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Efficient Design of CosineModulated Filterbanks via Convex Optimization
 Copyright © 2010 SciRes. IJCNS 942
"... Abstract—This paper presents efficient approaches for designing cosinemodulated filter banks with linear phase prototype filter. First, we show that the design problem of the prototype filter being a spectral factor of thband filter is a nonconvex optimization problem with low degree of nonconvex ..."
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Abstract—This paper presents efficient approaches for designing cosinemodulated filter banks with linear phase prototype filter. First, we show that the design problem of the prototype filter being a spectral factor of thband filter is a nonconvex optimization problem with low degree of nonconvexity. As a result, the nonconvex optimization problem can be cast into a semidefinite programming (SDP) problem by a convex relaxation technique. Then the reconstruction error is further minimized by an efficient iterative algorithm in which the closedform expression is given in each iteration. Several examples are given to illustrate the effectiveness of the proposed method over the existing ones. Index Terms—Convex optimization, cosinemodulated filter bank, prototype filter, semidefinite programming. I.
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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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 dual frequencyselective bounded real lemma and its applications to IIR filter design
, 2006
"... Given a transfer function H(s) of order n, the celebrated bounded real lemma characterises the untractable semiinfinite programming (SIP) condition
H(ω)
2
≤ γ
2
∀ω ∈ R of function bounded realness (BR)
by a tractable semidefinite programming (SDP). Some
recent results generalise this result fo ..."
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Cited by 2 (2 self)
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Given a transfer function H(s) of order n, the celebrated bounded real lemma characterises the untractable semiinfinite programming (SIP) condition
H(ω)
2
≤ γ
2
∀ω ∈ R of function bounded realness (BR)
by a tractable semidefinite programming (SDP). Some
recent results generalise this result for the SIP condition
H(ω)
2
≤ γ
2
∀ω ≤ ¯ω of frequencyselective bounded
realness (FSBR). The SDP characterisations are given at
the expense of an introduced Lyapunov matrix variable of dimension n × n. As a result, the dimension of the
resultant SDPs grows so quickly in respect to the function
order, making them much less computationally tractable
and practicable. Moreover, they do not allow to formulate
synthesis problems as SDPs.
In this paper, a completely new SDP characterizations for general FSBR for allpole transfer functions is proposed. Our motivation is the design of infiniteimpulseresponse (IIR) filters involving a few of simutaneous FSBRs. Our SDP characterizations are of moderate size and free from Lyapunov variables and thus allow to address problems involving transfer functions of arbitrary order. Examples are also provided to validate the effectiveness of the resulting SDP design formulation. Finally we also raise some issues arising with practicability of SDP for multidimensional filter design problems. In particular, any bilinear matrix inequality (BMI) optimization is shown to be solved by a SDP with any prescribed tolerance but the issue is dimensionality of this SDP.
Correspondence Optimal Design of FIR Triplet Halfband Filter Bank and Application in Image Coding
"... Abstract—This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formul ..."
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Abstract—This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formulated as the minimization of the least square error subject to peak error constraints and regularity constraints. By using the linear matrix inequality characterization of the trigonometric semiinfinite constraints, it can then be exactly cast as a SDP problem with a small number of variables and, hence, can be solved efficiently. Several design examples of the triplet halfband filter bank are provided for illustration and comparison with previous works. Finally, the image coding performance of the filter bank is presented. Index Terms—Image coding, perfect reconstruction, regularity, semidefinite programming (SDP), triplet halfband filter bank. 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