GATE EC Communications questions

Consider the amplitude modulated (AM) signal $A_{c} \cos \omega_{c} t+2 \cos \omega_{m} t \cos \omega_{c} t$. For demodulating the signal using envelope detector, the minimum value of $A_{c}$ should be

Consider the frequency modulated signal $10 \cos \left[2 \pi \times 10^{5} t+5 \sin (2 \pi \times 1500 t)+7.5 \sin (2 \pi \times 1000 t)\right]$ with carrier frequency of $10^{5} \mathrm{~Hz}$. The modulation index is

A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits. If the bits $0$ and $1$ are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is

A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits. Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantizer output is

A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits. The number of quantization levels required to reduce the quantization noise by a factor of $4$ would be

A zero- mean white Gaussian noise is passed through an ideal lowpass filter of ban width $10 \; \mathrm{kHz}$. The output is the uniformly sampled with sampling period $t_{s}=0.03 \; \mathrm{msec}$. The samples so obtained would be

A source generates three symbols with probabilities $0.25,0.25,0.50$ at a rate of $3000$ symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as

The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (here $W$ is message bandwidth and $\omega_{c}$ is carrier frequency both in rad/sec)

A message signal with bandwidth $10 \; \mathrm{kHz}$ is Lower-Side Band SSB modulated with carrier frequency $f_{c 1}=10^{6} \mathrm{~Hz}$. The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency $f_{c_{2}}=10^{9} \; \mathrm{Hz}$. The bandwidth of the output would be

Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function An Amplitude Modulated signal is given as $$x_{\mathrm{AM}}(t)=100(p(t)+0.5 g(t)) \cos \omega_{c} t$$ in the interval $0 \leq t \leq 1$. One set of possible values of the modulating signal and …

Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes It is desired to generate a stochastic process (as voltage process) with power spectral density $$S(\omega)=\frac{16}{16+\omega^{2}}$$ by driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with …

Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes The parameters of the system obtained in $\text{Q.78}$ would be

Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ $$x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t$$ The average side-band power for the $\text{AM}$ signal given above is

Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ $$x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t$$ The $\text{AM}$ signal gets added to a noise with Power Spectral Density $S_{n}(f)$ given in the figure below. The ratio of average …

Find the correct match between group $1$ and group $2.$ Group I …

Which of the following analog modulation scheme requires the minimum transmitted power and minimum channel bandwidth?

A device with input $x(t)$ and output $y(t)$ is characterized by: $y(t)=x^{2}(t)$. An FM signal with frequency deviation of $90 \; \mathrm{kHz}$ and modulating signal bandwidth of $5 \; \mathrm{kHz}$ is applied to this device. The bandwidth of the output signal is

Noise with uniform power spectral density of $\text{N}_{0}$ $\mathrm{W / Hz}$ is passed through a filter $\mathrm{H}(\omega)=2$ exp $\left(-j \omega t_{d}\right)$ followed by an ideal low pass filter of bandwidth $\text{B Hz.}$ The output noise power in Watts is

A carrier is phase modulated (PM) with frequency deviation of $10 \; \mathrm{kHz}$ by a single tone frequency of $1 \; \mathrm{kHz}$. If the single tone frequency is increased to $2 \; \mathrm{kHz}$, assuming that phase deviation remains unchanged, the bandwidth of the PM signal is

In a $\text{PCM}$ system, if the code word length is increased from $6$ to $8$ bits, the signal to quantization noise ratio improves by the factor