Windowed interpolation fast Fourier transform (FFT) methods are widely used in embedded harmonic detection for power systems due to their high accuracy and low complexity, effectively mitigating spectral leakage and the picket-fence effect caused by asynchronous sampling and non-integer-period truncation. To address the limitations of existing window functions and spectral line interpolation methods, this paper proposes an improved harmonic and interharmonic detection approach based on hybrid convolution windows and particle swarm optimization (PSO)-based spectral line interpolation. First, a time-domain convolution hybrid window is constructed by combining the advantageous characteristics of the Blackman-Harris window and the five-term maximum sidelobe decay (MSD) window, thereby enhancing spectral leakage suppression capability. Second, a spectral line interpolation model is established, where the PSO algorithm is employed to perform offline searches for the optimal weight combination, overcoming the limitations of traditional methods that rely on empirical parameter settings and further improving amplitude detection accuracy. Simulation results show that, compared with the original algorithm, the proposed method achieves superior performance in terms of harmonic and interharmonic detection accuracy and anti-interference capability.