Generalized Fractional Interpolated Discrete Fourier Transform with Rectangular Window for Frequency Estimation in Noisy Sinewave Signals

Accurate and efficient frequency estimation is essential in many scientific fields and has led to the development of various algorithms. Commonly used methods involve applying the Discrete Fourier Transform followed by spectral interpolation. This approach faces challenges especially under low signal-to-noise ratio conditions. To mitigate this limitation, the Generalized Fractional Interpolated Discrete Fourier Transform for frequency estimation of rectangular-windowed sinewaves is proposed. This non-iterative algorithm enhances frequency estimation by employing spectral components at fractional steps of the Discrete Fourier Transform frequency resolution. A non-iterative, closed-form equation for frequency estimation is derived, enabling efficient computation. The proposed algorithm is evaluated through numerical simulations and compared with existing interpolation methods for different frequencies, signal-to-noise ratios, and number of acquired samples. The method is validated using experimentally acquired sinewave signals.