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Jan-Apr 2025: Signals and Systems y T

The ECS204 course assignment involves analyzing an LCR circuit, including deriving its differential equation and frequency response, and generating plots for different inductance values. It also covers natural sampling modulation techniques, requiring the generation and display of modulated waves and their spectra. Additionally, the assignment includes sampling a given signal and reconstructing it using various filters, with an emphasis on understanding the effects of sampling frequency changes.

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Chirayu Sharma
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15 views3 pages

Jan-Apr 2025: Signals and Systems y T

The ECS204 course assignment involves analyzing an LCR circuit, including deriving its differential equation and frequency response, and generating plots for different inductance values. It also covers natural sampling modulation techniques, requiring the generation and display of modulated waves and their spectra. Additionally, the assignment includes sampling a given signal and reconstructing it using various filters, with an emphasis on understanding the effects of sampling frequency changes.

Uploaded by

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

Jan-Apr 2025 and output y(t).


HW9: Programming Assignment IISER Bhopal

1. Consider a LCR circuit with input x(t)

Write the differential equation description for this system and find the frequency
response. Characterize the system as a filter.
Generate a plot of this filter. Use logarithmically spaced angular frequencies from 1
rad/s to 105rad/s. Use logspace(d1, d2, N) to implement this. Assume the value of L
to be

(i) L = 10 mH
(ii) L = 4 mH

Determine and plot the output, using at least 99 harmonics in truncated FS


expansion if the input is a square wave of fundamental period T = 2π × 10−3s having
pulse width T0 = (π/2) × 10−3s.

2. Natural sampling involves the multiplication of your message signal m(t) with
rectangular pulse c(t). The pulse repetition frequency of the train is ωs , the duration
of each rectangular pulse is T0. The fundamental period of pulse train is T.
(i) Name the type of modulation performed in this problem.
(ii) Generate and display the modulated wave for a sinusoidal wave, given the
following specification:
Modulation frequency: 1 kHz
Pulse repetition frequency (1/T) = 10 kHz
Pulse duration T0 = 10µs
(iii) Compute and display the spectrum of the modulated wave. Specify the
requirements for which you can recover the original signal without distortion
using a low pass filter.
3. Consider a signal x(t) = sin(40πt)+0.5 cos(120πt)is sampled at a frequency xxxx Hz,
where xxxx is last 4 digits of your roll no.
Give the spectrum of the sampled signal. From the samples reconstruct a
continuous-time signal using the following filters:

(a) Zero-order hold filter


(b) First-order hold filter
(c) Ideal low-pass filter (sinc)
Explain your output if you multiply your sampling frequency by 2 2

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