Abstract: Several sampling theorems, which aid in the reconstruction of periodically nonuniform sampled signals in the linear canonical transform (LCT) domain, have high sidelobe and slow-decayed synthesizing functions. Focusing on this issue, the reconstruction theorem of a nonstationary signal was investigated in function spaces associated with the LCT. Periodically nonuniform averaging model and reconstruction algorithm were proposed based on the theories of multi-rate signal processing and multi-channel perfect reconstruction filter banks. Introducing window functions with high degree of freedom, the method was arranged to establish the reconstruction functions with compactly supported synthesizing capability, and to make the number of integral channel unconstrained from the range of function space, being suitable for those applications with limited sampling spots and hardware. Simulation results show that, compared with other conventional methods, the proposed method possesses the advantages with less interpolation error and fewer consumptions of hardware resources.