The physical realizability and realization of linear phase shift networks

Necessary and sufficient conditions for the physical realizability of linear phase shift networks are imposed upon the network transfer function. A technique is presented for approximating non-physically realizable transfer functions with those which are physically realizable. It is demonstrated that if the approximation is properly limited, the unit impulse response can be made non-negative for all values of time. These results are extended to networks whose transfer functions phase shift is the sum of two terms, one which varies linearly with frequency and a second which varies in discrete steps of $\pi$ radians.