Work in progress - operational notation of fractions for signal processing

This paper describes nontraditional notation, which seems to be helpful to learn about a kind of signal processing. Suppose the operator, which extracts the fractional part of a real number. Then a remainder k mod n is expressed using this operator, which relates remainders to real numbers, and hence it becomes easy to explain the properties of residue classes, especially when several moduli must be considered simultaneously. Since a residue class of polynomials has similar properties, analogous calculation is available as shown in examples for a cyclic code encoder and a perfectly linear phase recursive filter.