Finer Granularity DFT Bins With Moving Window for Capacitance Sensing

Abstract

In this article, the moving window discrete Fourier transform (MWDFT) with finer granularity bin indices is proposed for frequency estimation of periodic signals. The MWDFT structure is a cascade connection of comb filter and a complex resonator. The sign of comb filter is toggled between positive and negative using a multiplexer to select the integer and fractional bin indices. The sign of comb filter is chosen as negative for setting-up integer bin indices with certain resonator angle. The positive sign of comb filter rotates the zeros of the MWDFT to a specified angle in the anticlockwise direction in the z -plane. By selecting the positive feed forward coefficient, all odd harmonics of one-half of the fundamental frequency can be extracted from the MWDFT. This unique property of MWDFT with finer granularity bin indices is exploited to extract frequencies of finer resolution. A frequency locked loop is designed with MWDFT of finer granularity bins to estimate the frequency change of finer resolution. The proposed method is implemented on field programmable gate array (FPGA) as a capacitance measurement system. The method is able to provide better accuracy, wider frequency estimation range, and wider capacitance measurement range.