Analysis of the bias affecting the interpolated DFT frequency estimator

Area of Science:

• Signal Processing
• Digital Signal Processing
• Spectral Analysis

Background:

• The interpolated discrete Fourier transform (IDFT) is widely used for frequency estimation.
• The accuracy of IDFT-based estimators can be compromised by intrinsic approximation errors and wideband noise.
• Understanding and mitigating these biases are crucial for reliable frequency estimation.

Purpose of the Study:

• To derive an analytical expression for the overall bias of the complex-valued noisy sine wave frequency estimator from the IDFT algorithm.
• To investigate the impact of the number of analyzed samples and signal-to-noise ratio (SNR) on the bias-to-standard deviation ratio.
• To propose a novel frequency estimator that compensates for the IDFT's intrinsic approximation bias and compare its accuracy to classical methods.

Main Methods:

• Derivation of an analytical expression for the overall bias of the IDFT frequency estimator.
• Analysis of the bias contribution from rectangular windowing and wideband noise.
• Investigation of the influence of sample size and SNR on the bias-to-standard deviation ratio.
• Development and comparative accuracy assessment of a bias-compensating frequency estimator.

Main Results:

• An analytical expression for the overall bias of the IDFT frequency estimator was successfully derived.
• The study quantified the contributions of intrinsic approximation and wideband noise to the overall bias.
• The impact of sample size and SNR on the bias-to-standard deviation ratio was systematically investigated.
• The proposed bias-compensating estimator demonstrated improved accuracy compared to the classical frequency estimator.

Conclusions:

• The derived analytical expression provides a theoretical foundation for understanding IDFT frequency estimation bias.
• The proposed estimator effectively compensates for intrinsic approximation errors, leading to enhanced accuracy.
• This work contributes to more reliable frequency estimation techniques in the presence of noise and algorithmic approximations.