Chapter 9.6, Problem 5E

Interpretation Introduction

Interpretation:

Consider the receiver dynamics, ${\dot{\text{x}}}_{\text{r}}=\sigma \left({\text{y}}_{\text{r}}-{\text{x}}_{\text{r}}\right)$, ${\dot{\text{y}}}_{\text{r}}=\text{rs}\left(\text{t}\right)-{\text{y}}_{\text{r}}-\text{s}\left(\text{t}\right){\text{z}}_{\text{r}}$ and ${\dot{\text{z}}}_{\text{r}}={\text{s(t)y}}_{\text{r}}-{\text{bz}}_{\text{r}}$. If the receiverhas synchronized with the drive signal, then ${\text{x}}_{\text{r}}\left(\text{t}\right)\approx \text{ x}\left(\text{t}\right)$, and so, $\text{m}\left(\text{t}\right)$ may be recovered as $\widehat{\text{m}}\text{(t)}=\text{s(t)}-{\text{x}}_{\text{r}}\text{(t)}$. Test this approachnumericallyusing a sine wave for $\text{m}\left(\text{t}\right)$. Estimate how close $\widehat{\text{m}}\text{(t)}$ is to the actual message $\text{m(t)}$. Explain how the error depends upon the frequency of the sine wave.

Concept Introduction:

• ➢ UseLorenz equations by substituting $\text{s(t)}=\text{x(t)+ m(t)}$

• ➢ At the receiver end, the error is a function of $\text{m(t)}$.