Transfer function determination in structures and enclosures using adaptive linear prediction techniques

Abstract

Given a structure or enclosure with a finite number of bandlimited sources radiating energy into it, the transfer functions between any two points are found using adaptive pole‐zero digital filters with a leasts‐squared‐error criterion when the signals at the points in the structure or enclosure are known. The number of poles and zeros in the adaptive filter is chosen higher than the assumed number of resonances and antiresonances between the points of interest to insure that all the dominant features of the transfer function are matched by the adaptive filters. The mathematical basis for deriving the filter parameters directly from the observed input/output time series can be found from using a lattice method solution to the multichannel Yule‐Walker equations [B. Friedlander, Proc. IEEE 70 (8), 841–852 (1982)]. The computed poles and zeros of the adaptive filter provide more information than traditional Fourier cross spectra or statistical energy analysis methods.