Topic: Communication Systems
If $E_b$, the energy per bit of a binary digital signal, is $10^{-5}$ Ws (Watt-Second) and the one-sided power spectral density of the white noise, $N_0 = 10^{-6} \text{ W/Hz}$, then the output SNR of the matched filter is
- A. 26 dB
- B. 10 dB
- C. 20 dB
- D. 13 dB
Answer: D. 13 dB
Explanation: Energy per bit $E_b = 10^{-5} \text{ Ws}$.
Noise $N_0 = 10^{-6} \text{ W/Hz}$.
$SNR = 10 \log_{10}\left(\frac{2E_b}{N_0}\right) = 10 \log_{10}\left(\frac{2 \times 10^{-5}}{10^{-6}}\right) = 10 \log_{10}(20) = 13 \text{ dB}$.