Dataflow Diagram of Simple IIR

Dataflow Diagram of Simple IIR

$h(t)=-e^{-bT}$ So:

$$\begin{array}{rl}Y(z)& =X(z)H(z)\\ & =X(z)\frac{1}{1-e^{-bT}{z}^{-1}}\\ & =Y(z)z^{-1}{e}^{-bT}+X(z)\end{array}$$

We have to recall that $z^{-1}$ is the delay by $T$. With that information we directly have a difference equation in the temporal domain:

$$y(nT)=y([n-1]T)e^{-bT}+x(nT)$$

This means that the output signal $y(nT)$ is calculated by adding the weighted and delayed output signal $y([n-1]T)$ to the input signal $x(nT)$.