Problem 4: In this question, we will consider a nonlinear method for generating AM signals. Consider the system in the figure. т(t) x(t) Nonlinear y(t) Filter g(t) -> Device Acos(wct) Assume that the nonlinear device has the input-output relationship of the form y(t) = a,x(t) + azx²(t). Assume that the message is normalized, i.e. Įm(t)| < 1, and it has a bandwidth of "W". (a) Write the equation for y(t). (b) Describe the filter that yields an AM signal for g(t). Give the necessary filter type and the frequencies of interest. (Center frequency, cutoff frequency). (c) Write the equation for g(t). (d) Find a condition on a, and a2 such that the signal generated, g(t), is not overmodulated.

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Problem 4:
In this question, we will consider a nonlinear method for generating AM signals.
Consider the system in the figure.
x(t)
y(t)
g(t)
->
m(t)
Nonlinear
Filter
Device
Acos(@ct)
Assume that the nonlinear device has the input-output relationship of the form
y(t) = a1x(t) + azx²(t). Assume that the message is normalized, i.e. Im(t)| < 1,
and it has a bandwidth of "W".
(a) Write the equation for y(t).
(b) Describe the filter that yields an AM signal for g(t). Give the necessary filter type
and the frequencies of interest. (Center frequency, cutoff frequency).
(c) Write the equation for g(t).
(d) Find a condition on a, and az such that the signal generated, g(t), is not
overmodulated.
Transcribed Image Text:Problem 4: In this question, we will consider a nonlinear method for generating AM signals. Consider the system in the figure. x(t) y(t) g(t) -> m(t) Nonlinear Filter Device Acos(@ct) Assume that the nonlinear device has the input-output relationship of the form y(t) = a1x(t) + azx²(t). Assume that the message is normalized, i.e. Im(t)| < 1, and it has a bandwidth of "W". (a) Write the equation for y(t). (b) Describe the filter that yields an AM signal for g(t). Give the necessary filter type and the frequencies of interest. (Center frequency, cutoff frequency). (c) Write the equation for g(t). (d) Find a condition on a, and az such that the signal generated, g(t), is not overmodulated.
Problem 3:
Based on the following block diagram answer the following questions.
m,(0)
b(t)
c(1)
-20kHz
20kHz
+
m(1)
a(t)
4cos(105nt)
4cos(60000rt)
-10kHz
10kHz
(a) Sketch the amplitude spectra of the signals a(t), b(t), and c(t) in the block diagram,
respectively. Label the amplitude spectra of the frequency axis.
(b) Determine the bandwidths of the signals (t), b(t), and c(t) , respectively.
(c) Design and sketch the block diagram of the receiver that will recover signals, m, (t)
and m2 (t) from the modulated signal c(t). Specify the type and the cutoff
frequency for every filter you use in your design, give the specifications for any
other component you might use.
Transcribed Image Text:Problem 3: Based on the following block diagram answer the following questions. m,(0) b(t) c(1) -20kHz 20kHz + m(1) a(t) 4cos(105nt) 4cos(60000rt) -10kHz 10kHz (a) Sketch the amplitude spectra of the signals a(t), b(t), and c(t) in the block diagram, respectively. Label the amplitude spectra of the frequency axis. (b) Determine the bandwidths of the signals (t), b(t), and c(t) , respectively. (c) Design and sketch the block diagram of the receiver that will recover signals, m, (t) and m2 (t) from the modulated signal c(t). Specify the type and the cutoff frequency for every filter you use in your design, give the specifications for any other component you might use.
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