INVERSE Z-TRANSFORM BY MOBIUS-INVERSION AND THE ERROR-BOUNDS OF ALIASING IN SAMPLING

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 o f 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 m ethod are established and compared. In general, the AFT algorithm is n ot so vulnerable to the aliasing errors in the high-frequency componen ts as the DFT approach.