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Jan-Apr 2025: ECS204 Course: HW8

The document outlines a homework assignment for the ECS204 course on Signals and Systems at IISER Bhopal, covering topics such as convolution and Fourier transforms for both continuous and discrete-time signals. It includes problems on amplitude modulation, frequency division multiplexing, time division multiplexing, and sampling frequency requirements for signal reconstruction. Students are expected to analyze and construct systems for signal transmission and demodulation based on provided signal spectra.

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Chirayu Sharma
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13 views1 page

Jan-Apr 2025: ECS204 Course: HW8

The document outlines a homework assignment for the ECS204 course on Signals and Systems at IISER Bhopal, covering topics such as convolution and Fourier transforms for both continuous and discrete-time signals. It includes problems on amplitude modulation, frequency division multiplexing, time division multiplexing, and sampling frequency requirements for signal reconstruction. Students are expected to analyze and construct systems for signal transmission and demodulation based on provided signal spectra.

Uploaded by

Chirayu Sharma
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ECS204 Course: Signals and Systems

Jan-Apr 2025 IISER Bhopal


HW8

1. State the similarities and differences between

(a) Convolution of continuous-time signals and Convolution of discrete-time signals


(b) Fourier transform of continuous-time signals and Fourier transform of discrete-time
signals
(c) Fourier transform of continuous-time periodic signals and their corresponding Inverse
Fourier transforms
(d) Fourier transform of discrete-time periodic signals and their corresponding Inverse Fourier
transforms
(e) Fourier transform of continuous-time aperiodic signals and their corresponding Inverse
Fourier transforms
(f) Fourier transform of discrete-time aperiodic signals and their corresponding Inverse
Fourier transforms

2. A message signal x(t) = cos(4π10t) is used to modulate a carrier c(t) = cos(2π103 t) in


an Amplitude Modulation (AM) system. Calculate the frequency content in the modulated
signal.

X1 (ω) X2 (ω) X3 (ω)

1.5 1.5
1
0.5
−10π 10π ω −8π 8π ω −12π 12π ω
Figure 1: Spectrum of three signals x1 (t), x2 (t), x3 (t)

3. Consider Figure 1. Construct an Frequency Division Multiplexing system to transmit three


signals x1 (t), x2 (t), x3 (t) respectively using carriers ck (t) = cos(22k π103 t), k = 1, 2, 3. Pro-
vide a scheme to demodulate and receive the three signals x1 (t), x2 (t), x3 (t) at the receiver.

4. Construct a Time Division Multiplexing system to transmit three signals x1 (t), x2 (t), x3 (t)
respectively using pulse trains of appropriate ∆ and time-period T . Provide a scheme to
demodulate and receive the three signals x1 (t), x2 (t), x3 (t) at the receiver.

5. What should be the sampling frequency if one were to sample each of the time-domain signals
x1 (t), x2 (t), x3 (t) whose spectrum is shown in Figure 1? What type of filter would you use
to reconstruct the signals from its samples?

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