The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by $V_1=10 \sin 100 \pi t$, where time $t$ is in seconds.

The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is ________.

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 an additive white Gaussian noise (AWGN) channel with bandwidth $W$ and noise power spectral density $\frac{N_o}{2}$. Let $P_{a v}$ denote the average transmit power constraint. Which one of the following plots illustrates the dependence of the channel capacity $C$ on the bandwidth $W$ (keeping $P_{a v}$ and $N_0$ fixed)?

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?