Parzen-Windowed SDFT-Based Frequency Tracking Approach for Sensing Capacitance and Resistance

This paper generalizes the windowing technique used in the sliding discrete Fourier transform (SDFT) operation instead of applying only the default rectangular window. Further extending it in the design of frequency locked loops (FLLs). The SDFT operation on a time-series is equivalent to multiplying the signal by a rectangular window and then computing the DFT on the windowed segment to obtain its frequency components. Utilizing a window function other than a rectangular window negates the recursive efficiency of the sliding DFT; consequently, sparse kernels are proposed to convolve with the SDFT output, thus effectively applying the desired window in the frequency domain. These kernels are obtained for various window functions using Parseval’s theorem with a certain threshold. These kernels are applied along with kth bin SDFT as windowed SDFT. This structure can be used as a tuned filter to extract a particular frequency of interest from the input signal by filtering out other signal frequencies. Applying these kernels reduce the spectral leakage without losing the recursive nature of the SDFT. Eight windowed-FLLs viz. Hamming, Poisson-Hanning, Exponential, Bartlett, Kaiser, Gaussian, Blackman and Parzen are designed and compared on various performance metrics. Further the best performing FLL is compared with the existing state of the art FLLs in simulation and in hardware implementation. The designed Parzen windowed FLL achieved the highest frequency estimation range (3.9-77) kHz, capacitance measurement range (35-650) pF, resistance measurement range (0.52-10.25) kΩ, pull-in range (8-69) kHz, hold-in range (5-73) kHz, and lock-in range (37.5-42.5) kHz among them.