Noise-Based Frequency Spectrum Correction Method Using Interior Point Approach

The spectral correction of noisy real sinusoidal signals is of critical importance; however, the presence of spectral leakage and noise introduces significant challenges. This paper presents a novel approach based on the interior point (IP) method to address key limitations of conventional techniques, including high sensitivity to noise, low computational efficiency, and parameter decoupling. The correction problem is reformulated as an unconstrained optimization task. Following Welch spectral estimation, peak detection is performed using an adaptive threshold to identify the spectral peaks adjacent to the true peak, which serve as boundary constraints for the IP solution. This enables accurate estimation of the amplitude, frequency, and phase of the signal. This study innovatively formulates the correction process as a bounded optimization problem and incorporates an L1-norm sparse penalty term into the interior point (IP) framework to enhance robustness against noise. Additionally, an efficient adaptive solver is developed to improve convergence speed. Simulation results demonstrate that the proposed method offers significant advantages, particularly in terms of computational efficiency. Notably, for a signal containing 2048 samples, the IP method achieves a 4.2-fold reduction in execution time compared to the FFT+FT refinement approach, while maintaining comparable accuracy. More importantly, the method exhibits superior estimation accuracy. Under simulated conditions, the root mean square errors of amplitude, frequency, and phase estimation are reduced by over 20% relative to the ratio correction and energy centroid methods. In challenging scenarios such as short signals and non-integer period sampling, the frequency estimation error is decreased by approximately 10–20% compared to spectral refinement techniques, and the phase estimation error is reduced by 20–28% relative to the energy centroid method. These outcomes validate the method’s enhanced accuracy and robustness. The performance improvements primarily result from joint parameter optimization and adaptive boundary enforcement, enabling strong effectiveness under low signal-to-noise ratios, non-ideal sampling conditions, and short signal lengths.