Sampling of Analog Signals and Signal Reconstruction

© 2021 Institute for Communications Engineering, Technical University of Munich
Authors: Carolin Mirschina, Xiaohan Liu & Tasnad Kernetzky
Source Signal
$A = 1$
$f_0 = 4\ \rm{kHz}$
$\varphi = 0\ ^°$
Signal 4:
Five frequency components

$f = 0.5 \ \rm{kHz}:$
$ A_{0.5} = 0.20, \varphi_{0.5} = -10^{\circ}$

$f = 1 \ \rm{kHz}:$
$ A_1 = 0.50, \varphi_1 = 180^{\circ}$

$f = 2 \ \rm{kHz}:$
$ A_2 = 0.3, \varphi_2 = -60^{\circ}$

$f = 3 \ \rm{kHz}: $
$ A_3 = 0.14, \varphi_3 = 20^{\circ}$

$f = 4 \ \rm{kHz}:$
$ A_4 = 0.02, \varphi_4 = 80^{\circ}$
Time domain display:
$x(t)$
$x_\rm{A}$$(t)$
$y(t)$
$\varepsilon(t)$

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$t/\rm{ms}$

Frequency domain display:
$X(f)$
$X_\rm{A}$$(f)$
$Y(f)$
$E(f)$
Real part
Imaginary part
Magnitude

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$f/\rm{kHz}$
Sampling:
$f_\rm{A} = 10\ \rm{kHz}$
Signal reconstruction:
$f_\rm{G} = 5\ \rm{kHz}$
$r = 0$

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$f$
$H_\rm{E}(f)$
$f_1 =5.00\ \rm{kHz}$
$f_2 =5.00\ \rm{kHz}$

Signal power:
$P_x =0.200$
Distortion power:
$P_{\varepsilon} =0.000$
Signal-to-distortion Ratio:
$10 \cdot \lg (P_x / P_{\varepsilon}) =\rm{infinity}$
Exercises