Frequency estimation based on progressive spectral leakage shrinking for multi-tone signals

The frequency estimation of multi-tone exponential signals plays important roles in vast applications. However, mutual spectral interference among tones (especially for cases of densely distributed tones) severely deteriorates the estimation accuracy. To address this problem, we propose a progressive spectral leakage shrinking-based multi-tone estimator derived from a range-controlled single-tone estimator. Based on deducing an interpolator with controllable range flexibility, our proposed iterative single-tone estimator acquires high accuracy via frequency shift and compensation operations, highlighting the effect of shrinking spectral leakage. Furthermore, in the multi-tone estimator design, it is necessary to construct two types of residual signals iteratively (i.e., descending residual and exclusive residual), which are fed into our proposed range-controlled single-tone estimator to output the frequency estimates. Both the residual construction and the callback of the single-tone estimator facilitate the progressive spectral leakage shrinking as the iteration proceeds, which together entitles our multi-tone estimator with the characteristic of automatically suppressing mutual spectral interference without any prior information. The numerical results demonstrate that the proposed multi-tone estimator overall outperforms the existing estimators in accuracy, suppressing mutual spectral interference and robustness in dense spectrum recognition, etc., presenting the proposed multi-tone estimator with vast potential in future applications.