Linear Systems (Vestigal Sidebands): How do I solve this problem? I want to study it but I got low marks for this problem A shaping filter H,(w) used for vestigial side-band (VSB) modulation is shown below,H(c)NA.1/2--003 -0₂-0₂-00₂ -004where @₁ = 10000 rad/s, w₂= 12000 rad/s, w3 = 14000 rad/s, w₁ = 18000 rad/s,and w5 = 20000 rad/s. The carrier frequency is we = 11000 rad/s and the basebandsignal bandwidth is 7000 rad/s. Consider the block diagram in the lecture notes for VSBmodulation and demodulation.a) Sketch the corresponding receiving filter H(o). Assume H₂(w) = 0 forw≥ 7000л rad/s.b) Write the mathematical expression of H (w) in terms of the rectangular function(see the definition of the rectangular function below).c) By using the inverse Fourier transform, find the mathematical expression of h (t).

Given:Shaping filter for VSB modulation, with we need to do:a) Sktech of receiving filter assuming…

Answered: Linear Systems (Vestigal Sidebands):…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Linear Systems (Vestigal Sidebands): How do I solve this problem? I want to study it but I got low marks for this problem

A shaping filter H,(w) used for vestigial side-band (VSB) modulation is shown below,
H(c)
NA.
1/2-
-003 -0₂-0₂
-00₂ -004
where @₁ = 10000 rad/s, w₂= 12000 rad/s, w3 = 14000 rad/s, w₁ = 18000 rad/s,
and w5 = 20000 rad/s. The carrier frequency is we = 11000 rad/s and the baseband
signal bandwidth is 7000 rad/s. Consider the block diagram in the lecture notes for VSB
modulation and demodulation.
a) Sketch the corresponding receiving filter H(o). Assume H₂(w) = 0 for
w≥ 7000л rad/s.
b) Write the mathematical expression of H (w) in terms of the rectangular function
(see the definition of the rectangular function below).
c) By using the inverse Fourier transform, find the mathematical expression of h (t).

Expert Solution

Step 1: what is given and what is required:

Given:

Shaping filter for VSB modulation,

with

$omega subscript 1 equals 10000 straight pi space rad divided by straight s comma space straight omega subscript 2 equals 12000 straight pi space rad divided by straight s comma straight omega subscript 3 equals 14000 straight pi space rad divided by straight s comma straight omega subscript 4 equals 18000 straight pi space rad divided by straight s comma straight omega subscript 5 equals 20000 straight pi space rad divided by straight s comma and space carrier space frequency comma space straight omega subscript straight c equals 11000 straight pi space rad divided by straight s comma and space base minus band space signal space bandwidth comma space straight omega subscript straight m equals 7000 straight pi space rad divided by straight s.$

we need to do:

a) Sktech of receiving filter $H subscript 0 open parentheses omega close parentheses$ assuming $H subscript 0 open parentheses omega close parentheses equals 0 space for space open vertical bar straight omega close vertical bar greater or equal than 7000 straight pi space rad divided by straight s.$

b) write mathematical expression for $H subscript 0 open parentheses omega close parentheses$ in terms of rectangular function.

c) find impulse response h₀(t) by taking inverse Fourier ransform.

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