Texts: A normalized message signal with a bandwidth of π = 8 kHz and a power π = 0.5 W. It is required to transmit this signal via a channel with an available ππ bandwidth of 60 kHz and attenuation of 40 dB. The channel noise is additive and white with a power spectral density of π = 2 Γ 10^(-12) W/Hz. A frequency modulation scheme, with no pre-emphasis/de-emphasis filtering, has been proposed for this purpose.
a. If it is desirable to have a SNR of at least 40 dB at the receiver output, determine the minimum required transmitter power and the corresponding modulation index?
b. If the minimum required SNR is increased to 60 dB, how would your answer to part (a) change?
c. If in part (b), we are allowed to employ the first-order pre-emphasis/de-emphasis π
πΆ filters discussed in class with a time constant π = 75 πsec, how would your answer to part (b) change?