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22
Linear Matrix Inequality Formulation of Spectral Mask Constraints
, 2000
"... The design of a finite impulse response filter often involves a spectral 'mask' which the mag nitude spectrum must satisfy. This constraint can be awkward because it is semiinfinite, since it yields two inequality constraints for each frequency point. In current practice, spectral mask ..."
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Cited by 40 (7 self)
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The design of a finite impulse response filter often involves a spectral 'mask' which the mag nitude spectrum must satisfy. This constraint can be awkward because it is semiinfinite, since it yields two inequality constraints for each frequency point. In current practice, spectral masks are often approximated by discretization, but in this paper we will show that piecewise constant masks can be precisely enforced in a finite and convex manner via linear matrix inequalities.
Convex Optimization Problems Involving Finite autocorrelation sequences
, 2001
"... We discuss convex optimization problems where some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in opt ..."
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Cited by 40 (0 self)
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We discuss convex optimization problems where some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density, which results in a set of linear inequalities. They can also be cast as linear matrix inequalities via the KalmanYakubovichPopov lemma. The linear matrix inequality formulation is exact, and results in convex optimization problems that can be solved using interiorpoint methods for semidefinite programming. However, it has an important drawback: to represent an autocorrelation sequence of length n, it requires the introduction of a large number (n(n + 1)/2) of auxiliary variables. This results in a high computational cost when generalpurpose semidefinite programming solvers are used. We present a more efficient implementation based on duality and on interiorpoint methods for convex problems with generalized linear inequalities.
Optimal waveform design for UWB radios
 George Mason University
, 2004
"... Abstract—With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultrawideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless service ..."
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Cited by 22 (4 self)
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Abstract—With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultrawideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless services. Meanwhile, orthogonal pulse sets are often desired in order to apply highrate multidimensional modulation and (carrierfree) orthogonal frequencydivision multiple access. Motivated by these considerations, we suggest a digital finite impulse response (FIR) filter approach to synthesizing UWB pulses and propose filter design techniques by which optimal waveforms that satisfy the spectral mask can be efficiently obtained. For single pulse design, we develop a convex formulation for the design of the FIR filter coefficients that maximize the spectrum utilization efficiency in terms of both the bandwidth and power allowed by the spectral mask. For orthogonal pulse design, a sequential strategy is derived to formulate the overall pulse design problem as a set of convex subproblems, which are then solved in a sequential manner to yield a set of mutually orthogonal pulses. Our design techniques not only provide waveforms with high spectrum utilization and guaranteed spectral mask compliance but also permit simple modifications that can accommodate several other system objectives. Index Terms—Digital pulse design, finite impulse response (FIR) filter, ultrawideband communications. I.
Efficient Design of Oversampled NPR GDFT Filter Banks
, 2003
"... In this paper, we present a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized Discrete Fourier Transform (GDFT) filter bank. Such filter banks have several desirable properties for subband processing systems which are sensit ..."
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Cited by 15 (0 self)
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In this paper, we present a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized Discrete Fourier Transform (GDFT) filter bank. Such filter banks have several desirable properties for subband processing systems which are sensitive to aliasing, such as subband adaptive filters. Our design criteria for the prototype filter are explicit bounds (derived herein) on the aliased components in the subbands and the output, the distortion induced by the filter bank, and the imaged subband errors in the output. It is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem which can be efficiently solved. Our design technique provides an efficient and effective tool for exploring many of the inherent tradeoffs in the design of the prototype filter, including the tradeoff between aliasing in the subbands and the distortion induced by the filter bank. In our examples we calculate several of these tradeoffs and demonstrate that our method can generate filters with significantly better performance than filters obtained using current design methods.
Linear phase lowpass IIR digital differentiators
 IEEE Trans. Signal Process
"... Abstract—A novel approach to designing approximately linear phase infiniteimpulseresponse (IIR) digital filters in the passband region is introduced. The proposed approach yields digital IIR filters whose numerators represent linear phase finiteimpulseresponse (FIR) filters. As an example, lowp ..."
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Cited by 10 (0 self)
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Abstract—A novel approach to designing approximately linear phase infiniteimpulseresponse (IIR) digital filters in the passband region is introduced. The proposed approach yields digital IIR filters whose numerators represent linear phase finiteimpulseresponse (FIR) filters. As an example, lowpass IIR differentiators are introduced. The range and highfrequency suppression of the proposed lowpass differentiators are comparable to those obtained by higher order FIR lowpass differentiators. In addition, the differentiators exhibit almost linear phases in the passband regions. Index Terms—AlAlaoui operator, analog filters, bilinear transformation, digital differentiators, finiteimpulseresponse (FIR) filters, infiniteimpulseresponse (IIR) filters, linear phase, lowpass digital differentiators. I.
Stable IIR notch filter design with optimal pole placement
 IEEE Trans. Signal Process
, 2001
"... Abstract—This paper presents a twostage approach for designing an infinite impulse response (IIR) notch filter. First, the numerator of the transfer function of the IIR notch filter is obtained by placing the zeros at the prescribed notch frequencies. Then, the denominator polynomial is determined ..."
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Cited by 8 (0 self)
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Abstract—This paper presents a twostage approach for designing an infinite impulse response (IIR) notch filter. First, the numerator of the transfer function of the IIR notch filter is obtained by placing the zeros at the prescribed notch frequencies. Then, the denominator polynomial is determined by using an iterative scheme in which the optimal pole placements are found by solving a standard quadratic programming problem. For stability, the pole radius in the single notch filter design is specified by the designer, and in the multiple notch filter design, the pole radius is constrained by using the implications of Rouché’s theorem. Examples are included to illustrate the effectiveness of the proposed techniques. Index Terms—Notch filters, quadratic programming. I.
Efficient largescale filter/filterbank design via LMI characterization of trigonometric curves
 in Proc. of IEEE Inter. Conf. on Acoustics, Speech and Signal Processing (ICASSP 05
"... Abstract—Many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semiinfinite constraints. Recent advances in design methodology are based on various linear matrix inequality (LMI) characterizations of the semiinfinite ..."
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Cited by 5 (4 self)
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Abstract—Many filter and filterbank design problems can be posed as the optimization of linear or convex quadratic objectives over trigonometric semiinfinite constraints. Recent advances in design methodology are based on various linear matrix inequality (LMI) characterizations of the semiinfinite constraints, and semidefinite programming (SDP) solutions. Despite these advances, the design of filters of several hundredth order, which typically arise in multicarrier communication and signal compression, cannot be accommodated. This hurdle is due mainly to the large number of additional variables incurred in the LMI characterizations. This paper proposes a novel LMI characterization of the semiinfinite constraints that involves additional variables of miminal dimensions. Consequently, the design of highorder filters required in practical applications can be achieved. Examples of designs of up to 1200tap filters are presented to verify the viability of the proposed approach. Index Terms—Filter and filter bank, semidefinite programming, trigonometric polynomial. a linear TSIC in the filter coefficients [19], [32] (more precisely, (2) leads to two linear TSICs [16]). More general constraints [1], [2], [37] involving bounds on the frequency response of the FIR filter are also expressible in terms of linear TSIC. Imposing a passband ripple of in the passband, and a stopband attenuation of in the stopband is equivalent to the following linear TSICs (2) I.
The design of peak constrained least squares FIR filters with low complexity finite precision coefficients
 PROC. IEEE INT. SYMP. CIRC. SYST
, 2001
"... A method for the design of Finite Precision Coefficient (FPC) Peak Constrained Least Squares (PCLS) Finite duration Impulse Response (FIR) digital filters based on Adams ’ optimality criterion and an efficient local search method is presented. Simple quantization of the infinite precision filter coe ..."
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Cited by 4 (3 self)
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A method for the design of Finite Precision Coefficient (FPC) Peak Constrained Least Squares (PCLS) Finite duration Impulse Response (FIR) digital filters based on Adams ’ optimality criterion and an efficient local search method is presented. Simple quantization of the infinite precision filter coefficients typically leads to filter designs that fail to meet the frequency response and Passband to Stopband energy Ratio (PSR) specifications. It is shown that it is possible to implement computationally efficient filters (with reduced filter FPC wordlengths) that meet the passband and stopband attenuation specifications at the expense of a lower PSR energy ratio.
Optimized analog filter designs with flat responses by semidefinite programming
 IEEE Trans. Signal Processing
"... Abstract—Analog filters constitute indispensable components of analog circuits. Inspired by recent advances in digital filter design, this paper provides a flexible design for analog filters. Allpole filters have maximally flat passband, so our design minimizes their passband distortion. Analogous ..."
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Cited by 3 (1 self)
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Abstract—Analog filters constitute indispensable components of analog circuits. Inspired by recent advances in digital filter design, this paper provides a flexible design for analog filters. Allpole filters have maximally flat passband, so our design minimizes their passband distortion. Analogously, maximally flat filters have maximally flat passband, so our design maximizes their stopband attenuation. Its particular cases provide flexible alternatives to the classical counterparts. Semidefinite program (SDP) formulations for the posed filter design problems are presented, which are efficiently solved by existing optimization software. Several examples and comparisons are provided to validate the viability of our design. Index Terms—Analog filter, convex analysis, global optimization, semidefinite programming (SDP). I.
A UNIFIED QUADRATIC SEMIINFINITE PROGRAMMING APPROACH TO TIME AND FREQUENCY DOMAIN CONSTRAINED DIGITAL FILTER DESIGN ∗
"... Abstract. A unified quadratic semiinfinite programming approach is introduced to solve digital filter design problems with time or frequencydomain specification. An algorithm based on this approach is developed and the corresponding convergence result is presented. This computational method is the ..."
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Cited by 2 (2 self)
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Abstract. A unified quadratic semiinfinite programming approach is introduced to solve digital filter design problems with time or frequencydomain specification. An algorithm based on this approach is developed and the corresponding convergence result is presented. This computational method is then applied to the optimum filter design problems subject to time and frequency domain specifications, namely the time domain envelope constrained filter design problems and the frequencydomain least square FIR filter design problems. For illustration, two examples are given.