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22
Convex optimization problems involving ¯ nite autocorrelation sequences
, 2000
"... We discuss convex optimization problems where some of the variables are constrained to be ¯nite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in ¯lter design and system identi¯cation. Autocorrelation constraints in optimi ..."
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We discuss convex optimization problems where some of the variables are constrained to be ¯nite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in ¯lter design and system identi¯cation. 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 semide¯nite 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 semide¯nite programming solvers are used. We present a more e±cient implementation based on duality and on interiorpoint methods for convex problems with generalized linear inequalities. Submited to Mathematical Programming, Series B. Associated software and related papers are available at www.ee.ucla.edu/~vandenbe.
New linearprogrammingbased filter design
 IEEE Trans. Circuits Syst. II, Exp. Briefs
, 2005
"... Abstract—It is well known that the filterdesign problem with mask constraints can be formulated as a semiinfinite program. There are two approaches toward the solution of this semiinfinite program. The first griding approach relaxes the semiinfinite constraint by refining it in the finite gridi ..."
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Abstract—It is well known that the filterdesign problem with mask constraints can be formulated as a semiinfinite program. There are two approaches toward the solution of this semiinfinite program. The first griding approach relaxes the semiinfinite constraint by refining it in the finite griding domain so it does not always guarantee global optimal and feasible solution. The second semidefinite programming (SDP)based approach does guarantee the global optimal solution and excellently handles positive real constraints. However, the magnitude constraints are still persistent and not yet handled by SDP tool in an efficient manner. In this brief, a new tight polyhedral approximation for semiinfinite constrained domain is proposed. Based on it, we present a new linearprogrammingbased solution method for filter design, which unlike the griding approach yields global solution and unlike SDP based approach is practical for even longtap filters. Simulation results confirm the viability of the proposed method. Index Terms—Finiteimpulse response (FIR) filter, linear programming, semidefinite programming. I.
Constrained Eigenfilter Design without Specified Transition Bands
"... Abstract — The design of FIR filter with constraints in frequency domain and/or time domain is considered. We further considered the design specification without explicitly specified transition band. A constrained eigenfilter is proposed to design FIR filter with various design constraints, and with ..."
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Abstract — The design of FIR filter with constraints in frequency domain and/or time domain is considered. We further considered the design specification without explicitly specified transition band. A constrained eigenfilter is proposed to design FIR filter with various design constraints, and without transition band specification. We have suggested the possible design tradeoff between transition band bandwidth and the ripple size of the filter. The proposed algorithm can design filters with optimal tradeoff between transition band bandwidth and the peak constrained ripple size. The eigenfilter formulation further allows the filter design specification to incorporate time domain constraints. Various design examples are presented to illustrate the versatility of the digital filter obtained by the proposed filter design method. I.
unknown title
, 2010
"... F inite impulse response (FIR) filters have played a central role in digital signal processing since its inception. As befits that role, a myriad of design techniques is available, ranging from the quite straightforward windowing and frequencysampling techniques to some rather sophisticated optimi ..."
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F inite impulse response (FIR) filters have played a central role in digital signal processing since its inception. As befits that role, a myriad of design techniques is available, ranging from the quite straightforward windowing and frequencysampling techniques to some rather sophisticated optimizationbased techniques; e.g., [1]–[7]. Among the most prominent optimizationbased techniques is the ParksMcClellan algorithm [8] for the design of “equiripple ” linear phase FIR filters. One of the key features of that technique is the efficiency of the underlying Remez exchange algorithm. However, computing resources have grown more plentiful since the ParksMcClellan algorithm was developed [9], and this has spawned the development of more flexible design methodologies. Of particular note are METEOR [10] and the peakconstrained leastsquares (PCLS) approach [11], [12]. METEOR is a flexible platform for FIR filter design problems that can be formulated as the optimization of a linear objective subject to linear constraints; i.e., as a linear program. One such problem is the design of a linearphase lowpass filter with a “ripple ” constraint in the passband, a constraint on the stopband level, and the constraint that the passband response be a concave function of frequency. The PCLS approach provides efficient constraint exchange algorithms for finding filters that minimize a “least squares” approximation error subject to linear constraints; i.e., solve a quadratic program. One example is the design of a lowpass filter that minimizes the stopband energy subject to a bound on the stopband level. Linear and quadratic programs are two of the simpler forms of convex optimization problem, and effective algorithms for solving them have been available for some time. Around the time that METEOR
New Optimized IIR LowPass Differentiators
"... Abstract—In this paper a novel approach is proposed for approximating ParksMcClellan lowpass differentiators using optimized loworder IIR filters. Indeed, a suitable IIR filter is designed for approximating Parks McClellan Low pass differentiator using modified AlAlaoui’s method, and then denom ..."
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Abstract—In this paper a novel approach is proposed for approximating ParksMcClellan lowpass differentiators using optimized loworder IIR filters. Indeed, a suitable IIR filter is designed for approximating Parks McClellan Low pass differentiator using modified AlAlaoui’s method, and then denominator polynomial coefficients of resulting transfer function optimized by Genetic algorithm. A suitable fitness function is defined to optimize both magnitude and phase responses; moreover, appropriate weighting coefficients and GA parameters are reported for several cutoff frequencies. It is shown that the order4 proposed lowpass differentiators yield a frequency response which is almost equal to order30 ParksMcClellan lowpass differentiators. Furthermore, they yield steep rolloff properties, small magnitude error and almost linear phase in the passband; the percentage error of magnitude response is less than 0.5%.
OPTIMAL HANKELNORM APPROXIMATION OF IIR BY FIR SYSTEMS
"... This paper presents a constructive method to (sub)optimal finite impulse response (FIR) approximation of a given infinite impulse response (IIR) model. The method minimizes the Hankel norm of approximation error by using the explicit solution of normpreserve dilation problem. It has the advantage o ..."
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This paper presents a constructive method to (sub)optimal finite impulse response (FIR) approximation of a given infinite impulse response (IIR) model. The method minimizes the Hankel norm of approximation error by using the explicit solution of normpreserve dilation problem. It has the advantage over the existing methods that it provides an explicitly constructive solution and allows the tradeoff between the Chebyshev and least square criteria. The lower and upper bounds on the l 2 and Chebyshev norms of approximation error are given. The effectiveness and properties of the proposed algorithm are demonstrated through a computation example.
Design of FIR Digital Filters Without TransitionBand Fluctuations
"... This paper presents a new method for the design of finiteimpulseresponse (FIR) digital filters without transitionband fluctuations. We derive a fluctuationfree condition from gradient constraints on the magnitude of transitionband responses. Incorporating the condition, we formulate a new peak ..."
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This paper presents a new method for the design of finiteimpulseresponse (FIR) digital filters without transitionband fluctuations. We derive a fluctuationfree condition from gradient constraints on the magnitude of transitionband responses. Incorporating the condition, we formulate a new peakconstrained leastsquares (PCLS) design of FIR filters as an iterative quadratic programming (QP) problem. Each iteration of the algorithm uses a multipleexchange technique for giving a QP problem with a small number of constraints. The new algorithm obtains PCLS filters free from transitionband fluctuations efficiently. Design examples are included to illustrate the proposed algorithm. 1.
Sampling Rate Conversion
, 2007
"... in partial fulllment of the requirements for the degree of ..."
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EURASIP Journal on Applied Signal Processing 2003:6, 555–564 c ○ 2003 Hindawi Publishing Corporation A Methodology for Rapid Prototyping PeakConstrained LeastSquares BitSerial Finite Impulse Response Filters in FPGAs
, 2002
"... Areaefficient peakconstrained leastsquares (PCLS) bitserial finite impulse response (FIR) filter implementations can be rapidly prototyped in field programmable gate arrays (FPGA) with the methodology presented in this paper. Faster generation of the FPGA configuration bitstream is possible with ..."
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Areaefficient peakconstrained leastsquares (PCLS) bitserial finite impulse response (FIR) filter implementations can be rapidly prototyped in field programmable gate arrays (FPGA) with the methodology presented in this paper. Faster generation of the FPGA configuration bitstream is possible with a new applicationspecific mapping and placement method that uses JBits to avoid conventional generalpurpose mapping and placement tools. JBits is a set of Java classes that provide an interface into the Xilinx Virtex FPGA configuration bitstream, allowing the user to generate new configuration bitstreams. PCLS coefficient generation allows passbandtostopband energy ratio (PSR) performance to be traded for a reduction in the filter’s hardware cost without altering the minimum stopband attenuation. Fixedpoint coefficients that meet the frequency response and hardware cost specifications can be generated with the PCLS method. It is not possible to meet these specifications solely by the quantization of floatingpoint coefficients generated in other methods.
LMI Characterization for The Convex Hull of Trigonometric Curves and Applications
"... Abstract—In this paper, we develop a new linear matrix inequality (LMI) technique, which is practical for solutions of the general trigonometric semiinfinite linear constraint (TSIC) of competitive orders. Based on the new full LMI characterization for the convex hull of a trigonometric curve, it i ..."
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Abstract—In this paper, we develop a new linear matrix inequality (LMI) technique, which is practical for solutions of the general trigonometric semiinfinite linear constraint (TSIC) of competitive orders. Based on the new full LMI characterization for the convex hull of a trigonometric curve, it is shown that the semiinfinite optimization problem involving TSIC can be solved by LMI optimization problem with additional variables of dimension just n, the order of the the trigonometric curve. Our solution method is very robust which allows us to address almost all practical filter design problems. Unlike most previous works involving several complex mathematical tools, our derivation arguments are based on simple results of the convex analysis and some formal elementary transforms. Furthermore, many filter/filterbank design problems can be reformulated as the optimization of linear/convex quadratic objectives over the trigonometric semiinfinite constraints (TSIC). Based on this reformulation, these problems can be equivalently reduced to LMI optimization problems with the minimal size. Our examples of designing up to 1200tap filters verifies the viability of our formulation.