Sinewave frequency estimation based on fractional Interpolated Discrete Fourier Transform

Abstract

Frequency estimation is crucial in numerous scientific applications and have led to the development of various algorithms. Most approaches use the Discrete Fourier Transform followed by spectral interpolation. However, limitations arise when sinewave frequencies align closely with DFT lines especially for low Signal-to-Noise Ratios. Recent advances have employed non-integer Goertzel filters to compute Discrete Time Fourier Transform components, leading to improved frequency estimation. This work introduces the Generalized Fractional Interpolated Discrete Fourier Transform, which uses fractional values of the frequency resolution to improve frequency estimation, especially at low Signal-to-Noise Ratios. A closed-form, non-iterative, frequency estimation formula is derived. The effectiveness of the proposed algorithm is analysed through numerical simulations and compared with other interpolation methods for different frequencies, Signal-to-Noise Ratios and number of acquired samples.