A novel algorithm for implementing time-frequency transform with low computation

In this paper, a novel algorithm called two-dimensional sliding fast Fourier transform (2D SFFT) algorithm is proposed. This algorithm organizes one-dimensional data in two dimensions and calculates the spectrum of current data by using the existing spectrum and new collected data. The algorithm formula and accurate simulation results show the following: first, the computation required by the proposed 2D SFFT algorithm is lower than that required by the traditional sliding discrete Fourier transform algorithm when the sliding rate is larger than or equal to 4/M, where M is the sequence length. Moreover, the computation required by the proposed 2D SFFT algorithm is lower than that required by the fast Fourier transform (FFT) algorithm when the sliding rate is less than or equal to 6.25%. Finally, the error between the spectrum calculated by the 2D SFFT and FFT algorithms is less than 10^-10. The 2D SFFT algorithm is used to increase the power of the ultra-short pulse, which is initially invisible in the frequency-domain window of the mixed-domain oscilloscope. Therefore, the 100% probability of intercept of the mixed-domain oscilloscope is lower.