Frequency Estimation Based on Moving-Window DFT With Fractional Bin-Index for Capacitance Measurement

Abstract

A frequency estimation technique is proposed with fractional bin-index-based moving-window discrete Fourier transform (MWDFT). In order to increase the range of estimation frequencies, different MWDFTs with bin-indices $k = 0.5$ , 1, 1.5, 2, and 2.5 are chosen and incorporated in the frequency estimator. The structure of the MWDFT is modified with the positive feedforward coefficients for fractional bin-indices and negative coefficients for integer multiples. The frequency of the input signal is estimated by adaptively adjusting the sampling pulses for MWDFT with integer and fractional bin-indices. The proposed frequency estimator is validated through field programmable gate array implementation for measuring a capacitance range of 89.201–1420.69 pF. A relaxation oscillator with a measurand as capacitance exhibits a square wave whose frequency is inversely related to the measurand. The frequency of the square wave is estimated through the proposed DFT procedure instantaneously by extracting the fundamental sinusoidal signal and tracking the same with the feedback loop. The experimental investigation on the proposed method proves to be accurate and computationally efficient, and offers a wide operating range with less acquisition time.