The synthesis of linear filters with real or imaginary transfer functions

The synthesis of linear filters with symmetrical (even-function) or anti-symmetrical (odd-function) impulse responses has both theoretical interest and practical value. Such filters which can be called “time-symmetric” or “time-antisymmetric,” following the terminology of Storey and Grierson,1 are characterized by transfer functions which are purely real or purely imaginary. Alternate names, proposed and employed in this paper, are real or imaginary filters. Applications of real or imaginary filters include compensating systems which must have no phase distortion, such as those often used in the field of acoustics and in the compensation of signals generated by picture scanning devices.2,3