On causal linear phase IIR digital filters

The existence of causal linear phase infinite impulse response (IIR) digital filters is investigated. The conditions for their existence are derived, and a set of examples satisfying these conditions is given. It is shown that the sequences must be integer samples of a continuous-time function, bandlimited to (- pi , pi ), which is symmetric and has zero crossings at the negative integers, and the point of symmetry can be neither an integer nor a half integer. A number of interesting properties of the related discrete- and continuous-time functions are developed.<>