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Digital Transforms have important applications on subjects such as channelcoding, cryptography and digital signal processing. In this paper, two FourierTransforms are considered, the discrete time Fourier transform (DTFT) and thefinite field Fourier transform (FFFT). A finite field version of the DTFT isintroduced and the FFFT is redefined with a complex kernel, which makes it amore appropriate finite field version of the Discrete Fourier Transform. Thesetransforms can handle FIR and IIR filters defined over finite algebraicstructures.

Infinite Sequences, Series Convergence and the Discrete Time Fourier Transform over Finite Fields