Question

Consider the signal shown below:
This signal is passed through an AWGN channel with two sided noise power spectral density of $\frac{N_0}{2}$ and received by a filter matched to $s\left(t\right)$. The maximum signal-to-noise ratio possible at the output of the filter is .

• A. $\frac{32}{N_0}$
• B. $\frac{16}{N_0}$
• C. $\frac{8}{N_0}$
• D. $\frac{64}{N_0}$

Answer 1

The correct option is D $\frac{64}{N_0}$

For matched filter,
$(SNR{)}_{max}=\frac{2E_s}{N_0}$
$E_S$ = Energy of the signal $s\left(t\right)$
$={\int }_{-\infty }^{\infty }|s\left(t\right){|}^{2}dt={\int }_0^2(4{)}^{2}dt=32$
$(SNR{)}_{max}=\frac{2\left(32\right)}{N_0}=\frac{64}{N_0}$