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ABSTRACT: In this paper, we study a versatile iterative framework for the reconstruction of uniform samples from nonuniform samples
of bandlimited signals. Assuming the input signal is slightly oversampled, we first show that its uniform and nonuniform samples
in the frequency band of interest can be expressed as a system of linear equations using fractional delay digital filters.
Then we develop an iterative framework, which enables the development and convergence analysis of efficient iterative reconstruction
algorithms. In particular, we study the Richardson iteration in detail to illustrate how the reconstruction problem can be
solved iteratively, and show that the iterative method can be efficiently implemented using Farrow-based variable digital
filters with few general-purpose multipliers. Under the proposed framework, we also present a completed and systematic convergence
analysis to determine the convergence conditions. Simulation results show that the iterative method converges more rapidly
and closer to the true solution (i.e. the uniform samples) than conventional iterative methods using truncation of sinc series.
KeywordsFarrow structure–Iterative method–Nonuniform sampling–Signal reconstruction–Variable fractional delay digital filters
Journal of Signal Processing Systems 04/2012; 62(3):459-468. · 0.67 Impact Factor
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ABSTRACT: This paper proposes a new iterative framework for the correction of frequency response mismatch in time-interleaved analog-to-digital converters. Based on a general time-varying linear system model for the mismatch, we treat the reconstruction problem as a linear inverse problem and establish a flexible iterative framework for practical implementation. It encumbrances a number of efficient iterative correction algorithms and simplifies their design, implementation, and performance analysis. In particular, an efficient Gauss-Seidel iteration is studied in detail to illustrate how the correction problem can be solved iteratively and how the proposed structure can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. We also study important issues, such as the sufficient convergence condition and reconstructed signal spectrum, derive new lower bound of signal-to-distortion-and-noise ratio in order to ensure stable operation, and predict the performance of the proposed structure. Furthermore, we propose an extended iterative structure, which is able to cope with systems involving more than one type of mismatches. Finally, the theoretical results and the effectiveness of the proposed approach are validated by means of computer simulations.
IEEE Transactions on Instrumentation and Measurement 01/2012; · 1.21 Impact Factor
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ABSTRACT: The problem of robust beamforming for antenna arrays with arbitrary geometry and magnitude response constraints is one of considerable importance. Due to the presence of the non-convex magnitude response constraints, conventional convex optimization techniques cannot be applied directly. A new approach based on iteratively linearizing the non-convex constraints is then proposed to reformulate the non-convex problem to a series of convex subproblems, each of which can be optimally solved using second-order cone programming (SOCP). Moreover, in order to obtain a more robust beamformer against array imperfections, the proposed method is further extended by optimizing its worst-case performance using again SOCP. Different from some conventional methods which are restricted to linear arrays, the proposed method is applicable to arbitrary array geometries since the weight vector, rather than its autocorrelation sequence, is used as the variable. Simulation results show that the performance of the proposed method is comparable to the optimal solution previously proposed for uniform linear arrays, and it also gives satisfactory results under different array specifications and geometries tested.
IEEE Transactions on Antennas and Propagation 10/2011; · 2.15 Impact Factor
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ABSTRACT: In this paper, we study a versatile iterative framework for the correction of frequency response mismatch in time-interleaved ADCs. Based on a general time varying linear system model, we establish a flexible iterative framework, which enables the development of various efficient iterative correction algorithms. In particular, we study the Gauss-Seidel iteration in detail to illustrate how the correction problem can be solved iteratively, and show that the iterative structure can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. Simulation results show that the proposed iterative structure performs better than conventional compensation structures. Moreover, a preliminary study on the BER performance of OFDM systems due to TI ADC mismatch is conducted.
Green Circuits and Systems (ICGCS), 2010 International Conference on; 07/2010
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ABSTRACT: A new design method is proposed for the power or shaped beam pattern synthesis problem of narrowband conformal arrays, where only the magnitude response is specified. The proposed method iteratively linearizes the non-convex power pattern function to obtain a convex subproblem in the design variables, which can be solved optimally using second-order cone programming (SOCP). In addition, a wide variety of magnitude constraints such as non-convex lower bound magnitude constraints can be incorporated. An efficient technique for determining a reasonably good initial guess to the problem is also proposed to further improve the reliability of the method. Computer simulations show that the initial guesses so obtained converge to satisfactory solutions while satisfying various prescribed magnitude constraints. Design results show that the performance of the proposed method is comparable to the optimal solution previously obtained for uniform linear arrays with isotropic elements. Moreover, we show by means of examples that the proposed method is also applicable to general non-convex power pattern synthesis problems involving arbitrary array geometries, arbitrary polarization characteristics and mutual coupling effect.
IEEE Transactions on Antennas and Propagation 07/2010; · 2.15 Impact Factor
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ABSTRACT: A new design method is proposed for the power or shaped beam pattern synthesis problem of narrowband conformal arrays, where only the magnitude response is specified. The pro-posed method iteratively linearizes the non-convex power pattern function to obtain a convex subproblem in the design variables, which can be solved optimally using second-order cone program-ming (SOCP). In addition, a wide variety of magnitude constraints such as non-convex lower bound magnitude constraints can be in-corporated. An efficient technique for determining a reasonably good initial guess to the problem is also proposed to further im-prove the reliability of the method. Computer simulations show that the initial guesses so obtained converge to satisfactory solu-tions while satisfying various prescribed magnitude constraints. Design results show that the performance of the proposed method is comparable to the optimal solution previously obtained for uni-form linear arrays with isotropic elements. Moreover, we show by means of examples that the proposed method is also applicable to general non-convex power pattern synthesis problems involving arbitrary array geometries, arbitrary polarization characteristics and mutual coupling effect.
IEEE Transactions on Antennas and Propagation 01/2010; 58. · 2.15 Impact Factor
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ABSTRACT: This paper proposes a new design method for a class of two-channel perfect reconstruction (PR) filter banks (FBs) called multi-plet FBs with very sharp cutoff using frequency- response masking (FRM) technique. The multi-plet FBs are PR FBs and their frequency characteristics are controlled by a single subfilter. By recognizing the close relationship between the subfilter and the FRM-based halfband filter, very sharp cutoff PR multi-plet FBs can be realized with reduced implementation complexity. The design procedure is very general and it can be applied to both linear-phase and low-delay PR FBs. Design examples are given to demonstrate the usefulness of the proposed method.
Circuits and Systems I: Regular Papers, IEEE Transactions on 11/2008; · 1.97 Impact Factor
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ABSTRACT: This paper studies the theory and design of a class of perfect reconstruction (PR) uniform causal-stable infinite-impulse response (IIR) cosine modulated filter banks (CMFBs). The design approach is also applicable to the design of PR recombination nonuniform (RN) IIR CMFBs. The polyphase components of the prototype filters of these IIR CMFBs are assumed to have the same denominator so as to simplify the PR condition. In designing the proposed IIR CMFB, a PR FIR CMFB with similar specifications is first designed. The finite-impulse response prototype filter is then converted to a nearly PR (NPR) IIR CMFB using a modified model reduction technique. The NPR IIR CMFB so obtained has a reasonably low reconstruction error. Its denominator is designed to be a polynomial in z<sup>M</sup>, where M is the number of channels, to simplify the PR condition. Finally, it is employed as the initial guess to constrained nonlinear optimization software for the design of the PR IIR CMFB. Design results show that both NPR and PR IIR CMFBs with good frequency characteristics and different system delays can be obtained by the proposed method. By using these IIR CMFBs in the RN CMFBs, new RN NPR and PR IIR CMFBs can be obtained similarly.
Circuits and Systems II: Express Briefs, IEEE Transactions on 09/2008; · 1.41 Impact Factor
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ABSTRACT: This paper proposes a new Kalman-filter-based recursive frequency estimator for discrete-time multicomponent sinusoidal signals whose frequencies may be time-varying. The frequency estimator is based on the linear prediction approach and it employs the Kalman filter to track the linear prediction coefficients (LPCs) recursively. Frequencies of the sinusoids can then be computed using the estimated LPCs. Due to the coloredness of the linear prediction error, an iterative algorithm is employed to estimate the covariance matrix of the prediction error and the LPCs alternately in the Kalman filter in order to improve the tracking performance. Simulation results show that the proposed Kalman-filter-based iterative frequency estimator can achieve better tracking results than the conventional recursive least-squares-based estimators.
Circuits and Systems II: Express Briefs, IEEE Transactions on 07/2008; · 1.41 Impact Factor
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ABSTRACT: This paper proposes an efficient method for designing nearly perfect reconstruction (NPR) and perfect reconstruction (PR) cosine modulated filter banks (CMFBs) with prototype filters having an approximate cosine-rolloff (CR) transition band. It is shown that the flatness condition required for an NPR CMFB can be automatically satisfied by using a prototype filter with a CR transition band. The design problem is then formulated as a convex minimax optimization problem, and it can be solved by second-order cone programming (SOCP). By using the NPR CMFB so obtained as an initial guess to nonlinear optimizers such as Fmincon in Matlab, high-quality PR CMFBs can be obtained. The advantages of the proposed method are that it does not require a user-supplied initial guess of the prototype filter and bumps in the passband of the analysis filters can be effectively suppressed.
Circuits and Systems II: Express Briefs, IEEE Transactions on 07/2008; · 1.41 Impact Factor
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IEEE Trans. on Circuits and Systems. 01/2008; 55-II:576-580.
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IEEE Trans. on Circuits and Systems. 01/2008; 55-II:571-575.
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ABSTRACT: This paper studies the design of causal stable Farrow-based infinite-impulse response (IIR) variable fractional delay digital filters (VFDDFs), whose subfilters have a common denominator. This structure has the advantages of reduced implementation complexity and avoiding undesirable transient response when tuning the spectral parameter in the Farrow structure. The design of such IIR VFDDFs is based on a new model reduction technique which is able to incorporate prescribed flatness and peak error constraints to the IIR VFDDF under the second order cone programming framework. Design example is given to demonstrate the effectiveness of the proposed approach.
Circuits and Systems II: Express Briefs, IEEE Transactions on 12/2007; · 1.41 Impact Factor
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ABSTRACT: This paper introduces two new time-frequency analysis methods originated from the minimum variance spectral estimation (MVSE) for nonstationary time-series. First, a windowed MVSE (WMVSE) extends the conventional MVSE by windowing the observation data to obtain a time-frequency distribution for the time-series. Moreover, the window lengths are selected adaptively by the intersection of confidence intervals (ICI) rule to improve the time-frequency resolution. Secondly, a new recursive MVSE (RMVSE) is developed to process the input samples recursively at a lower arithmetic complexity for online time-frequency analysis. Simulation results show that the proposed WMVSE with adaptive windows offers better frequency resolutions than the Fourier-transformed-based time-frequency distributions, and the RMVSE has a good performance when tracking sinusoidal signals
Circuits and Systems, 2007. ISCAS 2007. IEEE International Symposium on; 06/2007
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ABSTRACT: This paper proposes two new methods for optimizing hardware resources in finite wordlength implementation of multiple-output (MO) linear time-invariant (LTI) systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first method relaxes the wordlength from integer to real-value and formulates the design problem as a geometric programming, from which an optimal solution of the relaxed problem can be determined. The second method is based on a discrete optimization method called the marginal analysis method, and it yields the desired wordlengths in integer values. By combining these two methods, a hybrid method is also proposed, which is found to be very effective for large scale MO LTI systems. To illustrate the effectiveness of the proposed methods, wordlength optimization problems of two-channel structural perfect reconstruction filter banks and multiplier-less fast Fourier transforms are studied in detail. Design results show that the proposed algorithms offer better results and a lower design complexity than conventional methods
Circuits and Systems I: Regular Papers, IEEE Transactions on 05/2007; · 1.97 Impact Factor
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ABSTRACT: This paper studies the design, signal round-off noise, and complexity optimization of a new digital intermediate frequency (IF) architecture for a software radio receiver (SRR). The IF under study consists of digital filters with fixed coefficients, except for a limited number of multipliers required in the Farrow-based sampling rate converter (SRC). The fixed-coefficient filters can be implemented efficiently using sum-of-power-of-two (SOPOT) coefficients and the multiplier-block technique, which gives minimum adder realization. Apart from the multipliers required in the SRC, the digital IF can be implemented without any multiplications. While most multiplier- less filter design and realization methods address only the coefficient round-off problem by minimizing the number of SOPOT terms used, the proposed design methodology aims to minimize more realistic hardware complexity measure, such as adder cells and registers, of the digital IF subject to a given spectral and accuracy specifications. The motivation is that the complexity is closely related to the target output accuracy, which is specified statistically by its total output noise power generated by rounding the intermediate data. Two novel algorithms for optimizing the internal wordlengths of linear time-invariant systems are proposed. The first one relaxes the solution to real valued and formulates the design problem as a constrained optimization. A closed-form solution can be determined by the Lagrange multiplier method. The second one is based on a discrete optimization method called the Marginal Analysis method, and it yields the desired wordlengths in integer values. Both approaches are found to be effective and suitable to large scale systems. A design example and the field programmable gate array (FPGA) realization of a multi-standard receiver are given to demonstrate the proposed method
Circuits and Systems I: Regular Papers, IEEE Transactions on 03/2007; · 1.97 Impact Factor
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ABSTRACT: This brief proposes a new method for designing infinite-impulse response (IIR) filter with peak error and prescribed flatness constraints. It is based on the model reduction of a finite-impulse response function that satisfies the specification by extending a method previously proposed by Brandenstein. The proposed model-reduction method retains the denominator of the conventional techniques and formulates the optimal design of the numerator as a second-order cone programming problem. Therefore, linear and convex quadratic inequalities such as peak error constraints and prescribed number of zeros at the stopband for IIR filters can be imposed and solved optimally. Moreover, a method is proposed to express the denominator of the model-reduced IIR filter as a polynomial in integer power of z, which efficiently facilitates its polyphase implementation in multirate applications. Design examples show that the proposed method gives better performance, and more flexibility in incorporating a wide variety of constraints than conventional methods
Circuits and Systems II: Express Briefs, IEEE Transactions on 03/2007; · 1.41 Impact Factor
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ABSTRACT: This paper proposes a methodology for automatic synthesis of digital filters to meet prescribed output accuracy. Given a given frequency domain specification and output accuracy, a multiplier-less digital filter with canonical signed digits (CSD) will first be designed using advanced filter design techniques. A novel algorithm, based on geometric programming and marginal analysis methods, is proposed to optimize the hardware resources in terms of the internal wordlength of the digital filters to meet the prescribed output accuracy. Because of the use of CSD and multiplier block, the hardware resources can be greatly reduced. Using the system coefficients and wordlength information so obtained, a system for generating the corresponding VHDL codes was also developed. Automatic hardware synthesis is then employed to target the design to different platforms. The effectiveness of the proposed methodology is evaluated by the realization of a digital intermediate frequency receiver in field programmable gate arrays. Design results show that, the proposed methodology greatly reduces the design time of the system, while requiring much less hardware resources than conventional methods
Circuits and Systems, 2006. APCCAS 2006. IEEE Asia Pacific Conference on; 01/2007
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International Symposium on Circuits and Systems (ISCAS 2007), 27-20 May 2007, New Orleans, Louisiana, USA; 01/2007
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ABSTRACT: This paper proposes a new class of two-channel structural perfect reconstruction (PR) finite-impulse response / infinite-impulse response (FIR/IIR) filter banks (FBs) called the multi-plet FBs. It generalizes the structural PR FBs proposed by Phoong and the conventional triplet FB in that it employs multiple lifting steps similar to the conventional lifting structure. Apart from the important structural PR property, the multi-plet FB can be systematically designed to meet a given specification on the passband/stopband ripples and transition bandwidth: a low-order prototype PR FB with a much wider transition band is first designed using nonlinear optimization in order to obtain a symmetric frequency response and prescribed passband and stopband ripples. As only a few variables are required, its performances can easily be controlled. A subfilter is then designed using second-order cone programming (SOCP) so that the prototype FB can be warped by means of frequency transformation to meet the desired transition bandwidth, while preserving the PR condition, passband/stopband ripples and lifting structure of the prototype FB. The design procedure is very general and it applies to both linear-phase/low-delay FIR and IIR multi-plet FBs. By formulating the K-regularity conditions as a set of linear equality constraints on the subfilter coefficients, multi-plet-based wavelet bases can easily be designed under the SOCP framework. Design examples show that the proposed approach offers more flexibility in controlling the frequency characteristics of the PR FBs and lower design complexity than conventional methods
Circuits and Systems I: Regular Papers, IEEE Transactions on 01/2007; · 1.97 Impact Factor
