Digital Transforms have important applications on subjects such as channel
coding, cryptography and digital signal processing.
In this paper, two Fourier Transforms are considered, the discrete time
Fourier transform (DTFT) and
the finite field Fourier transform (FFFT). A finite field version of the
DTFT is introduced and
the FFFT is redefined with a complex kernel, which makes it a more appropriate
finite field version of the
Discrete Fourier Transform. These transforms can handle FIR and IIR filters
defined over finite algebraic structures.