Optimal algebraic integer implementation with application to complex frequency sampling filters

Algebraic integers have been proven beneficial to discrete Fourier transform, discrete cosine transform, and nonrecursive finite-impulse response filter designs since algebraic integers can be dense in C, resulting in short-word-width, high-speed designs. This brief uses another property of algebraic integers; namely, algebraic integers can produce exact pole zero cancellation pairs that are used in recursive complex finite-impulse response, frequency sampling filter designs.