Accurate Frequency Estimation of Sinusoidal Signals Using DFT Interpolation

Frequency estimation of sinusoidal signals is widely applied in fields such as communication, radar systems, and audio processing. However, traditional frequency estimation methods face challenges in complex environments, such as strong noise and interference, which degrade their accuracy. This issue is particularly pronounced under small-sample and low signal-to-noise ratio (SNR) conditions. To address these limitations, this paper proposes a frequency offset estimation technique based on a three-point Discrete Fourier Transform (DFT).By analyzing the complex ratios and amplitude relationships of the three spectral bins near the DFT spectrum peak, we develop an accurate estimator for the normalized frequency offset. This estimator corrects the biases inherent in existing direct estimation methods. The proposed method demonstrates superior estimation accuracy compared to traditional direct methods. Performance analysis shows that the method maintains a lower mean square error (MSE) across varying SNR conditions, particularly for small number of samples.