We first define real-valued quantities \(\alpha\) and \(\beta\) to be the real and imaginary components of \(\gamma\); i.e., \[\alpha \triangleq \mbox{Re}\left\{\gamma\right\} \nonumber \] \[\beta \tr...We first define real-valued quantities \(\alpha\) and \(\beta\) to be the real and imaginary components of \(\gamma\); i.e., \[\alpha \triangleq \mbox{Re}\left\{\gamma\right\} \nonumber \] \[\beta \triangleq \mbox{Im}\left\{\gamma\right\} \nonumber \] and subsequently \[\gamma = \alpha + j\beta \nonumber \] Then we observe \[e^{\pm\gamma z} = e^{\pm\left(\alpha+j\beta\right)z} = e^{\pm\alpha z}~e^{\pm j\beta z} \nonumber \] It may be easier to interpret this expression by reverting to the time …
We first define real-valued quantities \(\alpha\) and \(\beta\) to be the real and imaginary components of \(\gamma\); i.e., \[\alpha \triangleq \mbox{Re}\left\{\gamma\right\} \nonumber \] \[\beta \tr...We first define real-valued quantities \(\alpha\) and \(\beta\) to be the real and imaginary components of \(\gamma\); i.e., \[\alpha \triangleq \mbox{Re}\left\{\gamma\right\} \nonumber \] \[\beta \triangleq \mbox{Im}\left\{\gamma\right\} \nonumber \] and subsequently \[\gamma = \alpha + j\beta \nonumber \] Then we observe \[e^{\pm\gamma z} = e^{\pm\left(\alpha+j\beta\right)z} = e^{\pm\alpha z}~e^{\pm j\beta z} \nonumber \] It may be easier to interpret this expression by reverting to the time …
