We develop an L p analog to AAK theory on the unit circle that interpolates continuously between the case p=., which classically solves for best uniform meromorphic approximation, and the case p=2, which is equivalent to H 2 -best rational approximation. We apply the results to the uniqueness problem in rational approximation and to the asymptotic behaviour of poles of best meromorphic approximants to functions with two branch points. As pointed out by a referee, part of the theory extends to every p ¥ [1, .] when the definition of the Hankel operator is suitably generalized; this we discuss in connection with the recent manuscript by V. A. Prokhorov, submitted for publication. gives rise to a best approximation of f ¥ L p by a meromorphic function g m with at most m poles in the disk via the formula:
International audienceThis article explores an optimization procedure for microwave filters and multiplexers. The procedure is initialized by a classical filter synthesis based on a segmented electromagnetic synthesis that provides the basic dimensions of the structure. The optimization loop, which combines a global electromagnetic analysis and a coupling identification, improves the structure response compared to an empirical optimizatio
Performing a stability analysis during the design of any electronic circuit
is critical to guarantee its correct operation. A closed-loop stability
analysis can be performed by analysing the impedance presented by the circuit
at a well-chosen node without internal access to the simulator. If any of the
poles of this impedance lie in the complex right half-plane, the circuit is
unstable. The classic way to detect unstable poles is to fit a rational model
on the impedance.
In this paper, a projection-based method is proposed which splits the
impedance into a stable and an unstable part by projecting on an orthogonal
basis of stable and unstable functions. When the unstable part lies
significantly above the interpolation error of the method, the circuit is
considered unstable. Working with a projection provides one, at small cost,
with a first appraisal of the unstable part of the system.
Both small-signal and large-signal stability analysis can be performed with
this projection-based method. In the small-signal case, a low-order rational
approximation can be fitted on the unstable part to find the location of the
unstable poles.Comment: Longer version of the paper published in IEEE Transactions on
Microwave Theory and Technique
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