Inverse Z-transform by Mobius inversion and the error bounds of aliasing in sampling

摘要

A general algorithm based on two special Mobius inversion formulae is developed to compute the inverse Z-transform. This approach to Fourier analysis uses what is called the arithmetic Fourier transform (AFT). With the new AFT algorithm. One can compute the inverse Z-transform of an infinite two-sided sequence. It is compared with the conventional DFT approach. Both methods have aliasing errors due to sampling. The error bounds of the aliasing effects in the DFT and the new proposed method are established and compared. In general, the AFT algorithm is not so vulnerable to the aliasing errors in the high-frequency components as the DFT approach.