High-Dynamic Frequency Tracking Using Wavelets

In this article, we investigate the use of wavelets for frequency tracking in the presence of high dynamics. In particular, we construct automatic frequency control loops that are based on correlating the incoming sinusoidal signal with Fourierbased functions and with Daubechies-4 wavelet functions. Both loops are compared based on their abilities to track an input frequency with varying degrees of frequency rate. For each loop, we show the steady-state frequency error and corresponding steady-state variance as a function of the frequency rate of the input signal. The results indicate that when the input frequency rate is close to zero (nearly constant frequency input), the Fourier-based loop achieves lower variance than does the wavelet-based loop. As the frequency rate increases (high dynamics), the performance of the Fourier-based loop degrades, and ultimately the Fourier-based loop ceases to track. Meanwhile, the wavelet-based loop achieves a lower steady-state error and continues to successfully track in frequency rate ranges where the Fourierbased loop breaks down. Thus, this study suggests that wavelets can be a viable alternative to traditional Fourier-based frequency tracking loops when the input is undergoing high dynamics. This type of dynamics could be found in applications such as space probes descending through a turbulent and unpredictable planetary atmosphere. However, during normal spacecraft cruise, more traditional Fourierbased loops will outperform wavelet-based loops.