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.