Two-Point Refined DFT Method for Unbiased Frequency Estimation of Noisy Real-Valued Sinusoids

The accuracy of discrete Fourier transform (DFT)-based frequency estimation for real-valued sinusoids is strongly affected by how the positive- and negative-frequency components are handled. In particular, the image component associated with negative frequencies can introduce spectral leakage and bias, especially when only short observation windows are available. To address this issue, this article introduces a two-point interpolated DFT (IpDFT) method for estimating the frequency of noisy real-valued sinusoids. The proposed approach employs a rectangular window with zero padding and is tailored to scenarios with very few observed cycles, where conventional techniques may suffer from degraded accuracy. Unlike existing methods, the proposed estimator explicitly exploits conjugate symmetry and parity properties of the underlying signal model to suppress both short- and long-range spectral leakage arising from the interaction between the positive- and negative-frequency components. Furthermore, the mutual influence of the two dominant spectral peaks is analytically characterized, enabling a rigorous theoretical performance assessment under additive white Gaussian noise. Simulations and controlled experiments show that the proposed method provides competitive accuracy across the tested range and offers its clearest advantage in short-record scenarios.