1.

An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral density \(\frac{{{{\rm{N}}_0}}}{2}\). The received signal is passed through a filter with impulse response h(t). Let

A. \({{\rm{E}}_{\rm{s}}} = {{\rm{E}}_{\rm{h}}};{\rm{SN}}{{\rm{R}}_{{\rm{max}}}}{\rm{\;}} = \frac{{2{{\rm{E}}_{\rm{s}}}}}{{{{\rm{N}}_0}}}\)
B. \({{\rm{E}}_{\rm{s}}} = {{\rm{E}}_{\rm{h}}};{\rm{SN}}{{\rm{R}}_{{\rm{max}}}}{\rm{\;}} = \frac{{2{{\rm{E}}_{\rm{s}}}}}{{2{{\rm{N}}_0}}}\)
C. \({{\rm{E}}_{\rm{s}}} > {{\rm{E}}_{\rm{h}}};{\rm{SN}}{{\rm{R}}_{{\rm{max}}}}{\rm{\;}} = \frac{{2{{\rm{E}}_{\rm{s}}}}}{{{{\rm{N}}_0}}}\)
D. \({{\rm{E}}_{\rm{s}}} = {{\rm{E}}_{\rm{h}}};{\rm{SN}}{{\rm{R}}_{{\rm{max}}}}{\rm{\;}} = \frac{{2{{\rm{E}}_{\rm{h}}}}}{{{{\rm{2N}}_0}}}\)
Answer» B. \({{\rm{E}}_{\rm{s}}} = {{\rm{E}}_{\rm{h}}};{\rm{SN}}{{\rm{R}}_{{\rm{max}}}}{\rm{\;}} = \frac{{2{{\rm{E}}_{\rm{s}}}}}{{2{{\rm{N}}_0}}}\)


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