Consider a frequency-modulated (FM) signal

$$ f(t)=A_c \cos \left(2 \pi f_c t+3 \sin \left(2 \pi f_1 t\right)+4 \sin \left(6 \pi f_1 t\right)\right) $$

where $A_c$ and $f_c$ are, respectively, the amplitude and frequency (in Hz ) of the carrier waveform. The frequency $f_1$ is in Hz , and assume that $f_c>100 f_1$.

The peak frequency deviation of the FM signal in Hz is $\qquad$

Consider a message signal $m(t)$ which is bandlimited to $[-W, W]$, where $W$ is in Hz . Consider the following two modulation schemes for the message signal:

Double sideband-suppressed carrier (DSB-SC):

$$ f_{\mathrm{DSB}}(t)=A_c m(t) \cos \left(2 \pi f_c t\right) $$

Amplitude modulation (AM):

$$ f_{\mathrm{AM}}(t)=A_c(1+\mu m(t)) \cos \left(2 \pi f_c t\right) $$

Here, $A_c$ and $f_c$ are the amplitude and frequency (in Hz ) of the carrier, respectively. In the case of AM, $\mu$ denotes the modulation index.

Consider the following statements:

(i) An envelope detector can be used for demodulation in the DSB-SC scheme if $m(t)>0$ for all $t$.

(ii) An envelope detector can be used for demodulation in the AM scheme only if $m(t)>0$ for all $t$.

Which of the following options is/are correct?

An amplitude modulator has output (in Volts)

$$s(t) = A \cos(400 \pi t) + B \cos(360 \pi t) + B \cos(440 \pi t)$$.

The carrier power normalized to $1\Omega$ resistance is 50 Watts. The ratio of the total sideband power to the total power is 1/9. The value of $B$ (in Volts, rounded off to two decimal places) is _______.

A super heterodyne receiver operates in the frequency range of 58 MHz – 68 MHz. The intermediate frequency f_1F and local oscillator frequency f_L0 are chosen such that f_1F $$\leq$$ f_L0.It is required that the image frequencies fall outside the 58 MHz – 68 MHz band. The minimum required f_1F (in MHz) is ___________.