| 摘要 |
A filter synthesizer and method are disclosed for generating and outputting a stable filter from frequency response data, including coherence values. A processing unit has a processor, memory, and stored programs. The processor, operating the modal analysis program, processes the frequency response data, generates orthogonal polynomial data from a cost function of the frequency response data including coherence values, and generates the modal parameters of a transfer function from the orthogonal polynomial data, which represents Forsythe polynomials. The processor generates the orthogonal polynomial data from least squares processing the cost function of the frequency response data, including coherence values. The processor generates the modal parameters, including a pole of the transfer function, and determines an instability condition from the pole. If a pole is unstable, the processor refits the frequency response data to generate a stable transfer function. A least squares optimization procedure is performed on the frequency response data, including the coherence values. A residue is generated corresponding to a pole, and the residue is revised in response to a condition of the pole being unstable. The modal parameters are generated by determining a companion matrix from the first orthogonal polynomial data and the frequency response data; performing QR decomposition on the companion matrix; and generating a pole as a eigenvalue of the companion matrix from the QR decomposition.
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