Extrapolation of Band-Limited Frequency Responses for Out-of-Band Modal Synthesis

The bandwidth of the measured or simulated frequency responses is sometimes relatively narrow, resulting in that some out-of-band modes of interest cannot be directly observed from the band-limited frequency responses. Although various kinds of curve fitting algorithms aim at generating linear or nonlinear transfer functions for these frequency samples, their fitting objective is commonly minimizing the in-band fitting errors, whereas their reproduction/identification capabilities for the out-of-band modes are usually ignored and may be not satisfying. To fill this research gap, this paper, based on the sufficient excavation of the in-band frequency responses information induced by the out-of-band partial fraction terms, develops an extrapolation method for the band-limited frequency responses in order to identify or synthesize the out-of-band modes. The effectiveness of the proposed out-of-band modal synthesis method is validated on artificially created rational functions with different numbers of out-of-band modes. The proposed frequency-domain extrapolation method can obtain unknown and much modal information from known and little modal information, which would be a desirable tool to identify the modes of interest not located within the available frequency interval.