Wavelet Applications

Systems Technology has introduced a number of innovative wavelet-based techniques to characterize time-varying dynamic systems. In traditional windowed Fourier transform techniques, the power versus frequency relationship is averaged over the entire time history. With wavelet transforms the power or auto-spectrum is computed as a function of both time and frequency. The resulting time-varying result is referred to as a scalogram.

Furthermore, unlike the windowed Fourier transform, the wavelet transform time window decreases as the frequency increases capturing more of the transient response at higher frequencies than the Fourier transform. Time-varying frequency responses are estimated from the ratios of wavelet transforms. These techniques have been used to identify changes in aircraft responses in the presence of failures and variations in human operator performance as simulated control surface rate limiting is introduced into the controlled element.

New metrics based on wavelet scalograms have also been introduced including the Power Frequency, which provides a time-varying measure of the frequency and intensity of pilot control activity. Analysis results have shown the Power Frequency to be an effective means of differentiating run-to-run and pilot-to-pilot differences when performing precision offset landings in an aircraft and precision hover tasks in a helicopter.

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