An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an inverse FIR synthesis system. We also provide a method to ensure the Hermitian symmetry property on the synthesis side, which is serviceable to processing real-valued signals. As an invertible analysis scheme corresponds to a redundant decomposition, there is no unique inverse FB. Given a particular solution, we parameterize the whole family of inverses through a null space projection. The resulting reduced parameter set simplifies design procedures, since the perfect reconstruction constrained optimization problem is recast as an unconstrained optimization problem. The design of optimized synthesis FBs based on time or frequency localization criteria is then investigated, using a simple yet efficient gradient algorithm.

This paper describes a simple sub-idle component map extrapolation method. Used in conjunction with gas turbine performance models, it enables designers to estimate sub-idle gas turbine performance during engine start-up. The lack of information available regarding component maps in the sub-idle regime creates major challenges for starting system designers or control system designers as the numerical convergence of performance models decreases rapidly below idle speed. The proposed component map extrapolation method alleviates this problem by extrapolating given component map data well below idle speed. The underlying equations of the method are based on the principles of incompressible similarity laws. Also known as pump laws, these equations are modified to account for compressibility effects by varying the similarity law exponents. To estimate the integrity of the extrapolated component maps and to build confidence in the sub-idle extrapolation method, extrapolate speed lines were compared to speed lines found in the original component map. Even though the extrapolation method is yet to be experimentally validated, preliminary estimates showed that the extrapolation method did produce adequate component maps. To demonstrate the potential of the component extrapolation method when used in conjunction with gas turbine performance models, a virtual test case engine was modeled and used to produce start-up performance data.

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