Multirate systems and filter banks
Multirate systems and filter banks
Linear robust control
Wavelets and subband coding
Robust and optimal control
Indefinite-quadratic estimation and control: a unified approach to H2 and H∞ theories
Indefinite-quadratic estimation and control: a unified approach to H2 and H∞ theories
A Unified Algebric Approach to Control Design
A Unified Algebric Approach to Control Design
Design of multirate filter banks by ℋ∞optimization
IEEE Transactions on Signal Processing
On linear H∞ equalization of communicationchannels
IEEE Transactions on Signal Processing
Nonuniform filter bank design with noises
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Minimax deconvolution design of multirate systems with channelnoises: a unified approach
IEEE Transactions on Signal Processing
A mixed norm performance measure for the design of multiratefilterbanks
IEEE Transactions on Signal Processing
Mixed H2/H∞ filtering design inmultirate transmultiplexer systems: LMI approach
IEEE Transactions on Signal Processing
Optimal noise reduction in oversampled PR filter banks
IEEE Transactions on Signal Processing
Quantization of filter bank frame expansions through moving horizon optimization
IEEE Transactions on Signal Processing
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We study the design of synthesis filters in noisy filter bank systems using an H∞ estimation point of view. The H∞ approach is most promising in situations where the statistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank is unknown, or is too difficult to model and analyze. For the important special case of unitary analysis polyphase matrices we obtain an explicit expression for the minimum achievable disturbance attenuation. For arbitrary analysis polyphase matrices, standard state-space H∞ techniques can be employed to obtain numerical solutions. When the synthesis filters are restricted to being FIR, as is often the case in practice, the design can be cast as a finite-dimensional semi-definite program. In this case, we can effectively exploit the inherent non-uniqueness of the H∞ solution to optimize for an additional criteria. By optimizing for average performance in addition to the H∞ criteria, we obtain mixed H2/H∞ optimal FIR synthesis filters. Alternatively, if the additional criteria is concerned with penalizing occasional occurrence of large values of reconstruction errors more than frequent occurrence of small to moderate ones, we obtain risk-sensitive FIR synthesis filters. Numerical examples and comparisons with existing methods are also included.