In Compressive sensing (CS), the random matrix is usually used as the measurement matrix, which is hard to design and difficult for computing. The random circulant matrix generated by random filter is suitable for signal measurement. A novel random filter is designed which is all pass in frequency domain, all real in both of time domain and frequency domain. The coherence property between the measurement basis and the signal basis is analyzed. The measurement vector can include all information of the original signal and it is convenient for computing. Numerical simulation results demonstrate that the filter is appropriate for signal collection and recovery.