Design Algorithms Of Hybrid Filter Bank A/D Converters

The demand for analog-to-digital converters (ADCs) with high speed andresolution has dramatically increased for sampling ultra wideband analog signals inmany domains, such as telecommunications and ultra wideband radars. ADCs are oftenthe most critical components in these applications and they tend to determine the overallsystem performance. However, it is difficult to use a single ADC to satisfy therequirements for conversion of an ultra wideband signal. In order to build a very fastADC, parallelization of channels based on the generalized sampling theorem is a wisechoice. The hybrid filter bank (HFB) architecture is a good candidate. The HFBovercomes the problem of extremely sensitivity to ADC mismatches and clock timingerrors from which time-interleaved structure suffers much, hence the speed andresolution of conversion can be improved. This dissertation researches the designalgorithms and applications of HFB. Specifically, we propose some design methods ofnear perfect reconstruction HFB, and study the effects of component variations ofanalog analysis filters on HFB by means of a new robust optimal design algorithm, andmeanwhile discuss two kinds of new HFB architecture. The main work in thisdissertation is five fold:1. Two eigenfilter methods are proposed to design HFB, which use low-orderanalog analysis filters and finite impulse response (FIR) digital synthesis filters andsatisfies near perfect reconstruction. The conventional eigenfilter technique (EIG)considers the distortion error measure and aliasing error measure. Both of the errormeasure are based on least-squares (LS) error criterion. First, the aliasing error measureis written as a quadratic form in terms of the unknown coefficients vector; then byintroducing a reference frequency, the distortion error measure can be also written as thesame form as the aliasing error measure. The eignefilter technique based on a total leastsquares error criterion (TLS EIG) does not need a reference frequency point fornormalization as done in EIG. Then, both of the problems are reduced to finding theeigenvector corresponding to the minimum eigenvalue of a positive-definite matrix.This eigenvector can be calculated efficiently using the iterative power method.Numerical experiments show the proposed approaches yield better performancecompared to existing techniques. Moreover, the solution of the TLS EIG is better thanthat of the EIG.2. A new FIR synthesis filters design method is formulated based on the minimization of a mixed norm that is the weighted sum of the2-norm and theChebyshev norm. In this case, the LS and minimax problems become special cases ofthe mixed norm problem. The problem is formulated as a convex optimization problemand solved using semidefinite programming (SDP). The proposed mixed norm methodallows designers to select the best suitable filters among a family of synthesis filters forspecific applications. Robust FIR synthesis filters are also designed with analog filterserrors. When the uncertainty in each frequency response of analog filters is described bya complex uncertainty ellipsoid at each frequency, the robust synthesis filters designproblem can be also formulated as an SDP problem. Design results show that the robustsynthesis filters designed perform better than the nominal optimal ones when analogfilters errors are considered.3. This paper presentsΗ∞norm and mixedΗ2Η∞norm optimal designs ofdigital synthesis filters of a hybrid filter bank. In this case, no assumptions of the inputsignal, such as band-limitedness, are necessary in both of the methods. First, a hybridinduced error system is constructed which is the connection of the HFB and desiredhigh-rate system in parallel. Then, we show that there exists a finite-dimensional digitalLTI system that has the sameΗ2norm andΗ∞norm with the error system. This isachieved in two steps:(1) using techniques in sampled-data control, the continuous-timepart of the HFB is discretized to obtain a finite-dimensional time-varying discrete-timesystem;(2) using the polyphase representation along with the lifting of inputs andoutputs, the system is converted into a standard model-matching form for theΗ∞optimal and mixedΗ2Η∞optimal design. Finally, both of problems can be solvedusing the theory of linear matrix inequalities such that FIR filters are directly obtainedwithout truncation of infinite impulse responses. Several design examples are providedto illustrate the effectiveness of the proposed approaches. Moreover, the input signalneeds not be oversampled and band-limited.4. To reconstruct the signal of interest in reduced frequency band using HFB,Chebyshev norm performance measure is presented to design FIR digital synthesisfilters of HFB. The FIR filters are designed to minimize performance measure of ahybrid error system. This hybrid and multirate problem is cast as a norm optimizationproblem involving only linear time-invariant, discrete-time system. Using thegeneralized Kalman-Yakubovich-Popov (KYP) lemma, the problem is reduced to anoptimization problem with a linear matrix inequality. Numerical experiments show theproposed approach yields better performance compared to existing techniques.5. Two improved HFB systems are proposed and discussed. A parallel architecture for wideband ADC, named cosine modulated hybrid filter bank, is presented to addressthis problem. First, the proposed architecture shifts the input signal spectrum by meansof mixers. The modulated signal is channelized into smaller frequency subband signalsusing identical lowpass analog filters. Then the subband signals are digitized throughidentical narrowband ADCs, respectively. Finally, the digitized signals are up-sampled,filtered and combined to reconstruct the digital representation of original wide-bandinput signal. The digital filters are designed to the eigenfilter method based on total leastsquares error criterion. Since the sample-and-hold circuits needed in this architecture aresimple identical narrowband baseband circuits, which makes the design easier andcheaper. A mixed norm performance measure is also presented to design FIR digitalsynthesis filters of hybrid filter banks with fractional delays. The mixed normperformance measure is based on the peak value as well as the energy of the error signal.A numerical example is also presented to show the effectiveness of the proposedmethod.