Estimation of resonant frequencies and quality factors from time domain computations

Abstract

A new frequency domain subspace algorithm for the estimation of resonant frequencies and quality factors given the output from time domain computations is developed and tested. It applies the discrete Fourier transform to the time domain signal and the estimates are computed from the frequency data within the frequency band of interest. Thus, out-of-band disturbances are suppressed through a band-pass filtering operation in frequency domain, which is free from the transient effects that are inevitable for standard time domain filtering techniques. We also propose an efficient procedure to generate short time domain excitations with an a priori specified frequency spectrum. By combining such excitations with the frequency domain subspace algorithm, we estimated to high accuracy the lowest 167 resonant frequencies of a three-dimensional bow-tie microwave resonator given two separate time domain computations with, in total, 23,000 time steps. A free-space computation for a cavity with an aperture shows that the estimation algorithm can be used to efficiently and accurately extrapolate time domain signals. The tests show that it is possible to reduce the overall computation time by several orders of magnitude for systems with undamped or weakly damped modes. It operates as a post-processing step and, thus, decouples the estimation of frequencies and amplitudes from the time-domain solver which offers a considerable flexibility.