Question

A signal bandlimited to 5 kHz is sampled at a rate higher than Nyquist rate such that the guard band is 3 kHz. The graph shows the probability of resulting samples. The data rate will be _ (in kbps).

• A. 24.74

Answer 1

The correct option is A 24.74
$\text{Guard Band}=f_s-2f_m=3Hz$
$\Rightarrow f_z=(2\times 5+3)kHz$
$f_z=13kHz$
$\therefore \text{Symbol rate,}r=f_s=13ksymbols/sec$
$\text{Entropy},H=-{\sum }_{m=1}^{4}P\left(x_i\right)lo{g}_{2}P\left(x_1\right)$
$=-[0.4lo{g}_{2}0.4+0.25lo{g}_{2}0.25+0.2lo{g}_{2}0.2+0.15lo{g}_{2}0.15]$
$=1.903bits/symbol$
$\text{Date rate}=R.H=13\times 1.903kbps=24.74kbps$