The fractional Fourier transform (FRFT) was combined with a tongue-like curve variable-step adaptive filtering technique based on correlation characteristics to process linear frequency modulation (LFM) signals contaminated by noise. Simulation results demonstrate that most of the noise in LFM signals can be filtered out by first applying the optimal-order FRFT to time-domain signals, followed by the tongue-like curve variable-step adaptive filtering algorithm in the optimal fractional Fourier domain. This procedure allows for effective extraction of the useful signals. Under low signal-to-noise ratio conditions, the adaptive filtering technology outperforms moving average processing and wavelet transform methods, making it more suitable for extracting weak target signals from high-intensity noise and broadening its range of applications. When the transformation order is optimal, the signal error converges to its minimal value rapidly, and the final extreme value reached is the smallest, resulting in the best filtering performance. The larger the frequency modulation slope of the LFM signal, the higher the corresponding optimal order, and the mean square error under the optimal order increases. For multi-component LFM signals with varying intensities, a sequential extraction approach of first extracting strong signals then weak signals can be applied to extract different components step by step. This approach effectively reduces interference from strong components on weak components, thereby optimizing the extraction performance of the weak signals.