Convolution and Sampling Theorems for Offset Fractional Fourier Transform

The offset fractional Fourier transform (OFrFT) has emerged as a mathematical tool for time-frequency analysis of non-stationary signals. However, there has been relatively little research on investigating properties including the convolution theorem and the sampling formulas. This paper investigates the new form of convolution theorem and its product theorem associated with the OFrFT. We also establish a sampling formula related to the transformation. Finally, a simple example is displayed to verify the results related to the sampling formula for the OFrFT.