Module 2 : Modeling Discrete Time Systems by Pulse Transfer Function

Lecture 3 : Pluse Transfer Function

1.1 Pulse transfer of discrete data systems with cascaded elements

Care must be taken when the discrete data system has cascaded elements. Following two cases will be considered here.

The block diagram for the first case is shown in Figure 2.

Figure 2: Discrete data system with cascaded elements, separated by a sampler
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The input-output relations of the two systems $ G_1$ and $ G_2$ are described by

$\displaystyle D(z) = G_1(z) R(z) $

and

$\displaystyle C(z) = G_2(z) D(z) $

Thus the input-output relation of the overall system is

$\displaystyle C(z) = G_1(z)G_2(z)R(z) $

We can therefore conclude that the z-transfer function of two linear system separated by a sampler are the products of the individual z-transfer functions.