Q$1)$ A DSB$/$ SC and an SSB$/$ SC transmission are each sent at $2$ MHz in the presence of noise. The modulating signal in each case is band $-$ limited to $5$ kHz $.$ The received signal power in each case is $2$ mw and the received noise is assumed to white with a $($one $-$ sided$)$ power spectral density of ${10}^{-9}\frac{w}{H}z.$ The receiver consists of a bandpass filter $($BPF$)$ whose bandwidth matches synchronous detector.

a$-$ Compare the $SN{R}_i$ at detector input.

b$-$ Compare the $SN{R}_0,$ at detector output.