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-jut dt -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

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I need help solving calculation part 1 

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
4x(t)
X (@) = | x(t)e-jwtdt
-00
2. The signal x(t) can be expressed as the sum of
two signals; x1 (t) and x2(t);
1
x(t)=x1(t)+x2(t)
where, x1 (t) = {a
-1<t<1
and
otherwise'
-1
+1
+2
t(s)
x2(t) = {0
S1 -1<t< 2
otherwise
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,(@) + X2(@)
3. Find the magnitude A(@) and phase p(w) spectra of x(t) and determine their values in
Table 1 and Table 2
Focus
Transcribed Image Text: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 4x(t) X (@) = | x(t)e-jwtdt -00 2. The signal x(t) can be expressed as the sum of two signals; x1 (t) and x2(t); 1 x(t)=x1(t)+x2(t) where, x1 (t) = {a -1<t<1 and otherwise' -1 +1 +2 t(s) x2(t) = {0 S1 -1<t< 2 otherwise 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,(@) + X2(@) 3. Find the magnitude A(@) and phase p(w) spectra of x(t) and determine their values in Table 1 and Table 2 Focus
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