Pole-zero techniques applied to voice-frequency telephone lines

Most textbooks about transmission lines derive differential equations pertaining to physical phenomena and, after suitable solutions are found, immediately define or describe several parameters: (1) the propagation function and its components, the attenuation and phase shift functions; (2) the velocity of propagation; and (3) the characteristic impedance. Although others exist, the characteristics mentioned are of fundamental importance and interest, and hereinafter will be referred to in the collective sense as the basic parameters.