Analog Communication Systems · Communications · GATE ECE

Marks 1

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 _______.

GATE ECE 2024

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 ___________.

GATE ECE 2016 Set 1

For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in MHz) is _________.

GATE ECE 2016 Set 3

Consider the signal $$s\left(t\right)\;=\;m\left(t\right)\;\cos\left(2{\mathrm{πf}}_\mathrm c\mathrm t\right)\;+\widehat m\left(t\right)\;\sin\left(2\mathrm\pi\;{\mathrm f}_\mathrm c\mathrm t\right)$$ where $$\widehat m\left(t\right)\;$$ denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared to f_c. The signal s(t) is a

GATE ECE 2015 Set 1

Consider an FM signal $$f\left(t\right)\;=\;\cos\left[2{\mathrm{πf}}_\mathrm c\mathrm t\;+\;{\mathrm\beta}_1\sin\;2{\mathrm{πf}}_1\mathrm t\;+\;{\mathrm\beta}_2\sin\;2{\mathrm{πf}}_2\mathrm t\right]$$ . The maximum deviation of the instantaneous frequency from the carrier frequency f_c is

GATE ECE 2014 Set 3

Consider an angle modulated signal x(t) = 6cos[2$$\mathrm\pi$$x10⁶ t+2sin(8000$$\mathrm\pi$$t) + 4cos(8000$$\mathrm\pi$$t)] V. The average power of x(t) is.

GATE ECE 2010

Consider the amplitude modulated (AM) signal $$A_c\cos\omega_ct\;+\;2\cos\omega_mt\;\cos\omega_ct$$. For demodulating the signal using envelope detector, the minimum value of A_c should be

GATE ECE 2008

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

GATE ECE 2005

An AM signal and a narrow-band FM signal with identical carriers, modulating signals and modulation indices of 0.1 are added together. The resultant signal can be closely approximated by

GATE ECE 2004

An AM signal is detected using an envelope detector. The carrier frequency and modulating signal frequency are 1 MHz and 2 KHz respectively. An appropriate value for the time constant of the envelope detector is

GATE ECE 2004

A 1 MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave of period 100 µsec. Which of the following frequencies will NOT be present in the modulated signal?

GATE ECE 2002

A modulated signal is given by, $$s\left(t\right)=m_1\left(t\right)\cos\left(2{\mathrm{πf}}_\mathrm c\mathrm t\right)\;+m_2\left(t\right)\sin\left(2{\mathrm{πf}}_\mathrm c\mathrm t\right)$$, where the baseband signal m₁(t) and m₂(t) have bandwidths of 10 kHz and 15 kHz, respectively. The bandwidth of the modulated signal, in kHz, is

GATE ECE 1999

A DSB-SC signal is generated using the carrier $$\cos\left(\omega_ct\;+\;\theta\right)$$ and modulating singal x(t). The envelope of the DSB-SC signal is

GATE ECE 1998

The image channel selectivity of super heterodyne receiver depends upon

GATE ECE 1998

$$v\left(t\right)\;=5\left[\cos\left(10^6\mathrm{πt}\right)\;-\;\sin\left(10^3\mathrm{πt}\right)\times\sin\left(10^6\mathrm{πt}\right)\right]$$ represents

GATE ECE 1994

Marks 2

Let a frequency modulated (FM) signal $$x(t) = A\cos ({\omega _c}t + {k_f}\int_{ - \infty }^t {m(\lambda )d\lambda )} $$, where $$m(t)$$ is a message signal of bandwidth W. It is passed through a non-linear system with output $$y(t) = 2x(t) + 5{(x(t))^2}$$. Let $${B^T}$$ denote the FM bandwidth. The minimum value of $${\omega _c}$$ required to recover $$x(t)$$ from $$y(t)$$ is

GATE ECE 2023

Let x$$_1$$(t) and x$$_2$$(t) be two band-limited signals having bandwidth $$B=4\pi\times10^3$$ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

GATE ECE 2023

Consider an FM broadcast that employs the pre-emphasis filter with frequency response

$${H_{pe}}(\omega ) = 1 + {{j\omega } \over {{\omega _0}}}$$,

where $$\omega$$₀ = 10⁴ rad/sec.

For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pairs of (R, C) values is/are ____________.

GATE ECE 2022

The un-modulated carrier power in an AM transmitter is 5kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is 50%. If it is reduced to 40%, then the maximum un-modulated carrier power (in kW) that can be used without overloading the transmitter is ___________

GATE ECE 2017 Set 2

A modulating signal given By $$x\left(t\right)=5\sin\left(4\mathrm\pi10^3\mathrm t\;-\;10\mathrm{πcos}2\mathrm\pi10^3\mathrm t\right)$$ V is fed to a phase modulator with phase deviation constant k_p=0.5rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is __________

GATE ECE 2017 Set 2

In the system shown in figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter H(f) is shown in figure (b). If it is desired that the output signal z(t) = 10x(t), the maximum value of W (in Hz) should be strictly less than ____________________.

GATE ECE 2015 Set 1

The signal m(t) as shown is applied both to a phase modulator (with k_p as the phase constant) and a frequency modulator (with k_f as the frequency constant) having the same carrier frequency.

The ratio k_p/k_f (in rad/Hz) for the same maximum phase deviation is

GATE ECE 2012

The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is

GATE ECE 2008

A Hilbert transformer is a

GATE ECE 2007

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 ω_c is carrier frequency both in rad/sec)

GATE ECE 2006

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

GATE ECE 2005

A device with input x(t) and output y(t) is characterized by: y(t) = x²(t). An FM signal with frequency deviation of 90 kHz and modulating signal bandwidth of 5 kHz is applied to this device. The bandwidth of the output signal is

GATE ECE 2005

Two sinusoidal signals of same amplitude and frequencies 10 kHz and 10.1 kHz are added together. The combined signal is given to an ideal frequency detector. The output of the detector is

GATE ECE 2004

A DSB-SC signal is to be generated with a carrier frequency f_c = 1MHz using a nonlinear device with the input-output characteristic $$v_0=a_0v_i\;+\;a_1v_i^3$$.where a₀ and a₁ are constants. The output of the nonlinear device can be filtered by an appropriate band-pass filter. Let $$v_0=A_c'\;\cos\left(2{\mathrm{πf}}_\mathrm c'\mathrm t\right)\;+\;m\left(t\right)$$ where m(t) is the message signal. Then the value of $$f_c'$$ (in MHz) is

GATE ECE 2003

Let $$m\left(t\right)\;=\cos\left[\left(4\mathrm\pi\times10^3\right)t\right]$$ be the message signal and $$c\left(t\right)\;=5\cos\left[2\mathrm\pi\times10^6t\right]$$ be the carrier.

c(t) and m(t) are used to generate an AM signal. The modulation index of the generated AM signal is 0.5. Then the quantity $$\frac{Total\;sideband\;power}{Carrier\;power}$$ is

GATE ECE 2003

Let $$m\left(t\right)\;=\cos\left[\left(4\mathrm\pi\times10^3\right)t\right]$$ be the message signal and $$c\left(t\right)\;=5\cos\left[2\mathrm\pi\times10^6t\right]$$ be the carrier.

c(t) and m(t) are used to generate an FM signal. If the peak frequency deviation of the generated FM signal is three times the transmission bandwidth of the AM singal, then the coefficient of the term $$\cos\left[2\mathrm\pi\left(1008\times10^3\right)t\right]$$ in the FM signal (in terms of the Bessel coefficients) is

GATE ECE 2003

In an FM system, a carrier of 100 MHz is modulated by a sinusoidal signal of 5 KHz. The bandwidth by Carson’s approximation is 1 MHz. If y(t) = (modulated waveform)³, then by using Carson’s approximation, the bandwidth of y(t) around 300 MHz and the and the spacing of spectral components are, respectively.

GATE ECE 2000

A superheterodyne radio receiver with an intermediate frequency of 455 KHz is tuned to a station operating at 1200 KHz. The associated image frequency is ______ KHz.

GATE ECE 1993

Which of the following demodulator(s) can be used for demodulating the signal $$x(t)\;=\;5\left(1+2\;\cos200\mathrm{πt}\right)\cos\;20000\;\mathrm{πt}$$ .

GATE ECE 1993

The maximum power efficiency of an AM modulator is

GATE ECE 1992