2. The signal x(t) can be expressed as the sum of two signals; x1(t) and x2(t); x(t)=x1(t)+x2(t) where, x1 (t) = { -1sts1 ,and otherwise -1 +1 +2 t(s) -1sts2 x,(t) = 0 Fig. 1 %3D otherwise (a) Find the CTFT of x1(t) using Fourier Pairs (use the table) (b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift) (c) Find the CTFT of x(t0 by adding the results of (a) and (b): X(@) = X,(w) +X2(w)
2. The signal x(t) can be expressed as the sum of two signals; x1(t) and x2(t); x(t)=x1(t)+x2(t) where, x1 (t) = { -1sts1 ,and otherwise -1 +1 +2 t(s) -1sts2 x,(t) = 0 Fig. 1 %3D otherwise (a) Find the CTFT of x1(t) using Fourier Pairs (use the table) (b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift) (c) Find the CTFT of x(t0 by adding the results of (a) and (b): X(@) = X,(w) +X2(w)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
I need help solving calculation part 2. Please include descriptions of each step
![Objectives:
1. Determine the Fourier transform of a CT signal using Integration form
2. Determine the Fourier transform of a CT signal using Fourier transform pairs and its properties
3. Plot the magnitude and phase spectra of a CT signal
I.
CALCULATION PART
1. Using integration form of Fourier transform, compute the CTFT for the CT signal x(t) in Fig. 1
x(t)
8.
X (@) =
x(t)e-jutdt
-00
2. The signal x(t) can be expressed as the sum of
two signals; x1(t) and x2(t);
x(t)=x1(t)+x2(t)
where, x, (t) = {6
-1 st<1
and
otherwise'
-1
+1
+2
t(s)
(1 -1 <t< 2
x2(t) = t0
Fig. 1
otherwise
(a) Find the CTFT of x1(t) using Fourier Pairs (use the table)
(b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift)
(c) Find the CTFT of x(t0 by adding the results of (a) and (b):
X(@) = X,(@) + X2(@)
3. Find the magnitude A(w) and phase (w) spectra of x(t) and determine their values in
Table 1 and Table 2
Table 1
T/8
T/4
Зп/8
Tt/2
5t/8
би /8
7TT/8
A(@)
$(@)
Table 2
-/8
-T/4-3T/8 -T/2 |-5T/8 -61/8 -71/8
A(@)
$(w)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcabe9831-0dc2-4a69-864f-16c869f00e6e%2F806ec17d-5efb-4ec6-bc84-839e12224325%2Feknfxhb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Objectives:
1. Determine the Fourier transform of a CT signal using Integration form
2. Determine the Fourier transform of a CT signal using Fourier transform pairs and its properties
3. Plot the magnitude and phase spectra of a CT signal
I.
CALCULATION PART
1. Using integration form of Fourier transform, compute the CTFT for the CT signal x(t) in Fig. 1
x(t)
8.
X (@) =
x(t)e-jutdt
-00
2. The signal x(t) can be expressed as the sum of
two signals; x1(t) and x2(t);
x(t)=x1(t)+x2(t)
where, x, (t) = {6
-1 st<1
and
otherwise'
-1
+1
+2
t(s)
(1 -1 <t< 2
x2(t) = t0
Fig. 1
otherwise
(a) Find the CTFT of x1(t) using Fourier Pairs (use the table)
(b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift)
(c) Find the CTFT of x(t0 by adding the results of (a) and (b):
X(@) = X,(@) + X2(@)
3. Find the magnitude A(w) and phase (w) spectra of x(t) and determine their values in
Table 1 and Table 2
Table 1
T/8
T/4
Зп/8
Tt/2
5t/8
би /8
7TT/8
A(@)
$(@)
Table 2
-/8
-T/4-3T/8 -T/2 |-5T/8 -61/8 -71/8
A(@)
$(w)
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