Dimensional Normalization in the Digital Computation of the Fractional Fourier Transform

The fast algorithm of the digital computation of the fractional Fourier transform(FRFT) requires the dimensional normalization, but how to do it for practical discrete signal is not settled yet. For this reason, the paper presents two engineering-oriented methods of the dimensional normalization. One is called as the discrete scaling transform method, another is called as the data zero-padding/interception method. Furthermore, their effects on the parameter estimation of the chirp signal are studied and for discrete scaling method, a relationship before and after the normalization is developed. Finally, these methods are verified by simulation examples. These engineering-oriented methods of the dimensional normalization makes the FRFT more practical in digital signal processing.