On the construction of a digital transfer function from its real part on unit circle

It is shown in this correspondence that the system function H(z) of a linear time invariant (LTI) causal digital filter with real impulse response coefficients can be obtained from the real part of its frequency response H
R
(e
^jω
) given in the form of a rational trigonomentric function, using algebraic methods rather than complex contour integration techniques.