Abstract
We present a resource-efficient frequency adaptation method to complement the Fourier analyzer proposed by Péceli. The novel frequency adaptation scheme is based on the adaptive Fourier analyzer suggested by Nagy. The frequency adaptation method was elaborated with a view to realizing a detector connectivity check on an FPGA in a new beam loss monitoring (BLM) system, currently being developed for beam setup and machine protection of the particle accelerators at the European Organisation for Nuclear Research (CERN). The paper summarizes the Fourier analyzer to the extent relevant to this work and the basic principle of the related frequency adaptation methods. It then outlines the suggested new scheme, presents practical considerations for implementing it and underpins it with an example and the corresponding operational experience.
Highlights
: We present a resource-efficient frequency adaptation method to complement the Fourier analyzer proposed by Péceli
With a view to decreasing sensitivity to noise, Ronk suggested extending these approaches by averaging the Fourier components used for the adaptation, obtaining the eBAFA from the BAFA [9], and the improved robust adaptive Fourier analyzer (AFA) (IRA)
The current best solution is in operation at CERN’s flagship machine, the Large Hadron Collider (LHC), where a connectivity check requiring the accelerator to be offline is enforced on each detector channel every 24 hours
Summary
Péceli’s resonator-based observer estimates the state variables of the conceptual signal model [2]. We are assuming the signal to be real-valued In this case, the conceptual signal model is described by the following equations: xn+1 = xn, xn = xi,n T ∈ CN×1, yn = cTn xn, i = −K, . K harmonics, it has N = 2K + 1 complex Fourier coefficients, including DC, which compose the state vector xn. Since the signal is assumed to be real-valued, the Fourier coefficients will form complex conjugate pairs: xi,n = x∗−i,n. The above imply that the complex Fourier coefficients of the input signal can be estimated by an appropriately designed observer. 1 and fs N deadbeat observer is obtained which settles in at most N steps and calculates the recursive discrete Fourier transform of the input signal [7].
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