Sampling rate conversion for linear canonical transform

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This paper investigates the sampling rate conversion problem in the LCT domain. Firstly, the discrete-time LCT is introduced and the formulas of interpolation and decimation in the LCT domain are derived. Then, based on the sampling theorem expansion in the LCT domain, the formulas of sampling rate conversion by real factors for the LCT in time domain are proposed. The spectral analysis of sampling rate conversion by real factors in the LCT domain is also illustrated. The sampling rate conversion theories in the Fourier domain and the fractional Fourier domain are shown to be special cases of the achieved results. The simulations verify the effectiveness of the obtained results.