due to noise and the tracking lag variance increase approximately linearly with the number of filters in tandem, whereas the tracking lag bias decreases approximately exponentially with the number of filters in tandem. Consequently, the tandem of adaptive filters can improve the tracking capability of an adaptive system in the situation where the step size is small or the dynamics of an unknown system to be modeled is high View full abstract»

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  • Optimal loop scheduling for hiding memory latency based on two-level partitioning and prefetching

    Page(s): 2853 - 2864
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (193 KB)  

    The large latency of memory accesses in modern computers is a key obstacle in achieving high processor utilization. As a result, a variety of techniques have been devised to hide this latency. These techniques range from cache hierarchies to various prefetching and memory management techniques for manipulating the data present in the caches. In DSP applications, the existence of large numbers of uniform nested loops makes the issue of loop scheduling very important. In this paper, we propose a new memory management technique that can be applied to computer architectures with three levels of memory, which is the scheme generally adopted in contemporary computer architectures. This technique takes advantage of access pattern information that is available at compile time by prefetching certain data elements from the higher level memory before they are explicitly requested by the lower level memory or CPU. It also maintains certain data for a period of time to prevent unnecessary data swapping. In order to take better advantage of the locality of references present in these loop structures, our technique introduces a new approach to memory management by partitioning it and reducing execution to each partition so that data locality is much improved compared with the usual pattern. These combined approaches-using a new set of memory instructions as well as partitioning the memory-lead to improvements in average execution times of approximately 35% over the one-level partition algorithm and more than 80% over list scheduling and hardware prefetching View full abstract»

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  • Bussgang-zero crossing equalization: an integrated HOS-SOS approach

    Page(s): 2798 - 2812
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (397 KB) |  | HTML iconHTML  

    An integrated higher order statistics (HOS) and second order statistics (SOS) based equalization technique is presented as an extension of the Bussgang equalization algorithm. This extension allows one to simultaneously take account of the statistical knowledge about the data source, as done in the conventional HOS approaches and, in particular, by Bussgang-like equalization algorithms such as super exponential, constant modulus, etc., and the spectral redundancy usually present in pulse-amplitude modulation (PAM) and quadrature-amplitude modulation (QAM) modulated signals, exploited by SOS-based approaches. The technique presented employs a new form of SOS equalization that naturally integrates into the Bussgang scheme. It is based on a zero crossing (ZC) property of the received signal when it is passed through a suitable filter. The novel equalization scheme is presented in a Bayesian estimation framework, after illustration of the general Bussgang paradigm and of the principles of the ZC approach. From simulated experiments, results show that the extended Bussgang-ZC equalizer not only outperforms conventional Bussgang equalizers but is also robust to situations where HOS and SOS approaches individually fail View full abstract»

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  • A new narrowband interference suppression scheme for spread-spectrum CDMA communications

    Page(s): 2832 - 2838
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (142 KB) |  | HTML iconHTML  

    This paper presents a new nonlinear approach for narrowband interference (NBI) suppression in code-division multiple-access (CDMA) systems. The proposed scheme is an adaptive nonlinear predictor that consists of an (N+1)-level quantizer, four adders, and two adaptive linear filters, where N is the number of users in the CDMA system. Both adaptive filters have the same coefficients at each iteration: one for feedforward estimation of NBI and the other for feedback compensation for the estimated result. It could be regarded as an improved version of the nonlinear predictor with offset outputs presented recently by Wang et al. (1996). Computer simulation results support that the improved offset predictor performs much better than the original one under the same complexity. As compared with the nearly optimal approximate conditional mean filter, it achieves almost the same performance even at very low signal-to-noise ratio but involves much less complexity View full abstract»

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  • Identification of input-output bilinear systems using cumulants

    Page(s): 2753 - 2761
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (257 KB) |  | HTML iconHTML  

    This paper is concerned with the identification of a discrete input-output bilinear system driven by an independent identically distributed (i.i.d.) stochastic input and corrupted by measurement noise. A novel algorithmic procedure for the direct computation of the unknown model parameters is developed based on crosscumulant information up to third order. Simulations and comparisons with a least squares type identification method are provided View full abstract»

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  • FIR differentiators for quantized signals

    Page(s): 2713 - 2720
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (209 KB) |  | HTML iconHTML  

    The impact of quantization noise on a signal whose rate is to be estimated using a FIR differentiator is analyzed, concentrating on the important constant-rate case in order that the filter be optimized for systems with low-frequency rates of change. Formulae for the mean-squared error of the filter, the corresponding spectral characteristics, and general formulae governing the filter coefficients are derived. The characteristics of four specific differentiators, including a representative wideband differentiator, are examined and compared. It is shown that a differentiator that is optimum in terms of its attenuation of white noise can also be considered optimum with respect to quantization noise attenuation in certain circumstances. An elegant relationship is derived between worst-case RMS error and the fractional value of the rate at which this error occurs. Minimization of this worst-case mean-squared error is shown to be achieved with a simple differentiator. However, the corresponding average error is poor, and a simple nonlinear filter that minimizes the worst-ease error, while retaining a similar average mean-squared error to that of the “optimum” differentiator, is proposed. The equivalence between FIR differentiators and the decoders used in single-loop sigma-delta modulators is also highlighted View full abstract»

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  • MSE-based regularization approach to direction estimation of coherent narrowband signals using linear prediction

    Page(s): 2481 - 2497
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB) |  | HTML iconHTML  

    This paper addresses the problem of directions of arrival (DOAs) estimation of coherent narrowband signals impinging on a uniform linear array (ULA) when the number of signals is unknown. By using an overdetermined linear prediction (LP) model with a subarray scheme, the DOAs of coherent signals can be estimated from the zeros of the corresponding prediction polynomial. Although the corrected least squares (CLS) technique can be used to improve the accuracy of the LP parameters estimated from the noisy array data, the inversion of the resulting matrix in the CLS estimation is ill-conditioned, and then, the CLS estimation becomes unstable. To combat this numerical instability, we introduce multiple regularization parameters into the CLS estimation and show that determining the number of coherent signals is closely related to the truncation of the eigenvalues. An analytical expression of the mean square error (MSE) of the estimated LP parameters is derived, and it is clarified that the number of signals can be determined by comparing the optimal regularization parameters with the corresponding eigenvalues. An iterative regularization algorithm is developed for estimating directions without any a priori knowledge, where the number of coherent signals and the noise variance are estimated from the noise-corrupted received data simultaneously View full abstract»

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  • A new class of orthonormal symmetric wavelet bases using a complex allpass filter

    Page(s): 2640 - 2647
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (200 KB) |  | HTML iconHTML  

    This paper considers the design of the whole sample symmetric (WSS) paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real-valued orthonormal symmetric wavelet bases. First, the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets, and its transfer function is given to satisfy these conditions. Second, the paraunitary filter banks are designed by using the derived transfer function from the viewpoints of the regularity and frequency selectivity. A new method for designing the proposed paraunitary filterbanks with a given degrees of flatness is presented. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm. Therefore, the filter coefficients can be easily obtained by solving the eigenvalue problem, and the optimal solution is attained through a few iterations. Furthermore, both the maximally flat and minimax solutions are also included in the proposed method as two specific cases. The maximally flat filters have a closed-form solution without any iteration. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method View full abstract»

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  • Linear redundancy of information carried by the discrete Wigner distribution

    Page(s): 2536 - 2544
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (266 KB) |  | HTML iconHTML  

    The discrete Wigner distribution (WD) encodes information in a redundant fashion since it derives N by N representations from N-sample signals. The increased amount of data often prohibits its effective use in applications such as signal detection, parameter estimation, and pattern recognition. As a consequence, it is of great interest to study the redundancy of information it carries. Richard and Lengelle (see Proc. IEEE Int.Conf. Acost., Speech, Signal Process., Istanbul, Turkey, p.85-8, 2000) have shown that linear relations connect the time-frequency samples of the discrete WD. However, up until now, such a redundancy has still not been algebraically characterized. In this paper, the problem of the redundancy of information carried by the discrete cross WD of complex-valued signals is addressed. We show that every discrete WD can be fully recovered from a small number of its samples via a linear map. The analytical expression of this linear map is derived. Special cases of the auto WD of complex-valued signals and real-valued signals are considered. The results are illustrated by means of computer simulations, and some extensions are pointed out View full abstract»

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  • Robust frequency-selective filtering using weighted myriad filters admitting real-valued weights

    Page(s): 2721 - 2733
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (376 KB) |  | HTML iconHTML  

    Weighted myriad smoothers have been proposed as a class of nonlinear filters for robust non-Gaussian signal processing in impulsive noise environments. However, weighted myriad smoothers are severely limited since their weights are restricted to be non-negative. This constraint makes them unusable in bandpass or highpass filtering applications that require negative filter weights. Further, they are incapable of amplifying selected frequency components of an input signal. In this paper, we generalize the weighted myriad smoother to a richer structure: a weighted myriad filter admitting real-valued weights. This involves assigning a pair of filter weights (one positive and the other negative) to each of the input samples. Equivalently, the filter can be described as a weighted myriad smoother applied to a transformed set of samples that includes the original input samples as well as their negatives. The weighted myriad filter is analogous to a normalized linear FIR filter with real-valued weights whose absolute values sum to unity. By suitably scaling the output of the weighted myriad filter, we extend it to yield the so-called scaled weighted myriad filter, which includes (but is more powerful than) the traditional unconstrained linear FIR filter. Finally we derive stochastic gradient-based nonlinear adaptive algorithms for the optimization of these novel myriad filters under the mean square error criterion View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

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Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota