GATE EC 2003 Set 1 Q74 — Analog Communications

A DSB-SC signal is to be generated with a carrier frequency $f_{t}=1 \; \mathrm{MHz}$ using a non-linear device with the input-output characteristic

$$v_{0}=a_{0} v_{i}+a_{1} v_{i}^{3}$$

where $a_{0}$ and $a_{1}$ are constants. The output of the non-linear device can be filtered by an appropriate band-pass filter.

Let $v_{i}=\mathrm{A}_{c}^{t} \cos \left(2 \pi f_{e}^{t} t\right)+m(t)$ where $m(t)$ is the message signal. Then the value of $f_{c}^{t}$ (in $\mathrm{MHz}$ ) is