Mixed transcendental and polynomial transforms

A MIXED TRANSCENDENTAL and polynomial transform is obtained by cascading a transmission line and a time constant. The substitution of the variable y for — exp (— sT) facilitates a variety of manipulations of these transforms. The impulse response of a system of transmission lines connected in cascade and in parallel can be only a finite number of impulses. This has zeros only in the finite y plane. If the transmission line is connected in feedback, then a train of impulses extending to infinite time can be generated. This must be represented by poles in the y plane. Each y-plane pole is an infinite column of s-plane poles.