To enhance the detection precision of Doppler wind lidar, this study addresses the challenge posed by significant background noise interference in echo signals. A Mahzender frequency detector-based incoherent lidar system is developed, and a comparative analysis is conducted on various denoising methods. The study evaluates the effectiveness of Fourier analysis, FIR filtering, moving average filtering, and wavelet denoising with both soft and hard thresholds. Results indicate that the semi-soft threshold denoising algorithm outperforms other methods, yielding reduced signal noise and smaller root mean square error. Additionally, it effectively integrates time and frequency domains. Thus, employing the wavelet denoising algorithm with semi-soft thresholds is advantageous for lidar applications requiring precise frequency shift measurements for wind speed determination.