Abstract: In communication, radar, and other applications, it is often necessary to perform high-precision spectral computations on sparse signals. Traditional methods based on Fast Fourier Transform (FFT) require substantial computational resources, leading to a decrease in the efficiency of spectral analysis. To resolve the conflict between high precision and real-time requirements, this paper proposes a spectral analysis method based on Sparse Fourier Transform (SFT). By utilizing the phase rotation effect of delayed sampling, this method achieves rapid spectral perception of wideband signals at low sampling rates. Experimental results show that this approach significantly reduces computational burden in under-sampled and aliased sparse signal testing scenarios, improving computational efficiency by more than 2 times compared to FFT. In typical sparse scenarios, the signal recovery accuracy exceeds 95%.