A Switch-Based Interpolated DFT for the Small Number of Acquired Sine Wave Cycles

Abstract

The frequency of a real sinusoid is often estimated by interpolated discrete Fourier transform (IpDFT) algorithms because of the high accuracy and low computational burden. However, conventional IpDFTs focus on frequency estimation when the number of acquired sine wave cycles (NASC) is more than two. Frequency estimation with the small NASC is applicable in manufacturing processes, radar level measurement, and other applications. The spectral leakage of the negative frequency (the image component) significantly distorts the positive frequency when the NASC is small, dramatically degrading estimation accuracy. In particular, it is a challenging task for existing IpDFTs to provide high estimation accuracy when the NASC is less than one. In this paper, a switch-based IpDFT is proposed to provide high frequency estimation accuracy for $\text {NASC} . The theoretical variance of the algorithm in white Gaussian noise is formulated, which includes the upper bound and the lower bound. Computer simulations and real measurements are conducted to corroborate the theoretical analysis and to demonstrate that the proposed algorithm achieves better accuracy and antinoise capability for $\text {NASC} than existing algorithms.