The study is intended to reconstruct the original signal through a linear measurement, and sampling at a speed lower than the Nyquist sampling frequency. Fractional Fourier Transform(FrFT) is applied to sparse represent signal on the Linear Frequency Modulation(LFM) basis to the LFM signal，so Ψ is substituted to the transforming matrix of Digital Fractional Fourier Transform(DFrFT)，and the optimal sparse basis is gained by modulation method, then the sparse representation and reconstruction of signal is researched. Similarly, modulation method is utilized to find the optimal sparse basis of tangent-shape Nonlinear Frequency Modulation(NLFM) signals and complete the compressive sensing research of sparse representation and reconstruction. Simulation results show that the optimal sparse basis can be found with this method; and the sparse representation and reconstruction of tangent-shape NLFM signals can be accomplished with good recovery results.