On the minimax design of passband linear-phase variable digital filters using semidefinite programming

Variable digital filters (VDFs) are useful to the implementation of digital receivers because its frequency characteristics such as fractional delays and cutoff frequencies can be varied online. In this letter, it is shown that the optimal minimax design of VDFs with passband linear-phase can be formulated and solved as a semi-definite programming (SDP) problem, which is a powerful convex optimization method. In addition, other objective functions, such as least squares, and linear and convex quadratic inequality constraints can readily be incorporated. Design examples using a variable fractional delay (VFD) and a variable cutoff frequency (VCF) FIR filters are given to demonstrate the effectiveness of the proposed approach. © 2004 IEEE.published_or_final_versio

On the design of real and complex fir filters with flatness and peak error constraints using semidefinite programming

This paper studies the problem of designing digital finite duration impulse response (FIR) filters with prescribed flatness and peak error constraints using semidefinite programming (SDP). SDP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. This property is utilized for the optimal minimax and least squares (LS) design of linear-phase and low-delay FIR filters with prescribed magnitude flatness and peak design error, which are formulated as a set of linear equality and convex quadratic inequality constraints, respectively. A method for structurally imposing these equality constraints in the SDP formulation is also proposed. Using these results, the design approach is further extended to the design of constrained complex coefficient FIR filters and variable digital filters (VDFs). Design examples are given to demonstrate the effectiveness of the approach.published_or_final_versio

Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming

This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived. © 2005 IEEE.published_or_final_versio

Design of complex-valued variable digital filters and its application to the realization of arbitrary sampling rate conversion for complex signals

The 47th Midwest Symposium on Circuits and Systems Conference, Salt Lake City, Utah, USA, 25-28 July 2004This paper studies the design of complex-valued variable digital filters (CVDFs) and their applications to the efficient arbitrary sample rate conversion for complex signals in software radio receivers. The design of CVDFs using either the minimax or least squares criteria is formulated as a convex optimization problem and solved using the second order cone programming (SOCP) or semidefmite programming (SDP). In addition, linear and convex quadratic inequality constraints can be readily incorporated. Design examples are given to demonstrate the effectiveness of the proposed approach.published_or_final_versio

The design of digital all-pass filters using second-order cone programming (SOCP)

This brief proposes a new method for designing digital all-pass filters with a minimax design criterion using second-order cone programming (SOCP). Unlike other all-pass filter design methods, additional linear constraints can be readily incorporated. The overall design problem can be solved through a series of linear programming subproblems and the bisection search algorithm. The convergence of the algorithm is guaranteed. Nonlinear constraints such as the pole radius constraint of the filters can be formulated as additional SOCP constraints using Rouche's theorem. It was found that the pole radius constraint allows an additional tradeoff between the approximation error and the stability margin. The effectiveness of the proposed method is demonstrated by several design examples and comparison with conventional methods. © 2005 IEEE.published_or_final_versio

A semi-definite programming (SDP) method for designing IIR sharp cut-off digital filters using frequency-response masking

IEEE International Symposium on Circuits and Systems Proceedings, Vancouver, Canada, 23-26 May 2004This paper studies the design of frequency response masking (FRM) filters with infinite duration impulse response (IIR) model and masking sub-filters. They are useful in realizing sharp cutoff digital filters with low passband delays. The designs of the model and masking filters are carried out by means of semidefinite programming (SDP) and model order reduction. Design results show that low complexity FRM filters with low passband delay can be obtained.published_or_final_versio

On the design and multiplierless realization of perfect reconstruction triplet-based FIR filter banks and wavelet bases

This paper proposes new methods for the efficient design and realization of perfect reconstruction (PR) two-channel finite-impulse response (FIR) triplet filter banks (FBs) and wavelet bases. It extends the linear-phase FIR triplet FBs of Ansari et al. to include FIR triplet FBs with lower system delay and a prescribed order of K regularity. The design problem using either the minimax error or least-squares criteria is formulated as a semidefinite programming problem, which is a very flexible framework to incorporate linear and convex quadratic constraints. The K regularity conditions are also expressed as a set of linear equality constraints in the variables to be optimized and they are structurally imposed into the design problem by eliminating the redundant variables. The design method is applicable to linear-phase as well as low-delay triplet FBs. Design examples are given to demonstrate the effectiveness of the proposed method. Furthermore, it was found that the analysis and synthesis filters of the triplet FB have a more symmetric frequency responses. This property is exploited to construct a class of PR M-channel uniform FBs and wavelets with M = 2 L, where L is a positive integer, using a particular tree structure. The filter lengths of the two-channel FBs down the tree are approximately reduced by a factor of two at each level or stage, while the transition bandwidths are successively increased by the same factor. Because of the downsampling operations, the frequency responses of the final analysis filters closely resemble those in a uniform FB with identical transition bandwidth. This triplet-based uniform M-channel FB has very low design complexity and the PR condition and K regularity conditions are structurally imposed. Furthermore, it has considerably lower arithmetic complexity and system delay than conventional tree structure using identical FB at all levels. The multiplierless realization of these FBs using sum-of-power-of-two (SOPOT) coefficients and multiplier block is also studied. © 2004 IEEE.published_or_final_versio

The design and multiplier-less realization of software radio receivers with reduced system delay

This paper studies the design and multiplier-less realization of a new software radio receiver (SRR) with reduced system delay. It employs low-delay finite-impulse response (FIR) and digital allpass filters to effectively reduce the system delay of the multistage decimators in SRRs. The optimal least-square and minimax designs of these low-delay FIR and allpass-based filters are formulated as a semidefinite programming (SDP) problem, which allows zero magnitude constraint at ω = π to be incorporated readily as additional linear matrix inequalities (LMIs). By implementing the sampling rate converter (SRC) using a variable digital filter (VDF) immediately after the integer decimators, the needs for an expensive programmable FIR filter in the traditional SRR is avoided. A new method for the optimal minimax design of this VDF-based SRC using SDP is also proposed and compared with traditional weight least squares method. Other implementation issues including the multiplier-less and digital signal processor (DSP) realizations of the SRR and the generation of the clock signal in the SRC are also studied. Design results show that the system delay and implementation complexities (especially in terms of high-speed variable multipliers) of the proposed architecture are considerably reduced as compared with conventional approaches. © 2004 IEEE.published_or_final_versio

The design of a class of perfect reconstruction two-channel FIR linear-phase filterbanks and wavelets bases using semidefinite programming

This paper proposes a new method for designing a class of two-channel perfect reconstruction (PR) linear-phase FIR filterbanks (FBs) and wavelets previously proposed by Phoong et al. By expressing the given K-regularity constraints as a set of linear equality constraints in the design variables, the design problem using the minimax error criterion can be solved using semidefinite programming (SDP). Design examples show that the proposed method is very effective and it yields equiripple stopband response while satisfying the given K-regularity condition.published_or_final_versio

A new method for designing causal stable IIR variable fractional delay digital filters

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. © 2007 IEEE.published_or_final_versio