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 00 x(t) X(@) = | x(t)e-jwt dt 2 -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) 1 where, x1(t) = {o (1 -1

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I need help solving calculation part 1. Please include steps and descriptions
I geórgiasouthern.desire2learn.com
ttps://georgiasouthern.desire2.
G Lab 4 Signal Processing - Goog..
G Find the CTFT of x1(t) using Fo...
b Answered: 1. Det
ect_4_CTFT
1 of 2
+ Automatic Zoom
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)
X(@) =
| x(t)e-jwt dt
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)
-1<t<1
where, x, (t) =
otherwise and
-1
+1
+2
t(s)
-1 <t<2
otherwise
x2(t) =
Fig. 1
(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(@)
3. Find the magnitude A(@) and phase (w) spectra of x(t) and determine their values in
Table 1 and Table 2
Table 1
24
Transcribed Image Text:I geórgiasouthern.desire2learn.com ttps://georgiasouthern.desire2. G Lab 4 Signal Processing - Goog.. G Find the CTFT of x1(t) using Fo... b Answered: 1. Det ect_4_CTFT 1 of 2 + Automatic Zoom 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) X(@) = | x(t)e-jwt dt 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) -1<t<1 where, x, (t) = otherwise and -1 +1 +2 t(s) -1 <t<2 otherwise x2(t) = Fig. 1 (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(@) 3. Find the magnitude A(@) and phase (w) spectra of x(t) and determine their values in Table 1 and Table 2 Table 1 24
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