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Signal Processing, IEEE Transactions on

Issue 11 • Date Nov. 1995

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Displaying Results 1 - 25 of 33
  • Corrections to "Detection of Non-Gaussian Signals Using Integrated Polyspectrum"

    Publication Year: 1995
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (175 KB)  

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  • Abstracts of manuscripts in review

    Publication Year: 1995
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    Freely Available from IEEE
  • Closed-form blind symbol estimation in digital communications

    Publication Year: 1995 , Page(s): 2714 - 2723
    Cited by:  Papers (96)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (976 KB)  

    We study the blind symbol estimation problem in digital communications and propose a novel algorithm by exploiting a special data structure of an oversampled system output. Unlike most equalization schemes that involve two stages-channel identification and channel equalization/symbol estimation-the proposed approach accomplishes direct symbol estimation without determining the channel characteristics. Based on a deterministic model, the new method can provide a closed-form solution to the symbol estimation using a small set of data samples, which makes it particularly suitable for wireless applications with fast changing environments. Moreover, if the symbols belong to a finite alphabet, e.g., BPSK or QPSK, our approach can be extended to handle the symbol estimation for multiple sources. Computer simulations and field RF experiments were conducted to demonstrate the performance of the proposed method. The results are compared to the Cramer-Rao lower bound of the symbol estimates derived in this paper View full abstract»

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  • The chirplet transform: physical considerations

    Publication Year: 1995 , Page(s): 2745 - 2761
    Cited by:  Papers (78)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2428 KB)  

    We consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis. We propose the use of quadratic chirp functions (which we will call q-chirps for short), giving rise to a parameter space that includes both the time-frequency plane and the time-scale plane as 2-D subspaces. The parameter space contains a “time-frequency-scale volume” and thus encompasses both the short-time Fourier transform (as a slice along the time and frequency axes) and the wavelet transform (as a slice along the time and scale axes). In addition to time, frequency, and scale, there are two other coordinate axes within this transform space: shear in time (obtained through convolution with a q-chirp) and shear in frequency (obtained through multiplication by a q-chirp). Signals in this multidimensional space can be obtained by a new transform, which we call the “q-chirplet transform” or simply the “chirplet transform”. The proposed chirplets are generalizations of wavelets related to each other by 2-D affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets, which are related to each other by 1-D affine coordinate transformations (translations and dilations) in the time domain only View full abstract»

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  • Fast computation of channel-estimate based equalizers in packet data transmission

    Publication Year: 1995 , Page(s): 2462 - 2473
    Cited by:  Papers (57)  |  Patents (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (900 KB)  

    Computationally efficient procedures are introduced for the real-time calculation of finite-impulse-response (FIR) equalizers for packet-based data transmission applications, such as wireless data networks. In such packet data applications, the FIR equalizer filters are computed indirectly by first estimating the channel pulse response from a known training pattern embedded in each packet and then computing the equalizer for use in the recovery of the remaining unknown data in the packet. We find that a minimum mean-square-error decision-feedback equalizer (MMSE-DFE) with a finite-length constraint on its feedforward and feedback filters can be very efficiently computed from this pulse response. We combine a recent theory of finite-spectral factorization for the MMSE-DFE with the theory of structured matrices to derive these efficient procedures for computing the equalizer settings. The introduced method is much more computationally efficient than direct computation by matrix inversion or the use of popular gradient or least-squares algorithms over the duration of the packet View full abstract»

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  • Direction-of-arrival estimation of correlated sources by adaptive beamforming

    Publication Year: 1995 , Page(s): 2782 - 2787
    Cited by:  Papers (2)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (592 KB)  

    This correspondence has analyzed the capability of minimum energy optimum/adaptive beamformer to estimate the bearings of two closely spaced narrowband equal-energy correlated sources. The analytical expression for minimum angular separation for resolution of such sources as a function of the correlation coefficient, signal power, and the parameters of the adaptive processor is derived. The approach of spatial smoothing is considered. The simple problem of definition of optimal size of the subarray for highly correlated sources is examined. Results of computer simulations are included to support our analysis View full abstract»

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  • Time-recursive computation and real-time parallel architectures: a framework

    Publication Year: 1995 , Page(s): 2762 - 2775
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1184 KB)  

    The time-recursive computation has been proven a particularly useful tool in real-time data compression, in transform domain adaptive filtering, and in spectrum analysis. Unlike the FFT-based ones, the time-recursive architectures require only local communication. Also, they are modular and regular, thus they are very appropriate for VLSI implementation and they allow a high degree of parallelism. In this two-part paper, we establish an architectural framework for parallel time-recursive computation. We consider a class of linear operators that consists of the discrete time, time invariant, compactly supported, but otherwise arbitrary kernel functions. We show that the structure of the realization of a given linear operator is dictated by the decomposition of the latter with respect to proper basis functions. An optimal way for carrying out this decomposition is demonstrated. The parametric forms of the basis functions are identified and their properties pertinent to the architecture design are studied. A library of architectural building modules capable of realizing these functions is developed. An analysis of the implementation complexity for the aforementioned modules is conducted. Based on this framework, the time-recursive architecture of a given linear operator can be derived in a systematic routine way View full abstract»

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  • The design of nonuniform modulated filterbanks

    Publication Year: 1995 , Page(s): 2550 - 2560
    Cited by:  Papers (26)  |  Patents (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1008 KB)  

    We present an approach to nonuniform filterbank design based on modulated filters and the principle of adjacent channel aliasing cancellation. The approach is a generalization of pseudo QMF designs to nonuniform channel arrangements and the essential idea is to form nonuniform filterbanks from uniform sections joined by “transition” filters. All channel filters are formed by modulating lowpass prototypes. To meet the aliasing cancellation conditions, the transition filters are modulated from complex lowpass prototypes, although the resulting channel filters are still real. The approach provides a computationally simple method for designing filterbanks with large numbers of channels because of the fact that channel filters are modulated from a few lowpass prototypes and because the lowpass prototype designs can be scaled. That is, designs for narrow channel spacing can be produced from designs for wider channel spacing by interpolating the lowpass prototype impulse response. The development is limited to the design of nonuniform filterbanks with integer decimation factors, although we demonstrate that the technique can be used to produce excellent rational decimation factor designs by combining channel outputs using an inverse polyphase transform View full abstract»

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  • Symmetric extension methods for M-channel linear-phase perfect-reconstruction filter banks

    Publication Year: 1995 , Page(s): 2505 - 2511
    Cited by:  Papers (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (684 KB)  

    The symmetric extension method has been shown to he an efficient way for subband processing of finite-length sequences. This paper presents an extension of this method to general linear-phase perfect-reconstruction filter banks. We derive constraints on the length and symmetry polarity of the permissible filter banks and propose a new design algorithm. In the algorithm, different symmetric sequences are formulated in a unified form based on the circular-symmetry framework. The length constraints in symmetrically extending the input sequence and windowing the subband sequences are investigated. The effect of shifting the input sequence is included. When the algorithm is applied to equal-length filter banks, we explicitly show that symmetric extension methods can always be constructed to replace the circular convolution approach View full abstract»

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  • Investigations in the numerical behavior of the adaptive rank-revealing QR factorization

    Publication Year: 1995 , Page(s): 2787 - 2791
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (380 KB)  

    We present a tracking procedure based on the rank-revealing QR (RRQR) factorization and investigate its numerical properties by applying it to the direction-of-arrival problem. We address numerical issues raised by the related work proposed earlier by Prasad et al. (1991), and we compare the performance of the proposed algorithm to that obtained using an EVD-based technique View full abstract»

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  • Time-varying analysis-synthesis systems based on filter banks and post filtering

    Publication Year: 1995 , Page(s): 2512 - 2524
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1240 KB)  

    Perfect reconstruction (PR) time-varying analysis-synthesis filter banks are those in which the filters are allowed to change from one set of PR filter banks to another as the input signal is being processed. Such systems have the property that, in the absence of coding, they faithfully reconstruct every sample of the input. Various methods have been reported for the time-varying filter bank design; all of them, however, utilize structures for conventional PR filter banks. These conventional structures that have been applied in the past result in different limitations in each method. This paper introduces a new structure for exactly reconstructing time-varying analysis-synthesis filter banks. This structure consists of the conventional filter bank followed by a time-varying post filter. The new method requires neither the redesign of the analysis sections nor the use of any intermediate analysis filters during transition periods. It provides a simple and elegant procedure for designing time-varying filter banks without the disadvantages of the previous methods View full abstract»

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  • Robust minimum variance filtering

    Publication Year: 1995 , Page(s): 2474 - 2483
    Cited by:  Papers (58)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (964 KB)  

    This paper deals with the robust minimum variance filtering problem for linear systems subject to norm-bounded parameter uncertainty in both the state and the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty. Two methods for designing robust filters are investigated. The first one deals with constant parameter uncertainty and focuses on the design of steady-state filters that yield an upper bound to the worst-case asymptotic error variance. This bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system, and it can be made tighter if a tight bound on the latter power spectrum can be obtained. The second method allows for time-varying parameter uncertainty and for general time-varying systems and is more systematic. We develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems View full abstract»

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  • On the stability of sequential updates and downdates

    Publication Year: 1995 , Page(s): 2642 - 2648
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (612 KB)  

    The updating and downdating of Cholesky decompositions has important applications in a number of areas. There is essentially one standard updating algorithm, based on plane rotations, which is backward stable. Three downdating algorithms have been treated in the literature: the LINPACK algorithm, the method of hyperbolic transformations, and Chambers' (1971) algorithm. Although none of these algorithms is backward stable, the first and third satisfy a relational stability condition. It is shown that relational stability extends to a sequence of updates and downdates. In consequence, other things being equal, if the final decomposition in the sequence is well conditioned, it will be accurately computed, even though intermediate decompositions may be almost completely inaccurate. These results are also applied to the two-sided orthogonal decompositions, such as the URV decomposition View full abstract»

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  • Smooth wavelets, transform coding, and Markov-1 processes

    Publication Year: 1995 , Page(s): 2561 - 2569
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (868 KB)  

    This paper compares the energy compacting properties of unitary transforms from transform coders and two-band paraunitary filter banks from subband coders using a cost criterion that is proposed. Stationary processes for which paraunitary filters have better energy compaction than unitary filters are denoted as subband optimal, and all subband optimal processes are analytically characterized for the case of length-4 filters. It is shown analytically for length-4 filters and empirically for longer-length filters that Markov-1 processes are subband optimal and that the Daubechies (1988) maximally smooth wavelet sequences achieve better energy compaction than the best unitary filters for Markov-1 inputs View full abstract»

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  • Completeness of arbitrarily sampled discrete time wavelet transforms

    Publication Year: 1995 , Page(s): 2570 - 2581
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (988 KB)  

    An arbitrarily sampled discrete time wavelet transform is said to be complete if it is uniquely invertible, i.e., if the underlying signal can be uniquely recovered from the available samples of the wavelet transform. We develop easy-to-compute necessary and sufficient conditions and necessary but not sufficient conditions for the completeness of an arbitrarily sampled dyadic discrete time wavelet transform of a periodic signal. In particular, we provide necessary and sufficient conditions for completeness of the sampled wavelet transform when the lowpass filter associated with the dyadic wavelet filter bank has no unit circle zeros other than those at z=1. We present necessary but not sufficient conditions for completeness when the lowpass filter associated with the dyadic wavelet filter bank has arbitrary unit circle zeros. We also provide necessary and sufficient conditions for completeness of a set of samples of both the lowpass approximation to the signal and its wavelet transform. All the conditions we derive use only information about the location of the retained samples and the analyzing wavelet filter bank. They can easily be checked without explicitly computing of the rank of a matrix. Finally, we present a simple signal reconstruction procedure that can be used once we have determined the arbitrarily sampled discrete time wavelet transform is complete View full abstract»

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  • Complex ambiguity functions using nonstationary higher order cumulant estimates

    Publication Year: 1995 , Page(s): 2649 - 2664
    Cited by:  Papers (2)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1420 KB)  

    The complex ambiguity function based on second-order statistics (CAF-SOS) has been used to simultaneously estimate the frequency-delay of arrival (FDOA) and time-delay of arrival (TDOA) between two signal measurements; its performance, however, is sensitive to the correlation between two additive noise sources. When the noise sources are assumed to be Gaussian, we develop a new complex ambiguity function based on higher order statistics (CAF-HOS) that reduces the unknown noise-correlation effect. The new CAF-HOS algorithm utilizes nonstationary higher order cross cumulant estimates and their Fourier transform. In fact, we suggest a nonstationary estimate of fourth-order cross-cumulants and obtain the analytical expressions for its mean value and variance. We compare the analytical expressions with results obtained by Monte Carlo runs. Also, we compare the performance of the new complex ambiguity function based on fourth-order statistics (CAF-FOS) against the CAF-SOS algorithm using different Gaussian noise sources, different signals of interest, different signal-to-noise ratios, and different lengths of data View full abstract»

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  • Maximum likelihood localization of sources in noise modeled as a stable process

    Publication Year: 1995 , Page(s): 2700 - 2713
    Cited by:  Papers (37)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1132 KB)  

    This paper introduces a new class of robust beamformers which perform optimally over a wide range of non-Gaussian additive noise environments. The maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric α-stable (SαS) process. Transform-based approximations of the likelihood estimation are used for the general SαS class of distributions while the exact probability density function is used for the Cauchy case. It is shown that the Cauchy beamformer greatly outperforms the Gaussian beamformer in a wide variety of non-Gaussian noise environments, and performs comparably to the Gaussian beamformer when the additive noise is Gaussian. The Cramer-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the SαS beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments View full abstract»

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  • Sinusoidal signals with random amplitude: least-squares estimators and their statistical analysis

    Publication Year: 1995 , Page(s): 2733 - 2744
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (952 KB)  

    The asymptotic properties of constrained and unconstrained least-squares estimates of the parameters of a random-amplitude sinusoid are analyzed. An explicit formula for the asymptotic covariance matrix of the estimation errors is derived for both the constrained and unconstrained estimators. Accuracy aspects are investigated with the following main results. For a certain weighting matrix, which is shown to be the same for the constrained and unconstrained methods, the estimation errors achieve their lower bounds. It is proven that in the optimal case, the constrained method always outperforms the unconstrained method. It is also proven that the accuracy of the optimal estimators improves as the number of least-squares equations increases. A formula for the sample length needed for the asymptotic theory to hold is derived, and its dependence on the lowpass modulating sequence is stressed. Simulations provide illustrations of the difference between the constrained and unconstrained estimators as well as the difference between the optimal and basic estimates. The influence of the number of least-squares equations and the characteristics of the lowpass envelope on the estimation accuracy is also investigated View full abstract»

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  • The effects of array calibration errors on DF-based signal copy performance

    Publication Year: 1995 , Page(s): 2724 - 2732
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (776 KB)  

    This paper studies the effect of array calibration errors on the performance of various direction finding (DF) based signal copy algorithms. Unlike blind copy methods, this class of algorithms requires an estimate of the directions of arrival (DOAs) of the signals in order to compute the copy weight vectors. Under the assumption that the observation time is sufficiently long, the following algorithms are studied: classical beamforming, least squares, total least squares, linearly constrained minimum variance beamforming, and structured stochastic estimation. Expressions for the mean-square error of the signal estimates are derived as a function of the calibration errors for both the case where the DOAs are known precisely and for the case where the DOAs must be estimated View full abstract»

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  • Modeling, analysis, and optimum design of quantized M-band filter banks

    Publication Year: 1995 , Page(s): 2540 - 2549
    Cited by:  Papers (28)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (924 KB)  

    This paper provides a rigorous modeling and analysis of quantization effects in M-band subband codecs, followed by optimal filter bank design and compensation. The codec is represented by a polyphase decomposition of the analysis/synthesis filter banks and an embedded nonlinear gain-plus-additive noise model for the pdf-optimized scalar quantizers. We construct an equivalent time-invariant but nonlinear structure operating at the slow clock rate that allows us to compute the exact expression for the mean square quantization error in the reconstructed output. This error is shown to consist of two components: a distortion component and a dominant random noise component uncorrelated with the input signal. We determine the optimal paraunitary and biorthogonal FIR filter coefficients, compensators, and integer bit allocation to minimize this MSE subject to the constraints of filter length, average bit rate, and perfect reconstruction (PR) in the absence of quantizers. The biorthogonal filter bank results in a smaller MSE but the filter coefficients are very sensitive to signal statistics and to average bit constraints. By comparison, the paraunitary structure is much more robust. We also show that the null-compensated design that eliminates the distortion component is more robust than the optimally-compensated case that minimizes the total MSE, but only at nominal conditions. Both modeling and optimal design are validated by simulation in the two-channel case View full abstract»

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  • Diagonalizing properties of the discrete cosine transforms

    Publication Year: 1995 , Page(s): 2631 - 2641
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (948 KB)  

    Since its introduction in 1974 by Ahmed et al., the discrete cosine transform (DCT) has become a significant tool in many areas of digital signal processing, especially in signal compression. There exist eight types of discrete cosine transforms (DCTs). We obtain the eight types of DCTs as the complete orthonormal set of eigenvectors generated by a general form of matrices in the same way as the discrete Fourier transform (DFT) can be obtained as the eigenvectors of an arbitrary circulant matrix. These matrices can be decomposed as the sum of a symmetric Toeplitz matrix plus a Hankel or close to Hankel matrix scaled by some constant factors. We also show that all the previously proposed generating matrices for the DCTs are simply particular cases of these general matrix forms. Using these matrices, we obtain, for each DCT, a class of stationary processes verifying certain conditions with respect to which the corresponding DCT has a good asymptotic behavior in the sense that it approaches Karhunen-Loeve transform performance as the block size N tends to infinity. As a particular result, we prove that the eight types of DCTs are asymptotically optimal for all finite-order Markov processes. We finally study the decorrelating power of the DCTs, obtaining expressions that show the decorrelating behavior of each DCT with respect to any stationary processes View full abstract»

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  • Multiscale representation and estimation of fractal point processes

    Publication Year: 1995 , Page(s): 2606 - 2617
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1068 KB)  

    Fractal point processes have a potentially important role to play in the modeling of a wide range of natural and man-made phenomena. However, the lack of a suitable framework for their representation has frequently made their application in many problems difficult. We introduce natural multiscale representations for an important class of these processes based on mixtures of Poisson processes. In turn, this framework leads to efficient new algorithms for both the synthesis and the analysis of such processes. These include algorithms for optimal fractal dimension and interarrival time estimation that are of interest in a range of applications. Several aspects of the performance of these algorithms are also addressed View full abstract»

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  • Detection of harmonic sets

    Publication Year: 1995 , Page(s): 2618 - 2630
    Cited by:  Papers (6)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1176 KB)  

    We examine the detection problem of signals with narrowband, harmonically related components received by a passive sensor array. We investigate detector structures based on the Fourier method. The harmonic detector estimates the total signal power by combining the DFT coefficients from harmonic frequency bins. This power estimate is normalized by the estimated background noise power and then compared to a threshold. We investigate two harmonic detector structures: one that operates with coherent, correlated signals and the other with uncorrelated harmonic signals. We derive statistical laws governing both detector structures that facilitate setting a power threshold for a given probability of false alarm; and present upper- and lower-bounds for the probability of detection. The results developed and presented demonstrate the inherent advantage of the harmonic detector. At operating conditions characterized by low signal-to-noise power ratio values the harmonic detector exhibits enhanced detection performance by combining the estimated signal power from harmonic frequency bins. We generalize results from single-bin and harmonic detector structures and present them as special cases of a unifying framework View full abstract»

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  • Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction

    Publication Year: 1995 , Page(s): 2525 - 2539
    Cited by:  Papers (43)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1636 KB)  

    We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2π/M rather than π/M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband. The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system View full abstract»

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  • Filtering random noise from deterministic signals via data compression

    Publication Year: 1995 , Page(s): 2595 - 2605
    Cited by:  Papers (51)  |  Patents (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1008 KB)  

    We present a novel technique for the design of filters for random noise, leading to a class of filters called Occam filters. The essence of the technique is that when a lossy data compression algorithm is applied to a noisy signal with the allowed loss set equal to the noise strength, the loss and the noise tend to cancel rather than add. We give two illustrative applications of the technique to univariate signals. We also prove asymptotic convergence bounds on the effectiveness of Occam filters 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
Sergios Theodoridis
University of Athens