Consider a frequency-modulated (FM) signal

where  and  are, respectively, the amplitude and frequency (in Hz) of the carrier waveform. The frequency  is in Hz, and assume that .

The peak frequency deviation of the FM signal in Hz is __________.

Consider a message signal  which is bandlimited to , where  is in Hz. Consider the following two modulation schemes for the message signal:

• Double sideband-suppressed carrier (DSB-SC):

• Amplitude modulation (AM):

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

Consider the following statements:

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

(ii) An envelope detector can be used for demodulation in the AM scheme only if  for all .

Which of the following options is/are correct?

An amplitude modulator has output (in Volts)

The carrier power normalized to  resistance is 50 Watts. The ratio of the total sideband power to the total power is . The value of  (in Volts, rounded off to two decimal places) is_______.

Let a frequency modulated (FM) signal , where  is a message signal of bandwidth . It is passed through a non-linear system with output  . Let  denote the FM bandwidth. The minimum value of  required to recover  from  is

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

Where .

For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of  values is/are ________.

Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of . If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is_________

Consider a superheterodyne receiver tuned to . If the local oscillator feeds a  signal to the mixer, the image frequency (in integer) is ________ kHz.

A  sinusoidal message signal having amplitude  is fed to a delta modulator (DM) operating at a sampling rate of . The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is __________ V.

A sinusoidal message signal having root mean square value of  and frequency of 1kHz is fed to a phase modulator with phase deviation constant . If the carrier signal is , the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is _________ .

For the modulated signal  , the message signal  and the carrier frequency  is . The signal  is passed through a demodulator, as shown in the figure below. The output  of the demodulator is

 and  as defined below, are the phase modulated and the frequency modulated waveforms, respectively, corresponding to the message signal  shown in the figure.

and

where  is the phase deviation constant in radians/volt and  is the frequency deviation constant in radians/second/volt. If the highest instantaneous frequencies of  and  are same, then the value of the ratio  is __________ seconds.

The baseband signal shown in the figure is phase modulated to generate the PM signal. The time t on the x-axis in the figure is in milliseconds. If the carrier frequency isand, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _______ (rounded off to 2 decimal places)

Consider the following amplitude modulated signal:

The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is ________

Let and . It is given that. The signal is applied to the input of a non-linear device, whose output is related to the input as, where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with centre frequency and bandwidth  to produce amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then a/b is  

A modulating signal given by x(t)=5 sin V is fed to a phase modulator with phase deviation constant If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is ____________

The unmodulated carrier power in an AM transmitter is 5 kW. 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 unmodulated carrier power (in kW) that can be used without overloading the transmitter is ___________

A super-heterodyne receiver operates in the frequency range of 58 MHz - 68 MHz. The intermediate frequency and local oscillator frequency are chosen Such that It is required that the image frequencies fall outside the 58 MHz - 68 MHz band. The minimum required  (in MHz) is______________

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal s(t) = 5cos 1600πt + 20cos 1800πt + 5cos 2000πt. The value of the modulation index is________________

For a super-heterodyne 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 ________        

Consider the signal

 where denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared to . The signals s(t) is a

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 ________

Figure a

Figure b

Consider sinusoidal modulation in an AM system. Assuming no over modulation, the modulation index (μ) when the maximum and minimum values of the envelope, respectively, are 3 V and 1 V, is ________.

In the figure, M(f) is the Fourier transform of the message signal m(t) where A = 100 Hz and B = 40 Hz. Given  and , where . The cut-off frequencies of both the filters are .

The bandwidth of the signal at the output of the modulator (in Hz) is _____

A modulated signal is, where the baseband signal m(t) has frequency components less than 5 kHz only. The minimum required rate (in kHz) at which y(t) should be sampled to recover m(t) is _______.

The phase response of a pass-band waveform at the receiver is given by  

Where  is the centre frequency, and α and β are positive constants. The actual signal propagation delay from the transmitter to receiver is        

Consider an FM signal

.

The maximum deviation of the instantaneous frequency from the carrier frequency  is

In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of ______.

A message signal m(t) =is used to modulate the phase of a carrier to get the modulated signal y(t)= .The bandwidth of y(t)

The complex envelope of the band-pass signal , centred about , is

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

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

The Column-1 lists the attributes and the Column-2 lists the modulation systems. Match the attribute to the modulation system that best meets is.        

A message signal

 modulates the carrier  where MHz to produce an AM signal. For demodulating the generated AM signal using an envelope detector, the time constant RC of the detector circuit should satisfy

Suppose that the modulating signal is  and the carrier signal is , which one of the following is a conventional AM signal without over-modulation?        

Consider an angle modulated signal . The average power of x(t) is

For a message signal  and carrier of frequency, which of the following represents a single side-band (SSB) signal?

A message signal given by

Is amplitude-modulated with a carrier of frequency  to generate

What is the power efficiency achieved by this modulation scheme?

Consider the amplitude modulated (AM) signal  . For demodulating the signal using envelope detector, the minimum value of  should be

Consider the frequency modulated signal  with carrier frequency of Hz. The modulation index is

The signal  is

In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be        

A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t) where

The resulting signal is then passed through an ideal low-pass filter with bandwidth 1 kHz. The output of the low-pass filter would be:

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 is carrier frequency both in rad/sec)

A message signal with bandwidth 10 kHz is Lower-Side Band SSB modulated with carrier frequency Hz. The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency.

The bandwidth of the output would be:         

Let , where * denotes convolution and with u(t) being the unit step function

The impulse response of filter matched to the signal is given as:

Let , where * denotes convolution and with u(t) being the unit step function

An Amplitude Modulated signal is given as

In the interval . One set of possible values of the modulating signal and modulation index would be

Consider the following Amplitude Modulated (AM) signal, where:

The average side band power for the AM signal given above is:

Consider the following Amplitude Modulated (AM) signal, where:

The AM signal gets added to a noise with power Spectral Density given in the figure below. The ratio of average sideband power to mean noise power would be:

 Find the correct match between group 1 and group 2.        

The power in the signal  is:

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 . 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

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

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

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

A 100 MHz carrier of 1V amplitude and a 1 MHz modulating signal of 1V amplitude are fed to a balanced modulator. The output of the modulator is passed through an ideal high-pass filter with cut-off frequency of 100MHz. The output of the filter is added with 100 MHz signals of 1 V amplitude and 90º phase shift as shown in Figure, the envelope of the resultant signal is

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

Consider a system shown in Figure. Let X (f) and Y (f) denote the Fourier transforms of x (t) and y (t) respectively. The ideal HPF has the cut-off frequency 10 kHz.        

The positive frequencies where Y (f) has spectral peaks are

The input to a coherent detector is DSB-SC signal plus noise. The noise at the detector output is

A DSB-SC signal is to be generated with a carrier frequency using a nonlinear device with the input-output characteristic

Where  and  are constants, the output of the nonlinear device can be filtered by an appropriate band-pass filter. Let  where m(t) is the message signal. Then the value of (in MHz) is

Let  be the message signal and  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 is

Let  be the message signal and  be the carrier.

c(t) and m(t) are used to generate an AM signal. If the peak frequency deviation of the generated FM signal is three times the transmission bandwidth of the AM signal, then the coefficient of the term  in the FM signal (in terms of the Bessel coefficients) is

Choose the correct one from among the alternatives A, B, C, D after matching an item in Group 1 with the most appropriate item in Group 2.         

A super-heterodyne receiver is to operate in the frequency range 550 kHz – 1650 kHz, with the intermediate frequency of 450 kHz. Let  denote the required capacitance ratio of the local oscillator and I denote the image frequency (in KHz) of the incoming signal. If the receiver is tuned to 700 kHz, then

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

Consider a sampled signal

where  and

When y(t) is passed through an ideal low-pass filter with a cut-off frequency of 5 KHz, the output of the filter is

An angle modulated signal is given by

. The maximum frequency and phase deviations of s (t) are

In Figure ,  and . The output y(t) will be        

A DSBSC modulated signal  is corrupted by an additive white Gaussian noise of power spectral density W/Hz. The message power spectral density  is as shown in Figure and  is uniformly distributed over the range 0 to 2π.        

(a) Express the signal autocorrelation function  in terms of the message autocorrelation function. Clearly state the necessary assumptions.

(b) Determine the signal power spectral density

(c) Find the power of the modulated signal and the noise power in the transmissions bandwidth.

The periodic modulating signal m(t) is shown in Figure Using Carson’s rule estimate  (bandwidth of the FM signal) and  (bandwidth of the PM signal) for  and. Assume the essential bandwidth of m(t) to consist only up to and including the third harmonic.

A baseband signal g(t) band limited to 100 Hz modulates a carrier of frequency  Hz. The modulated signal  is transmitted over a channel whose input x and output y are related by . The spectrum of g(t) is shown in Figure. Sketch the spectrum of the transmitted signals and the spectrum of the received signal.

The amplitude modulated wave from  is fed to an ideal envelope detector. The maximum magnitude of  is greater than 1. Which of the following could be the detector output?

A message m(t) band-limited to the frequency  has a power of . The power of the output signal in the Figure is

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 1MHz. If , than by using

Carson’s approximation, the bandwidth of y(t) around
300 MHz and the spacing of spectral components are, respectively.

The input to a channel is a band pass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by

The group delay  and the phase delay  in seconds, of the channel are

A modulated signal is given by,

where the baseband signal  and  have bandwidths of 10 kHz and 15 kHz, respectively. The bandwidth of the modulated signal, in kHz, is

A modulated signal is given by

, where a,  and  are positive constants, and  .

The complex envelope of s(t) is given by

A baseband signal m(t) modulates a carrier to produce the angle modulated signal, , where m(t) is shown in Figure. Determine the value of  so that the peak-to-peak frequency deviation of the carrier is 100 kHz.        

The image channel selectivity of super heterodyne receiver depends upon

A DSB-SC signal is generated using the carrier  and modulating signal x(t). The envelope of the DSB-SC signal is

An SSB signal is demodulated by using a synchronous demodulator. However, the locally arranged carrier has a phase error θ . Determine the effect of the error on demodulation. What will be the effect of this error if the input is DSB-SC in place of SSB?

The figure is shows the first stage of a super heterodyne receiver. The desired input signal is at a frequency of 700MHz. The local oscillator (L. O) frequency is 1 GHz.  The mixer is an ideal multiplier with a gain independent of frequency. A band-pass filter (BPF) is used to select the Intermediate Frequency (IF) output at 300MHz.        

(a) What is the image frequency of the desired input?

(b) A Low Pass Filter (LPF) can be used before the mixer to reject the image frequency. If a perfect rejection (zero transmission) of the image is desired, what type of LPF should be employed?

(c) The input in the figure is corrupted by an undesired 750 MHz signal which has the same amplitude as that of the desired signal at 700MHz. Let the BPF be of second order. At the BPF output, the undesired signal should be 20 dB below the desired signal. Calculate the Q required for the BPF.

A block diagram of a system is shown in the figure. Draw the spectrum of the output signal with relative amplitudes of the frequencies.

The image channel rejection in a super heterodyne receiver comes from

An FM signal with a modulation index 9 is applied to a frequency Tripler. The modulation index in the output signal will be

The image (second) channel selectivity of a super heterodyne communication receiver is determined by        

A PLL can be used to demodulate

Match the following

Match the following

 represents

A 10 MHz carrier is frequency modulated by a sinusoidal signal of 500Hz, the maximum frequency deviation being 50 kHz. The bandwidth required, as given by the Carson’s rule is _________.

Match The Following

Which of the following demodulator(s) can be used for demodulating the signal

A super-heterodyne radio receiver with an intermediate frequency of 455 KHz is tuned to a station operating at 1200 KHz. The associated image frequency is __________ KHz.

Obtain an expression for the signal  in figure, for . Assume that  and that the BPF is an ideal unity gain filter with pass band form 800 Hz to 1200 Hz.

The maximum power efficiency of an AM modulator is

Coherent demodulation of FSK signal can be effected using