A dynamic adaptive sampling technique in frequency-domain transient analysis

The transient response of a structure may be obtained directly by solving a problem in the time domain. However, there are certain advantages in obtaining the time-domain waveform from frequency-domain data. Taking samples to characterize the frequency spectrum of a resonant structure with no prior knowledge of its behavior, poses difficulty. There is no foolproof way to determine the sampling resolution that will yield an accurate result while keeping the number of samples to a minimum. We propose a frequency sampling technique using a dynamic adaptive algorithm. The algorithm zeroes in on the resonant peaks without user intervention and computes the samples to the required resolution. The resolution is relaxed where appropriate, to achieve economy of samples. A modified discrete Fourier transform formula is used to process the nonuniformly spaced frequency data into the time-domain waveform. Computation time is vastly reduced. This technique enables the frequency-domain approach to be used for modeling transients in very high-Q structures accurately.