Linear Distortions of Periodic Signals

© 2017 Institute for Communications Engineering, Technical University of Munich
Authors: Jimmy He & Tasnad Kernetzky
Source parameter settings
$A_1 =0.5$ V
$f_1 =0.5$ kHz
$\varphi_1 =0^{\circ}$
$A_2 =0.5$ V
$f_2 =1.7$ kHz
$\varphi_2 =90^{\circ}$
$x(t)$ [V]   $y(t)$ [V]   $z(t)$ [V]   $\varepsilon(t)$ [V]   $\varepsilon^2(t)$ [V2]

  $P_\varepsilon = $ 0.050$\\ $ V2  

$t_* =0$ ms

$x(t_*) =$ 0.500$\\ $ V   $y(t_*) =$ -0.280$\\ $ V   $z(t_*) =$ 0.710$\\ $ V

$\varepsilon(t_*) =$ 0.210$\\ $ V $\varepsilon^2(t_*) =$ 0.050$\\ \text{V}^2$


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$t \ \text{[ms]}$
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Channel parameter settings
$\alpha_1 =0.8$
$\alpha_2 =0.6$
$\tau_1 =0.5$ ms
$\tau_2 =0.7$ ms

Matching parameter settings
$k_\text{M} =1.32$
$\tau_\text{M} =1.6$ ms
Exercises
The following curves are on display:
blue: the input signal $x(t) = x_1(t) + x_2(t) = A_1\cdot \cos\left(2\pi f_1\cdot t- \varphi_1\right)+A_2\cdot \cos\left(2\pi f_2\cdot t- \varphi_2\right), $
red: output signal $y(t) = \alpha_1 \cdot x_1(t-\tau_1) + \alpha_2 \cdot x_2(t-\tau_2),$
green: the matching output signal $z(t)= k_{\rm M} \cdot y(t-\tau_{\rm M}) + \alpha_2 \cdot x_2(t-\tau_2),$
magenta: the difference signal   $\varepsilon(t) = z(t) - x(t)$   ⇒   Power $P_\varepsilon$.